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FUNCTIONAL DATA ANALYSIS
In the previous code, we preproccessed the data so they are now in the right form for functional data analysis. Because the recordings seem to have some common shape in most metrics, we want tu use tools of FDA to study relationships in data.
The procedure of the analysis is as follows:
- load the data,
- transform them into variable that can be used for FDA,
- smooth the measurements,
- plot smoothed curves and
- apply some advanced analysis (functional linear model, functional ANOVA, etc.).
suppressPackageStartupMessages() function to suppress messages and warnings.
# libraries
library(ggplot2) |> suppressPackageStartupMessages() |> suppressWarnings()
library(dplyr) |> suppressPackageStartupMessages() |> suppressWarnings()
library(tidyr) |> suppressPackageStartupMessages() |> suppressWarnings()
library(openxlsx) |> suppressPackageStartupMessages() |> suppressWarnings()
library(lubridate) |> suppressPackageStartupMessages() |> suppressWarnings()
library(viridis) |> suppressPackageStartupMessages() |> suppressWarnings()
library(fda.usc) |> suppressPackageStartupMessages() |> suppressWarnings()
library(fda) |> suppressPackageStartupMessages() |> suppressWarnings()
library(patchwork) |> suppressPackageStartupMessages() |> suppressWarnings()
library(fdapace) |> suppressPackageStartupMessages() |> suppressWarnings()
library(GET) |> suppressPackageStartupMessages() |> suppressWarnings()
# options for graphics
options(repr.plot.width = 20, repr.plot.height = 10, repr.plot.res = 300)
setwd('Z:/GAMU-STRECITY/04_Codes/FDA')
## data frame of time points with date format
df_times_date <- read.xlsx("Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/time_points.xlsx")
## data frame of time points without date format
df_times <- read.csv('Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/time_points.csv', row.names = NULL)[, 2:5]
## data frame of time segments
seg_tp_load <- read.xlsx("Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/time_points_segments.xlsx")
# change characters to dttm format
for(j in 2:dim(seg_tp_load)[2]) {
seg_tp_load[, j] <- seg_tp_load[, j] |> as.POSIXct()
}
seg_tp <- seg_tp_load
## data frame of registered times
Times_of_segments <- read.csv('recordings/registration/Times_of_segments.csv')[, c(2, 3)] |>
mutate(time = as.POSIXct(time))
participant_info <- read.xlsx("Z:/GAMU-STRECITY/04_Codes/FDA/auxiliary data/participant_info.xlsx")
center_EDA_curves = TRUE; otherwise, use center_EDA_curves = FALSE.
center_EDA_curves <- TRUE
In the next section, we define a function that does the described process above automatically. Then, we can apply the smoothing to other metrics and finally work with the functional data (define models, etc.).
Functional model
Finally, we can fit the functional linear model. Generally, we have two options for modelling the dependence of two functional objects $-$ concurrent model and fully functional regression model.
- Concurrent model: this model relates the value of outcome $y$ in time $t$ (i.e. $y_i(t)$) to the value of covariates $z_j$ at the same time $t$ (i.e. $z_{ij}(t)$). Therefore, the model can me described as $$y_i(t) = \beta_0(t) + \sum_{j=1}^K\beta_j(t) z_{ij}(t) + \varepsilon_i(t) \tag{1}$$ for $K$ covariates.
- Fully functional regression model: we can generalize the previous model by taking $K\rightarrow \infty$. Then, we have parameter $\beta_1(t, s)$, which defines the dependence of $y_i(t)$ on covariate $z_i(s)$ at each time $t$. The model is decribed as $$y_i(t) = \beta_0(t) + \int_{\Omega_t}\beta_1(t, s) z_{i}(s)\text d s + \varepsilon_i(t) \tag{2},$$ where ${\Omega_t} = \{s|s<t\}$ for historical linear model and ${\Omega_t} = \{s\ \text{unconstrained}\}$ for full integration regression.
We will use the model $(1)$.
fd object: First, we have to define appropriate data objects. Because different curves are defined by the different number of observed points, but by the same basis, we should be able to merge the curves into one fd object. We have to do this for outcome and also for covariates. Therefore, we define function convert_to_fd() that will do this for input BSmooth object, which is an output of data_to_function() function.
convert_to_fd <- function(BSmooth) {
# first, we create data frame, in columns are the coefficients of B-spline basis
merged_coefs <- BSmooth[[1]]$fd$coef
for (i in 2:length(BSmooth)) {
merged_coefs <- cbind(merged_coefs, BSmooth[[i]]$fd$coef)
}
# add names to columns
colnames(merged_coefs) <- names(BSmooth)
# now, create fd object
merged_fd <- fd(coef = merged_coefs, basisobj = BSmooth[[1]]$fd$basis)
return(merged_fd)
}
# options for graphics
options(repr.plot.width = 20, repr.plot.height = 10, repr.plot.res = 100)
Now, we load the files from smooth_data folder.
files_load <- list.files('recordings/smooth_data')
files_load
- 'Acceleration_smooth_norder1.RData'
- 'Acceleration_smooth_pos.RData'
- 'Air_pressure_smooth.RData'
- 'Altitude_smooth.RData'
- 'EDA_smooth.RData'
- 'Entrant_AIR_TEMP_2_smooth.RData'
- 'Entrant_BODY_TEMP_3_smooth.RData'
- 'GEO_altitude_smooth.RData'
- 'GEO_cadence_smooth.RData'
- 'GEO_HR_smooth.RData'
- 'Heart_rate_smooth.RData'
- 'Noise_smooth.RData'
- 'Pollution_PM1_smooth.RData'
- 'Pollution_PM10_smooth.RData'
- 'Pollution_PM25_smooth.RData'
- 'Speed_smooth.RData'
- 'Speed_smooth_norder1.RData'
- 'Steps_smooth_norder1.RData'
- 'Steps_smooth_norder4.RData'
- 'Temperature_smooth.RData'
files_load <- files_load[!files_load %in% c(
'Acceleration_smooth_nopos.RData', 'Acceleration_smooth_pos.RData',
'GEO_cadence_smooth.RData', 'Pollution_PM10_smooth.RData',
'Steps_smooth_norder4.RData', 'Speed_smooth.RData'
)]
for(i in files_load) {load(paste0('recordings/smooth_data/', i), verbose = TRUE)}
Loading objects: BSmooth_accel Loading objects: BSmooth_air_pressure Loading objects: BSmooth_altitude Loading objects: BSmooth_EDA Loading objects: BSmooth_air_temp Loading objects: BSmooth_body_temp Loading objects: BSmooth_GEO_altitude Loading objects: BSmooth_GEO_HR Loading objects: BSmooth_HR Loading objects: BSmooth_noise Loading objects: BSmooth_pollution1 Loading objects: BSmooth_pollution25 Loading objects: BSmooth_Speed Loading objects: BSmooth_Steps Loading objects: BSmooth_temp
Function for plotting the functional observations.
plot_fd <- function(fd_obj, ylab = 'Value', xlab = 'Time') {
# add to graphs vertical lines indicating segments
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
rangeval <- fd_obj$basis$rangeval
time_vec <- seq(rangeval[1], rangeval[2], by = 1)
# data frame with evaluated curves
df_plot_smooth <- eval.fd(fd_obj, evalarg = time_vec) |>
as.data.frame() |>
pivot_longer(cols = everything(), names_to = "ID", cols_vary = 'slowest') |>
mutate(time = rep(time_vec, length(unique(ID))),
ID = substr(ID, 4, 7))
df_plot_smooth |> ggplot(aes(x = time, y = value, colour = ID)) +
geom_line(linewidth = 1) +
# facet_wrap(~ID, nrow = 2) +
geom_vline(xintercept = important_times, linewidth = 0.6, col = 'grey', linetype = 'dashed') +
theme_bw() +
theme(panel.grid.major.x = element_blank(),
panel.grid.minor = element_blank(),
axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1)) +
scale_x_continuous(breaks = important_times,
labels = Times_of_segments$Time_point) +
scale_color_viridis(discrete = TRUE, option = "B") +
labs(x = xlab, y = ylab)
}
Models
Now, we want to model heart rate and EDA on covariates. Therefore, we create fd objects for each metric. Plot the result.
# convert metrics to fd objects
HR_fd <- convert_to_fd(BSmooth_HR)
EDA_fd <- convert_to_fd(BSmooth_EDA)
altitude_fd <- convert_to_fd(BSmooth_altitude)
airpressure_fd <- convert_to_fd(BSmooth_air_pressure)
noise_fd <- convert_to_fd(BSmooth_noise)
speed_fd <- convert_to_fd(BSmooth_Speed)
steps_fd <- convert_to_fd(BSmooth_Steps)
acceleration_fd <- convert_to_fd(BSmooth_accel)
temperature_fd <- convert_to_fd(BSmooth_temp)
air_temperature_ENT_fd <- convert_to_fd(BSmooth_air_temp)
body_temperature_ENT_fd <- convert_to_fd(BSmooth_body_temp)
altitude_GEO_fd <- convert_to_fd(BSmooth_GEO_altitude)
HR_GEO_fd <- convert_to_fd(BSmooth_GEO_HR)
pollution1_fd <- convert_to_fd(BSmooth_pollution1)
pollution25_fd <- convert_to_fd(BSmooth_pollution25)
fd_objects <- ls()[grepl('_fd', ls())]
fd_objects <- fd_objects[!fd_objects %in% c('convert_to_fd', 'merged_fd', 'plot_fd')]
fd_objects
- 'acceleration_fd'
- 'air_temperature_ENT_fd'
- 'airpressure_fd'
- 'altitude_fd'
- 'altitude_GEO_fd'
- 'body_temperature_ENT_fd'
- 'EDA_fd'
- 'HR_fd'
- 'HR_GEO_fd'
- 'noise_fd'
- 'pollution1_fd'
- 'pollution25_fd'
- 'speed_fd'
- 'steps_fd'
- 'temperature_fd'
There are vertical differences between curves for heart rate and also EDA (if center_EDA_curves = TRUE). We want to get rid of it (the model should then include also some dummy variable for identifying the participants or better use mixed model). Fot that we subtract the mean value of heart rate for each participant.
# compute and subtract the mean HR for each curve so they will be aligned
rangeval <- HR_fd[1]$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = 101)
pom <- HR_fd$coefs
EHR <- c()
for (i in 1:length(colnames(HR_fd$coefs))) {
EHR <- c(EHR, mean(eval.fd(HR_fd[i], tt)))
pom[, i] <- (HR_fd[i] - mean(eval.fd(HR_fd[i], tt)))$coefs[, 1] |> c()
}
HR_fd$coefs <- pom
The same for Heart rate from GEO data.
# compute and subtract the mean HR for each curve so they will be aligned
rangeval_GEO <- HR_GEO_fd[1]$basis$rangeval
tt_GEO <- seq(rangeval_GEO[1], rangeval_GEO[2], length = 101)
pom_GEO <- HR_GEO_fd$coefs
EHR_GEO <- c()
for (i in 1:length(colnames(HR_GEO_fd$coefs))) {
EHR_GEO <- c(EHR_GEO, mean(eval.fd(HR_GEO_fd[i], tt_GEO)))
pom_GEO[, i] <- (HR_GEO_fd[i] - mean(eval.fd(HR_GEO_fd[i], tt_GEO)))$coefs[, 1] |> c()
}
HR_GEO_fd$coefs <- pom_GEO
The same for EDA curves (if center_EDA_curves = TRUE).
# compute and subtract the mean EDA for each curve so they will be aligned
if (center_EDA_curves) {
rangeval_EDA <- EDA_fd[1]$basis$rangeval
tt_EDA <- seq(rangeval_EDA[1], rangeval_EDA[2], length = 101)
pom_EDA <- EDA_fd$coefs
EEDA <- c()
for (i in 1:length(colnames(EDA_fd$coefs))) {
EEDA <- c(EEDA, mean(eval.fd(EDA_fd[i], tt_EDA)))
pom_EDA[, i] <- (EDA_fd[i] - mean(eval.fd(EDA_fd[i], tt_EDA)))$coefs[, 1] |> c()
}
EDA_fd$coefs <- pom_EDA
}
Plot the metrics
# plot the metrics
par(mfrow = c(1, 2))
plot_fd(HR_fd, ylab = 'HR_fd')
plot_fd(EDA_fd, ylab = 'EDA_fd')
plot_fd(altitude_fd, ylab = 'altitude_fd')
plot_fd(airpressure_fd, ylab = 'airpressure_fd')
plot_fd(noise_fd, ylab = 'noise_fd')
plot_fd(speed_fd, ylab = 'speed_fd')
plot_fd(steps_fd, ylab = 'steps_fd')
plot_fd(acceleration_fd, ylab = 'acceleration_fd')
plot_fd(temperature_fd, ylab = 'temperature_fd')
plot_fd(air_temperature_ENT_fd, ylab = 'air_temperature_ENT_fd')
plot_fd(body_temperature_ENT_fd, ylab = 'body_temperature_ENT_fd')
plot_fd(altitude_GEO_fd, ylab = 'altitude_GEO_fd')
plot_fd(HR_GEO_fd, ylab = 'HR_GEO_fd')
plot_fd(pollution1_fd, ylab = 'pollution1_fd')
plot_fd(pollution25_fd, ylab = 'pollution25_fd')
Outlier detection
In functional linear model, we are also interested in model diagnostics. Now, we check, whether there are outliers in our data. We check all the functional covariates. Two functions are used:
functional_boxplot()fromfdaoutlierpackage ... returns indices of possible outliersfBoxplot()fromGETpackage ... creates functional boxplot
library(fdaoutlier)
rangeval <- HR_fd$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = 1001)
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 150)
Warning message: "package 'fdaoutlier' was built under R version 4.4.1"
Heart Rate
data_out <- eval.fd(HR_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1864'
- 'ID_3304'
- 'ID_5321'
- 'ID_5951'
- 'ID_6812'
Altitude
data_out <- eval.fd(altitude_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1604'
- 'ID_1864'
- 'ID_2476'
- 'ID_2837'
- 'ID_8805'
Noise
data_out <- eval.fd(noise_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
EDA
data_out <- eval.fd(EDA_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1487'
- 'ID_1538'
- 'ID_1864'
- 'ID_2476'
- 'ID_3266'
- 'ID_3304'
- 'ID_3626'
- 'ID_4874'
- 'ID_5321'
- 'ID_6811'
- 'ID_6812'
- 'ID_7238'
- 'ID_8252'
- 'ID_8791'
Temperature
data_out <- eval.fd(temperature_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
Acceleration
data_out <- eval.fd(acceleration_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1538'
- 'ID_1864'
- 'ID_2837'
- 'ID_5196'
- 'ID_5321'
- 'ID_5951'
- 'ID_6811'
- 'ID_8791'
Steps
data_out <- eval.fd(steps_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1487'
- 'ID_1626'
- 'ID_1864'
- 'ID_5196'
- 'ID_5951'
- 'ID_6812'
- 'ID_8403'
- 'ID_8805'
- 'ID_8991'
Speed
data_out <- eval.fd(speed_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1487'
- 'ID_1626'
- 'ID_1746'
- 'ID_1864'
- 'ID_2362'
- 'ID_2404'
- 'ID_2476'
- 'ID_3082'
- 'ID_5321'
- 'ID_6071'
- 'ID_6211'
- 'ID_7004'
- 'ID_8805'
- 'ID_8991'
Air pressure
data_out <- eval.fd(airpressure_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_3134'
- 'ID_3626'
- 'ID_8403'
Air temperature ENTRANT
data_out <- eval.fd(air_temperature_ENT_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
Body temperature ENTRANT
data_out <- eval.fd(body_temperature_ENT_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1626'
- 'ID_5794'
Altitude GEO
data_out <- eval.fd(altitude_GEO_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_2476'
- 'ID_5561'
- 'ID_7004'
- 'ID_8805'
Heart rate GEO
data_out <- eval.fd(HR_GEO_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_3304'
- 'ID_5321'
- 'ID_5951'
- 'ID_6811'
- 'ID_8805'
- 'ID_8991'
Pollution 1
data_out <- eval.fd(pollution1_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1538'
- 'ID_2293'
- 'ID_3082'
- 'ID_5794'
- 'ID_8252'
Pollution 25
data_out <- eval.fd(pollution25_fd, evalarg = tt)
rownames(data_out) <- tt
# fdaoutlier package
colnames(data_out)[functional_boxplot(t(data_out), depth_method = "mbd")$outliers]
# GET package
data_out <- curve_set(obs = data_out, r = tt)
plot(fBoxplot(data_out, coverage=0.5, type="area", factor=1.5)) + theme_bw()
- 'ID_1538'
- 'ID_2293'
- 'ID_3082'
- 'ID_5794'
- 'ID_8252'
Majority of outliers is no problem for us, but for some variables (EDA, Noise, HR), we should be careful about them.
- Heart rate - some outliers detected, but no need to extract them from analysis,
- Altitude - some outliers detected, but no need to extract them from analysis,
- Noise - one and no outlier detected, no problem,
- EDA - some outliers detected, potentially we can omit them in the analysis,
- Temperature - one outlier , but different by the two methods,
- Acceleration - many outliers, no problem,
- Steps - similar situation,
- Speed - similar situation,
- Air pressure - three curves have lower values then the rest, maybe center them,
- Air temp entrant - no outlier,
- Body temp entrant - one outlier (5794),
- Geo altitude - seems OK,
- Geo HR - seems OK,
- Pollution 1 - some outliers, maybe ID 1538 to omit,
- Pollution 25 - similar situation.
# We omit the ID 3626 for centered case
if (center_EDA_curves) {
EEDA <- EEDA[!colnames(EDA_fd$coefs) %in% c("ID_3626")]
EDA_fd <- EDA_fd[!colnames(EDA_fd$coefs) %in% c("ID_3626")]
}
Functions for fitting the functional regression model
This functions fit the functional regression model with specified outcome and covariates, calculates the $R^2$ and permutation $F$-test, constructs the pointwise confidence intervals for regression parameters using bootstrap principle and plot and save all the results.
Unfortunately, the function fRegress() from fda package requires to define outcome and covariates in the global environment. Therefore, we have to extract the fRegress() from the global function for fitting the model and calculating all the metrics. We have created different functions:
model_fRegress_1()is used to prepare the outcome and covariates for fitting the functional model. It also return thebetafdParobject.model_fRegress_2()is used after the fitting the functional regression model. We have to input the fitted model and other variables, then the function plot the results and calculate functional $R^2$ and permutation $F$-test.bootstrap_CI()is used after calculating the bootstrapped parametric functions. It plots the pointwise bootstrap confidence intervals for all parametric functions. The basic bootstrap CI's are considered instead of percentile bootstrap intervals.plot_GET()function plots the output ofGETpackage, which constructs the global envelope test. The plot is complemented by the parametric function $\widehat\beta_j(t)$ estimated by functional model along with its pointwise CI's calculated using bootstrap procedure.
########################################################################################
## First function for regression before fitting the functional model
########################################################################################
model_fRegress_1 <- function(outcome, covariates, basis_params, path_plot, factors = NA) {
#=========================================
# create folder for graphs
if(!substr(path_plot, 9, nchar(path_plot)) %in% list.files('figures/')) {
dir.create(path_plot)
}
ncovariates <- length(covariates)
# defining formula of the model
formula <- paste0('outcome ~ ')
for(cov in names(covariates)[-ncovariates]) {formula <- paste0(formula, cov, '+')}
formula <- paste0(formula, names(covariates)[ncovariates])
if(!is.na(factors[1])) {for(nam in names(factors)) {formula <- paste0(formula, '+', nam)}}
formula <- as.formula(formula)
# Define IDs that are in both fd objects.
common_IDs <- list(colnames(outcome$coefs))
for (i in 1:ncovariates) {
common_IDs <- c(common_IDs, list(colnames(covariates[[i]]$coefs)))
}
common_IDs <- Reduce(intersect,
common_IDs)
if(!is.na(factors[1])) {common_IDs <- common_IDs[common_IDs %in% paste0('ID_', participant_info$ID)]}
message(paste0("Final number of observations = ", length(common_IDs), "."))
# select IDs that are common
outcome <- outcome[common_IDs]
for (cov in names(covariates)) {
covariates[[cov]] <- covariates[[cov]][common_IDs]
}
#=========================================
# betaFdpar for beta0
betafdPar <- list(fdPar(fd(rep(0, basis_params$beta_0$nbetabasis),
create.bspline.basis(rangeval = outcome$basis$rangeval,
nbasis = basis_params$beta_0$nbetabasis,
norder = basis_params$beta_0$norder)),
lambda = basis_params$beta_0$lambda))
# betaFdpar for other beta functions
for (i in 1:ncovariates) {
betafdPar_j <- list(fdPar(fd(rep(0, basis_params[[i+1]]$nbetabasis),
create.bspline.basis(rangeval = covariates[[i]]$basis$rangeval,
nbasis = basis_params[[i+1]]$nbetabasis,
norder = basis_params[[i+1]]$norder)),
lambda = basis_params[[i+1]]$lambda))
betafdPar <- c(betafdPar, betafdPar_j)
}
if(!is.na(factors[1])){
for (i in 1:length(factors)) {
if(!names(factors)[i] %in% names(basis_params)) {
betafdPar_j <- list(fdPar(fd(0, create.constant.basis(rangeval = outcome$basis$rangeval))))
} else {
betafdPar_j <- list(fdPar(fd(rep(0, basis_params[[i+1+ncovariates]]$nbetabasis),
create.bspline.basis(rangeval = outcome$basis$rangeval,
nbasis = basis_params[[i+1+ncovariates]]$nbetabasis,
norder = basis_params[[i+1+ncovariates]]$norder)),
lambda = basis_params[[i+1+ncovariates]]$lambda))
}
betafdPar <- c(betafdPar, betafdPar_j)
}}
return(list(outcome = outcome,
covariates = covariates,
betafdPar = betafdPar,
formula = formula,
common_IDs = common_IDs))
}
########################################################################################
## Second function for regression after fitting the functional model
########################################################################################
model_fRegress_2 <- function(model_concurrent, outcome, covariates, basis_params,
path_plot, nperm = 200, factors = NA, HR = TRUE, lenght_tt = 1001) {
#=========================================
ncovariates <- length(covariates)
# defining formula of the model
formula <- paste0('outcome ~ ')
for(cov in names(covariates)[-ncovariates]) {formula <- paste0(formula, cov, '+')}
formula <- paste0(formula, names(covariates)[ncovariates])
if(!is.na(factors[1])) {for(nam in names(factors)) {formula <- paste0(formula, '+', nam)}}
formula <- as.formula(formula)
# Define IDs that are in both fd objects.
common_IDs <- list(colnames(outcome$coefs))
for (i in 1:ncovariates) {
common_IDs <- c(common_IDs, list(colnames(covariates[[i]]$coefs)))
}
common_IDs <- Reduce(intersect,
common_IDs)
# select IDs that are common
outcome <- outcome[common_IDs]
for (cov in names(covariates)) {assign(cov, covariates[[cov]][common_IDs])}
yhatfd <- model_concurrent$yhatfdobj # Fitted smooths.
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) # time vector
#=========================================
message('Plotting the fitted curves ...')
df_est <- eval.fd(yhatfd, tt) |>
as.data.frame() |>
pivot_longer(cols = contains('reps'), values_to = 'est',
names_to = 'rep', cols_vary = 'slowest')
df_obs <- eval.fd(outcome, tt) |>
as.data.frame() |>
pivot_longer(cols = contains('ID'), values_to = 'obs',
names_to = 'ID', cols_vary = 'slowest') |>
mutate(ID = factor(ID))
df_plot <- cbind(df_est, df_obs) |>
mutate(time = rep(tt, length(common_IDs)))
if(HR) {
df_plot <- df_plot |> mutate(
est = est + rep(EHR[colnames(HR_fd$coefs) %in% common_IDs], each = length(tt)),
obs = obs + rep(EHR[colnames(HR_fd$coefs) %in% common_IDs], each = length(tt))
)
}
if(center_EDA_curves) {
df_plot <- df_plot |> mutate(
est = est + rep(EEDA[colnames(EDA_fd$coefs) %in% common_IDs], each = length(tt)),
obs = obs + rep(EEDA[colnames(EDA_fd$coefs) %in% common_IDs], each = length(tt))
)
}
if(HR) {
ylab <- 'Heart Rate'
} else {
ylab <- 'EDA'
}
p1 <- df_plot |> ggplot(aes(x = time, y = obs, colour = ID)) +
geom_line(aes(linetype = 'obs'), linewidth = 0.3) +
geom_line(aes(y = est, linetype = 'est'), linewidth = 0.3) +
facet_wrap(~ID, ncol = 5, scales = "free_y") + # , scales = "free_y"
theme_bw() +
scale_color_discrete(labels = 1:length(unique(df_plot$ID))) +
theme(strip.background = element_blank(),
strip.text.x = element_blank(),
panel.grid.minor.x = element_blank(),
axis.text.x = element_text(size = 8),
axis.text.y = element_text(size = 8)
) +
labs(x = 'Time', y = ylab) +
scale_linetype_manual(name='Curve', values = c('dashed', 'solid'),
labels = c('estimated', 'observed'))
ggsave(paste0(path_plot, '/model_samples.pdf'), width = 12, height = 7)
# add to graphs vertical lines indicating segments
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
#=========================================
n_beta <- length(model_concurrent$betaestlist)
message('Plotting the beta functions ...')
for (j in 1:n_beta) {
df_beta <- data.frame(time = tt,
beta = c(eval.fd(model_concurrent$betaestlist[[j]]$fd, tt)))
p_beta <- df_beta |> ggplot(aes(x = time, y = beta)) +
geom_line(col = 'deepskyblue2', linewidth = 1) +
theme_bw() +
labs(x = expression(t), y = bquote(widehat(beta)[.(j-1)]*'(t)')) +
geom_hline(yintercept = 0, linetype = 'dashed', col = 'grey2', alpha = 0.7) +
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7)) +
geom_vline(xintercept = important_times, linewidth = 0.2,
col = 'grey', linetype = 'dashed') +
scale_x_continuous(breaks = important_times,
labels = Times_of_segments$Time_point)
assign(paste0('p_beta_', j-1), p_beta)
ggsave(paste0(path_plot, '/beta_', j-1 , '.pdf'), plot = p_beta, width = 12, height = 7)
}
#=========================================
## Functional R^2
message('Calculating the functional R^2 ...')
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
nomin <- mean.fd((outcome - yhatfd)^2)
denom <- mean.fd((center.fd(outcome))^2)
Rvalues <- 1 - eval.fd(tt, nomin)/eval.fd(tt, denom)
# sequence of knots ... set them to every 30 second (for all curves the same)
breaks <- seq(rangeval[1], rangeval[2], by = 30)
bbasis <- create.bspline.basis(rangeval = rangeval, norder = 4, breaks = breaks)
curv.Lfd <- int2Lfd(2)
curv.fdPar <- fdPar(bbasis, curv.Lfd, 1e-1)
Rvalues_smooth <- smooth.basis(tt, Rvalues, curv.fdPar)
Rvalues_sm <- eval.fd(Rvalues_smooth$fd, tt)
# Calculate RMSE, integrated R2 and max of R2
RMSE <- eval.fd(tt, nomin) |> mean() |> sqrt()
maxR2 <- max(Rvalues)
integratedR2 <- metric.lp(fdata(Rvalues_smooth$fd),
fdata(rep(0, length(fdata(Rvalues_smooth$fd)$argvals)),
fdata(Rvalues_smooth$fd)$argvals)) |> c()
#=========================================
message('Plotting the functional R^2 ...')
plot_R2 <- data.frame(time = tt, R2 = c(Rvalues_sm)) |>
ggplot(aes(x = time, y = R2)) +
geom_line(col = 'deepskyblue2', linewidth = 0.8) +
geom_hline(aes(yintercept = 0), linetype = 'dashed', col = 'grey2',
alpha = 0.7, linewidth = 0.4) +
theme_bw() +
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7)) +
geom_vline(xintercept = important_times, linewidth = 0.2,
col = 'grey', linetype = 'dashed') +
scale_x_continuous(breaks = important_times,
labels = Times_of_segments$Time_point) +
labs(x = expression(t), y = expression(R^2*(t)))
scales <- layer_scales(plot_R2)$y$range$range
plot_R2 <- plot_R2 +
annotate("text", x = 20, y = scales[2] - 0.01 * ceiling(2*(scales[2] - scales[1])),
label = paste0('RMSE = ', round(RMSE, 4)),
size = 4, vjust = "inward", hjust = "inward") +
annotate("text", x = 20, y = scales[2] - 0.035 * ceiling(2*(scales[2] - scales[1])),
label = paste0('max(R^2) =' ,round(maxR2, 4)),
size = 4, vjust = "inward", hjust = "inward") +
annotate("text", x = 20, y = scales[2] - 0.06 * ceiling(2*(scales[2] - scales[1])),
label = paste0('Integrated R^2 = ', round(integratedR2, 4)),
size = 4, vjust = "inward", hjust = "inward")
ggsave(paste0(path_plot, '/R2.pdf'), plot = plot_R2, width = 12, height = 7)
#=========================================
message('Calculating the functional F-ratio test ...')
# F-Ratio
F.res <- Fperm.fd(outcome,
model_concurrent$xfdlist,
model_concurrent$betalist,
nperm = nperm, argvals = tt, plotres = FALSE)
#=========================================
message('Plotting the results of the functional F-ratio test ...')
df_res_metrics <- data.frame(RMSE = RMSE,
maxR2 = maxR2,
integratedR2 = integratedR2,
pval = F.res$pval,
qval = F.res$qval,
Fobs = F.res$Fobs)
options(ggplot2.discrete.colour = c("deepskyblue2", "grey3", 'tomato'))
plot_Fres <- data.frame(time = tt, F = F.res$Fvals, p = F.res$pvals.pts, q = F.res$qvals.pts) |>
ggplot(aes(x = time, y = F)) +
geom_line(aes(col = ' observed F statistic', linetype = ' observed F statistic'),
linewidth = 0.8) +
geom_hline(aes(yintercept = 0), linetype = 'dashed', col = 'grey2',
alpha = 0.7, linewidth = 0.4) +
theme_bw() +
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7),
legend.position = 'bottom') +
geom_vline(xintercept = important_times, linewidth = 0.2, col = 'grey', linetype = 'dashed') +
scale_x_continuous(breaks = important_times,
labels = Times_of_segments$Time_point) +
labs(x = expression(t), y = expression(F*(t)), col = 'Curve:', linetype = 'Curve:') +
geom_line(aes(y = q, col = 'pointwise 0.05 critical value',
linetype = 'pointwise 0.05 critical value')) +
geom_hline(aes(yintercept = F.res$qval, col = 'maximum 0.05 critical value',
linetype = 'maximum 0.05 critical value'))
scales <- layer_scales(plot_Fres)$y$range$range
plot_Fres <- plot_Fres +
annotate("text", x = 20, y = scales[2] - 0.01 * ceiling(2*(scales[2] - scales[1])),
label = paste0('p-value = ', round(df_res_metrics$pval, 4)),
family = 'serif', fontface = 'plain', size = 4, vjust = "inward", hjust = "inward") +
annotate("text", x = 20, y = scales[2] - 0.035 * ceiling(2*(scales[2] - scales[1])),
label = paste0('q-value = ', round(df_res_metrics$qval, 4)),
family = 'serif', fontface = 'plain', size = 4, vjust = "inward", hjust = "inward") +
annotate("text", x = 20, y = scales[2] - 0.06 * ceiling(2*(scales[2] - scales[1])),
label = paste0('Observed F-statistic = ', round(df_res_metrics$Fobs, 4)),
family = 'serif', fontface = 'plain', size = 4, vjust = "inward", hjust = "inward")
ggsave(paste0(path_plot, '/F_res.pdf'), plot = plot_Fres, width = 12, height = 7)
#=========================================
message('DONE :-)')
return(list(model = model_concurrent,
df_res_metrics = df_res_metrics,
plots = list(p1, plot_Fres, plot_R2, p_beta_0, p_beta_1)))
}
########################################################################################
## Function for Bootstrap CI for parametric functions
########################################################################################
bootstrap_CI <- function(N_repeats = 100, beta_BS, n_beta, model_concurrent, path_plot, lenght_tt = 1001) {
N_repeats_NA <- N_repeats - sum(is.na(beta_BS[1, , 1]))
message(paste0('Plotting the bootstrap CIs for beta functions (from ', N_repeats_NA,
' bootstrap samples) ...'))
beta_BSnew <- array(data = NA, dim = c(lenght_tt, N_repeats_NA, n_beta))
for(j in 1:n_beta) {
beta_BSnew[, , j] <- beta_BS[, , j] |>
as.data.frame() |>
select_if(~ !any(is.na(.))) |>
as.matrix()
}
for (j in 1:n_beta) {
df_beta <- data.frame(time = tt,
beta = c(eval.fd(model_concurrent$betaestlist[[j]]$fd, tt)))
p_beta_CI <- df_beta |> ggplot(aes(x = time, y = beta)) +
geom_line(col = 'deepskyblue2', linewidth = 1) +
theme_bw() +
labs(x = expression(t), y = bquote(widehat(beta)[.(j-1)]*'(t)')) +
geom_hline(yintercept = 0, linetype = 'dashed', col = 'grey2', alpha = 0.7) +
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7)) +
geom_vline(xintercept = important_times, linewidth = 0.2,
col = 'grey', linetype = 'dashed') +
scale_x_continuous(breaks = important_times,
labels = Times_of_segments$Time_point) +
geom_line(aes(x = time,
y = 2*beta - apply(beta_BSnew[, , j], 1, quantile, probs = 0.025)),
col = 'black') +
geom_line(aes(x = time,
y = 2*beta - apply(beta_BSnew[, , j], 1, quantile, probs = 0.975)),
col = 'black')
plot(p_beta_CI)
ggsave(paste0(path_plot, '/beta_', j-1 , '_CI', '.pdf'),
plot = p_beta_CI, width = 12, height = 7)
}
message('DONE :-)')
return(list(beta_BS = beta_BSnew, N_repeats_NA = N_repeats_NA))
}
Global envelopes
The GET package provides central regions (i.e. global envelopes) and global envelope tests with intrinsic graphical interpretation. The central regions can be constructed from (functional) data. The tests are Monte Carlo or permutation tests, which demand simulations from the tested null model. The methods are applicable for any multivariate vector data and functional data (after discretization).
We use GET package for constructing $100(1-\alpha)\%$ global envelope for test statistic of $H_0: \beta_j(t) = 0$.
plot_GET <- function(beta_num, tt, model_concurrent, res, beta_BSnew, path_plot, title = '') {
df_beta <- data.frame(time = tt, beta = c(eval.fd(model_concurrent$betaestlist[[beta_num]]$fd, tt)))
p1 <- plot(res,
sign.col="tomato",
digits = 6) +
theme_bw() +
labs(x = expression(t), y = bquote(widehat(beta)[.(beta_num - 1)](t))) + # expression(widehat(beta)[beta_num - 1](t))
geom_hline(yintercept = 0, linetype = 'dashed', col = 'grey2', alpha = 0.7) +
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle = 55, vjust = 1, hjust = 1, size = 7),
legend.position = "bottom") +
geom_vline(xintercept = important_times, linewidth = 0.2, col = 'grey', linetype = 'dashed') +
scale_x_continuous(breaks = important_times,
labels = Times_of_segments$Time_point,
expand = c(0.01, 0.01)) +
geom_line(data = df_beta, aes(x = time, y = beta), col = 'deepskyblue2', linewidth = 1) +
geom_line(data = df_beta, aes(x = time,
y = 2*beta - apply(beta_BSnew[, , beta_num], 1, quantile, probs = 0.975)),
col = 'grey', linewidth = 0.8) +
geom_line(data = df_beta, aes(x = time,
y = 2*beta - apply(beta_BSnew[, , beta_num], 1, quantile, probs = 0.025)),
col = 'grey', linewidth = 0.8) +
ggtitle(label = title,
subtitle = paste0("Graphical functional GLM: p = ", round(attr(res, "p"), 6)))
ggsave(paste0(path_plot, '/beta', beta_num - 1, '_GET.pdf'), width = 20, height = 10, dpi = 300)
return(p1)
}
GET_function <- function(J, outcome, model_1, nsim, model_concurrent,
beta_BSnew, path_plot, sex = FALSE, lenght_tt = 1001) {
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt) # 1001
# for outcome
eval0 <- eval.fd(outcome, evalarg = tt)
rownames(eval0) <- tt
data_GET0 <- curve_set(obs = eval0, r = tt)
# create curve_set
my_curve_set <- list(Y = data_GET0)
# for covariates
ncovariates <- length(names(model_1$covariates))
for (j in 1:ncovariates) {
cov <- model_1$covariates[[names(model_1$covariates)[j]]]
evalj <- eval.fd(cov, evalarg = tt)
rownames(evalj) <- tt
assign(paste0('data_GET', j), curve_set(obs = evalj, r = tt))
my_list <- list(curve_set(obs = evalj, r = tt))
names(my_list) <- paste0('covariate', j, '_fd')
my_curve_set <- c(my_curve_set, my_list)
}
############################################################################
## Create formulas and curve_set
# defining formula of the model
formula.full <- paste0('Y ~ ')
for(j in 1:(ncovariates - 1)) {formula.full <- paste0(formula.full, 'covariate', j, '_fd+')}
formula.full <- paste0(formula.full, 'covariate', ncovariates, '_fd')
# delete the covariate of interest
if(sex) {
formula.reduced <- formula.full
formula.full <- paste0(formula.full, '+Sex')
} else {
formula.reduced <- gsub(paste0('covariate', J, '_fd\\+'), '', formula.full)
if(formula.full == formula.reduced) {
formula.reduced <- sub(paste0('\\+covariate', J, '_fd'), '', formula.full)}
}
formula.full <- as.formula(formula.full)
formula.reduced <- as.formula(formula.reduced)
############################################################################
## Now, we calculate and plot the global envelope.
if(sex) {
res <- graph.flm(nsim = nsim, # Increase the number of simulations
formula.full = formula.full,
formula.reduced = formula.reduced,
curve_sets = my_curve_set,
factors = data.frame(Sex = factor(Sex)),
GET.args = list(typeone = 'fwer',
alpha = 0.05, central = 'mean'))
} else {
res <- graph.flm(nsim = nsim, # Increase the number of simulations
formula.full = formula.full,
formula.reduced = formula.reduced,
curve_sets = my_curve_set,
GET.args = list(typeone = 'fwer',
alpha = 0.05, central = 'mean'))
}
############################################################################
## Plot the envelope
p1 <- plot_GET(beta_num = J + 1, tt = tt, model_concurrent = model_concurrent,
res = res, beta_BSnew = BS_CI$beta_BS, path_plot = path_plot,
title = paste('Model: covariate of interest =', names(model_1$covariates)[J]))
return(list(res = res, plot = p1))
}
MODELS for Heart Rate
Now, we want to model heart rate on other covariates. We use the functions defined above. For new model, we only change the first cell below and the second cell then computes everything for us. Especially, we have to specify:
outcome... fd objectcovariates... named list of the covariatespath_plot... path where to save the figuresbasis_params... list of the parameters used for defining B-spline basis for each covariate and interceptN_repeats... number of bootstrapped sampled used to construct pointwise CI's, it should be at least1000nperm... number of permutations for permutation $F$-test, it should be at least200nsim... number of simulations for calculating Global Envelope Test, it should be at least2499
# Set the numbers for all models
N_repeats <- 101#1001
nperm <- 200
nsim <- 2499
lenght_tt <- 501
HR ~ air + noise
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd)
path_plot <- 'figures/model_HR_alt_noise_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 39. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 240 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.736482 | 0.4111378 | 6.871452 | 0.01 | 0.4733055 | 0.6124866 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 8, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + Sex (const basis for sex)
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
- If we specify for the name of the factor corresponding list of parameters, then the <b>B-splines</b> of specified order will be created
- Otherwise (if we do not specify the basis parameters for factor), the <b>constant basis</b> will be used for this parametric function.
- Be careful, the code is slightly different for cases with factors.
# Omit NA values
participant_info <- participant_info |> na.omit()
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd)
path_plot <- 'figures/model_HR_alt_noise_Sex'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e6),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2))
factors <- list(Sex = participant_info$Sex |> as.factor())
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params,
factors = factors)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))] |> as.numeric())
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
if(!is.na(factors[1])) {for (fact in names(factors)) {
assign(paste0(fact, '_BS'),
factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |>
as.numeric())}}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
formula_BS <- as.formula(formula_BS)
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 38 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 50 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.89276 | 0.3533194 | 6.522793 | 0.1 | 0.7696907 | 0.6040062 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + Sex (B-spline for sex)
- First, we have to define some variables. - Then, execute the cell below. It should compute everything :)- If we specify for the name of the factor corresponding list of parameters, then the <b>B-splines</b> of specified order will be created
- Otherwise (if we do not specify the basis parameters for factor), the <b>constant basis</b> will be used for this parametric function.
- Be careful, the code is slightly different for cases with factors.
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd)
path_plot <- 'figures/model_HR_alt_noise_Sex_Bspl_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e6),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
Sex = list(nbetabasis = 90, norder = 4, lambda = 1e2))
factors <- list(Sex = participant_info$Sex |> as.factor())
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params,
factors = factors)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |>
substr(4, 9))] |> as.numeric())
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
if(!is.na(factors[1])) {for (fact in names(factors)) {
assign(paste0(fact, '_BS'),
factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |>
as.numeric())}}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
formula_BS <- as.formula(formula_BS)
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 38. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 388 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.518559 | 0.379981 | 9.999879 | 0.035 | 0.5320388 | 0.5997903 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + temp (Empatica)
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd)
path_plot <- 'figures/model_HR_alt_noise_tempEmpatica_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 33. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 310 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.567088 | 0.4293899 | 9.358159 | 0.085 | 0.7230028 | 0.6613453 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + temp (Entrant)
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = air_temperature_ENT_fd)
path_plot <- 'figures/model_HR_alt_noise_tempEntrant_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 24. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 400 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.7833585 0.7707040 0.6411206 0.5989976 0.5591936 0.5567340 [7] 0.4314782 0.4308269 0.3292914 -0.2052906 Largest eigenvalues: [1] 71305842 68558264 63966446 63807462 62130543 60536319 59385986 59044419 [9] 58049990 57661764 Smallest eigenvalues: [1] 0.71853851 0.66259093 0.62569180 0.60368678 0.55828907 0.53387336 [7] 0.35931978 0.28792571 0.23412785 -0.02906518 Largest eigenvalues: [1] 71740708 68564664 64559704 63913320 62362347 60651116 60397994 59151830 [9] 58500236 57794954 Smallest eigenvalues: [1] 0.710052060 0.618438059 0.611693430 0.596946399 0.585326044 [6] 0.505858641 0.467334208 0.450768258 0.378575725 -0.006726297 Largest eigenvalues: [1] 73331066 69249948 65354311 65085678 63167356 61412096 61283824 59682595 [9] 57963532 57747546 Smallest eigenvalues: [1] 0.7244335 0.7151224 0.5995001 0.5602164 0.5355778 0.4924939 [7] 0.4578872 0.3087752 0.2930759 -0.1939169 Largest eigenvalues: [1] 71495511 67957762 64014011 63836671 62613106 60914767 59288142 59087033 [9] 58063514 57856818 Smallest eigenvalues: [1] 0.7279014 0.6492877 0.6290261 0.5610432 0.5528180 0.4826807 [7] 0.4282515 0.3683406 0.2521219 -0.1287820 Largest eigenvalues: [1] 72077437 68198721 64455298 63964059 62946666 60980525 60214498 60068511 [9] 58064986 57517102
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.332604 | 0.6563847 | 15.7536 | 0.04 | 1.331577 | 1.469169 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + t + acc
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd,
acceleration = acceleration_fd)
path_plot <- 'figures/model_HR_alt_noise_temp_acc_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 542 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.8716439 0.8501062 0.7929519 0.7713887 0.6455789 0.5548213 [7] 0.5194145 0.4788490 -0.4087386 -1.0159171 Largest eigenvalues: [1] 109094934 103323420 97119957 94954556 94213710 91296769 88575342 [8] 88373363 87993404 87132788 Smallest eigenvalues: [1] 0.8557968106 0.7229404645 0.6594665701 0.5557379678 0.5422057556 [6] 0.4321785672 0.3714286997 0.2567776285 -0.0004305333 -0.4461854063 Largest eigenvalues: [1] 107788521 103895440 97704523 94911701 94800499 91854015 88973768 [8] 88530748 87937287 86863972 Smallest eigenvalues: [1] 0.95617144 0.83615029 0.77603592 0.72014785 0.61883550 0.59588516 [7] 0.57500011 0.48375912 0.47367886 -0.07217484 Largest eigenvalues: [1] 107029316 104565286 98917906 94797645 94227685 92569418 89524993 [8] 89240025 87865751 87181746 Smallest eigenvalues: [1] 0.88903281 0.85415649 0.83938379 0.66807084 0.63514111 0.59359886 [7] 0.52903317 0.40630874 0.38543263 -0.02795208 Largest eigenvalues: [1] 108777428 103540862 97800530 95763571 93832821 91213188 88964505 [8] 88594098 88370138 87006314 Smallest eigenvalues: [1] 0.84517789 0.80242398 0.78417866 0.74331729 0.65735267 0.50320455 [7] 0.48770975 0.47987454 0.07809825 -2.90820653 Largest eigenvalues: [1] 107606289 102983787 97583320 94480015 94310069 91581818 89544119 [8] 88368008 87381864 86752878 Smallest eigenvalues: [1] 0.8767251 0.7641281 0.6903513 0.6899957 0.6759859 0.6012802 [7] 0.5681353 0.4129215 0.2298728 -0.3584217 Largest eigenvalues: [1] 107118755 104322380 98145549 94592468 94477774 92135811 89324916 [8] 88446711 87472383 86947660 Smallest eigenvalues: [1] 0.9425468 0.8593926 0.8020653 0.6709320 0.6411257 0.5624229 [7] 0.5281958 0.3182029 0.2251623 -2.3065338 Largest eigenvalues: [1] 109381624 102855028 97403627 95094153 93216803 91042402 88693590 [8] 88262843 88219053 86680832 Smallest eigenvalues: [1] 0.9793056 0.8830834 0.8528803 0.7423535 0.7366995 0.6568983 [7] 0.5380016 0.5306911 0.4647761 -0.9306622 Largest eigenvalues: [1] 106774425 103657270 97533434 94344429 93753823 91646752 88686610 [8] 88561281 86967833 86690831 Smallest eigenvalues: [1] 0.8620713 0.8345827 0.7921674 0.7864393 0.7653780 0.7149577 [7] 0.5435019 0.2804479 0.2590612 -0.6677662 Largest eigenvalues: [1] 108347208 103382835 97389200 94668865 93726606 91721318 89061022 [8] 88501653 87204644 86440562 Smallest eigenvalues: [1] 0.9248331 0.6657690 0.6508995 0.6476453 0.6139276 0.5751912 [7] 0.5529175 0.1137819 0.1129087 -0.4302189 Largest eigenvalues: [1] 107884656 103136876 96894110 94266256 94158391 91295424 88743480 [8] 88210669 86920306 86605328 Smallest eigenvalues: [1] 0.9367047 0.8178849 0.7746082 0.7375337 0.6664622 0.5742880 [7] 0.5233158 0.4224464 0.1813183 -0.5176218 Largest eigenvalues: [1] 108482198 101209235 96599139 94288358 92808975 90257072 87507470 [8] 87483956 87129999 86260201 Smallest eigenvalues: [1] 0.7259332 0.6515320 0.5377519 0.5130425 0.5025229 0.4464642 [7] 0.4102184 0.2321810 0.1791797 -2.1334504 Largest eigenvalues: [1] 107900317 103756697 98097775 94472480 94077132 91873205 89605613 [8] 88812775 87459066 86974019 Smallest eigenvalues: [1] 0.7756044 0.7713757 0.6778960 0.6680832 0.6666396 0.5664970 [7] 0.3704883 0.3122338 0.2164667 -0.2031463 Largest eigenvalues: [1] 106579960 102699521 97292159 94277333 93782746 91450928 89095276 [8] 88500515 87313442 86978433 Smallest eigenvalues: [1] 0.91335919 0.89520322 0.87913816 0.83613568 0.81550818 0.65470353 [7] 0.61304205 0.58381315 0.52573348 -0.06385793 Largest eigenvalues: [1] 109255818 102699872 96524215 94837443 94009624 91089688 88594344 [8] 88125984 88060248 86595372 Smallest eigenvalues: [1] 0.8775120 0.8293961 0.8105373 0.7200255 0.6885267 0.6219314 [7] 0.5301660 0.4469277 0.1792715 -2.0455835 Largest eigenvalues: [1] 108624441 102834392 97500082 94720128 93733308 91457423 89161646 [8] 88303223 87771817 86908930 Smallest eigenvalues: [1] 0.7521986 0.7140749 0.6393041 0.6341570 0.4694921 0.4609641 [7] 0.4565301 0.3118130 -0.2560743 -1.0004415 Largest eigenvalues: [1] 109813170 104552660 97754487 95956241 94953492 91573470 89263114 [8] 89036468 88834676 87443726 Smallest eigenvalues: [1] 0.84292248 0.83022099 0.70296779 0.63382788 0.60175781 0.59602276 [7] 0.56356554 0.17243779 0.06940894 -0.87560339 Largest eigenvalues: [1] 111111281 104172734 98278983 96055219 94836706 92110016 89538795 [8] 89360785 89176574 87808022 Smallest eigenvalues: [1] 0.80474852 0.75327496 0.69504463 0.67465972 0.65300462 0.57327132 [7] 0.48274075 0.23477979 0.03917412 -0.40234313 Largest eigenvalues: [1] 106621807 103648986 97663072 93845629 93748058 91372162 88790057 [8] 87687497 86934356 86068218 Smallest eigenvalues: [1] 1.00569653 0.92170723 0.86554213 0.82924199 0.78461078 0.65505115 [7] 0.62696409 0.61083886 0.52060238 -0.07317702 Largest eigenvalues: [1] 108020603 103256367 97347436 94733080 94180548 91801077 88468679 [8] 88400840 87312882 86835531 Smallest eigenvalues: [1] 0.9828879 0.8888334 0.8733402 0.8216811 0.8128000 0.7098531 [7] 0.6284019 0.5901828 0.5794624 -0.5336554 Largest eigenvalues: [1] 107810962 103853571 97670558 94828284 94640803 92014184 88713559 [8] 88658728 87821305 87013622 Smallest eigenvalues: [1] 0.86106846 0.72612204 0.66710711 0.59103210 0.50407716 0.44237890 [7] 0.31378560 0.04838675 -0.41357046 -1.21846072 Largest eigenvalues: [1] 107911500 101461426 96554062 94116748 92651142 89533877 88434473 [8] 87705250 87221475 86587759 Smallest eigenvalues: [1] 1.0105503 0.9272241 0.8232121 0.6689654 0.6675312 0.6307643 [7] 0.5613469 0.5076451 0.3327870 -0.7584954 Largest eigenvalues: [1] 108595086 102713623 97737496 95261716 93786521 91373556 88580367 [8] 88349848 87812232 87136291 Smallest eigenvalues: [1] 0.67186094 0.59062408 0.57712804 0.51831994 0.48281029 0.33969755 [7] 0.19649300 0.04754508 -0.45909282 -7.88695366 Largest eigenvalues: [1] 109859402 102163601 97898935 94423681 93532238 90602329 88491583 [8] 87810057 87651098 87075944 Smallest eigenvalues: [1] 0.9691789 0.8993445 0.8745925 0.8147007 0.7282038 0.6765138 [7] 0.5023434 0.3951217 0.3560023 -0.4517029 Largest eigenvalues: [1] 106687716 101620679 96230323 93384956 93292999 90444369 88224084 [8] 87363053 86451488 86001756 Smallest eigenvalues: [1] 0.8269466 0.6486635 0.5877420 0.5833506 0.5580785 0.5562149 [7] 0.3167155 0.1897060 0.1119832 -0.2710390 Largest eigenvalues: [1] 110083820 103888411 98725361 96988817 94606953 92121870 89489991 [8] 89410307 89123731 87590916 Smallest eigenvalues: [1] 0.90259676 0.77598750 0.76610736 0.73986927 0.70359734 0.56244895 [7] 0.50755074 0.21551415 -0.01288411 -0.37890855 Largest eigenvalues: [1] 109972615 104150154 98416980 97195654 95009565 92483433 89644301 [8] 89290875 88739858 87603347 Smallest eigenvalues: [1] 0.8249515 0.8056391 0.7462270 0.7058730 0.5916069 0.5387958 [7] 0.5069774 0.4396740 0.1689024 -0.4893813 Largest eigenvalues: [1] 107866296 103029059 97481412 94368401 93955912 91523955 89456441 [8] 88214044 87416701 86802248 Smallest eigenvalues: [1] 1.0108922 1.0074571 0.7852222 0.7610551 0.7448131 0.7382305 [7] 0.7157412 0.6635559 0.4472582 -0.9911224 Largest eigenvalues: [1] 109974759 102489800 97306224 94942024 93895458 91133827 88863288 [8] 88283750 88112620 87416503 Smallest eigenvalues: [1] 0.7517393 0.7205585 0.7067084 0.6406682 0.5487647 0.5431366 [7] 0.4959984 0.4772563 -0.5758258 -0.7563566 Largest eigenvalues: [1] 109151133 103322879 98304579 95473427 93879987 91448782 89447386 [8] 89014655 88615177 87876250 Smallest eigenvalues: [1] 0.7648631 0.6427379 0.6021311 0.5652321 0.4304333 0.4168429 [7] 0.3955647 0.3789174 0.2004489 -0.1222338 Largest eigenvalues: [1] 108807190 103618677 97468941 96203635 93682485 91491469 89030734 [8] 88771061 88480784 87021496 Smallest eigenvalues: [1] 0.7599520 0.6508359 0.6405970 0.6228885 0.6104181 0.4975251 [7] 0.4713674 0.4455729 0.3979905 -1.1733023 Largest eigenvalues: [1] 106528919 102604497 97430072 93867185 93142475 91316857 88800696 [8] 88112860 87031399 86447180 Smallest eigenvalues: [1] 0.8313580 0.7744583 0.7732968 0.7473390 0.7223690 0.5250136 [7] 0.4067012 0.3953674 0.1247483 -0.0459836 Largest eigenvalues: [1] 108266457 104298619 98306048 94997368 94655852 92181544 89046244 [8] 88313367 87643053 86786942 Smallest eigenvalues: [1] 1.0552175 0.9608836 0.9083536 0.8137891 0.7781124 0.7438965 [7] 0.6948925 0.5189620 0.4813227 -1.0088539 Largest eigenvalues: [1] 106699382 103106029 97778397 94321857 94104653 92054902 89669240 [8] 88138439 86955873 86566445 Smallest eigenvalues: [1] 0.8944665 0.8242692 0.8182314 0.7297219 0.7265837 0.4879771 [7] 0.3421240 0.2953817 0.1839575 -0.1180448 Largest eigenvalues: [1] 109727803 102722836 97390325 96205036 93920377 91170760 88597655 [8] 88435746 88083203 86942749 Smallest eigenvalues: [1] 0.83615608 0.78956872 0.76253242 0.67900651 0.64088357 0.42124548 [7] 0.40264341 0.38268260 0.04521849 -0.72919639 Largest eigenvalues: [1] 110624173 103817345 97698846 96733444 94965707 91729065 89678882 [8] 89352591 88281902 87754046 Smallest eigenvalues: [1] 0.7984311 0.6197636 0.5600151 0.4993678 0.4878135 0.4169297 [7] 0.3508084 0.2233203 -0.7349728 -2.2766328 Largest eigenvalues: [1] 109481613 103874477 97868626 96117700 93884409 91367848 89188963 [8] 89098061 88235056 87095535 Smallest eigenvalues: [1] 0.8706013173 0.8610741155 0.8597516267 0.7058094619 0.7050977434 [6] 0.6072916516 0.5770936741 0.4804878217 0.2032625075 -0.0006889913 Largest eigenvalues: [1] 108647480 103905178 97762464 95010765 94988390 92074367 89101300 [8] 88216332 87757327 86968930 Smallest eigenvalues: [1] 0.8811104 0.8738058 0.8170923 0.8132223 0.6630131 0.6149969 [7] 0.5533124 0.5485668 0.4056408 -0.1229492 Largest eigenvalues: [1] 107731888 102078202 96846730 94246720 93245361 90368466 88533930 [8] 88296384 87380286 87166346 Smallest eigenvalues: [1] 0.7682205 0.7445157 0.7171476 0.6187419 0.5623426 0.5067172 [7] 0.4341715 0.4123718 0.3190856 -1.8207411 Largest eigenvalues: [1] 107640565 102984281 97826348 94136615 93362157 91212927 88176374 [8] 87611097 87375017 86125369 Smallest eigenvalues: [1] 0.9086733 0.8761694 0.8598913 0.8198902 0.7888336 0.6401377 [7] 0.5215863 0.5155420 0.4402819 -0.0659769 Largest eigenvalues: [1] 107956720 102803663 97290066 94485231 94188649 91494736 88401617 [8] 87895718 87272025 86170483 Smallest eigenvalues: [1] 0.84292621 0.70832028 0.61463364 0.56821280 0.55563854 0.52773288 [7] 0.28009234 0.05289292 -0.05679742 -2.37513446 Largest eigenvalues: [1] 106622952 100943621 96184452 92970191 92206616 89956206 87962146 [8] 87517159 86609039 86195159 Smallest eigenvalues: [1] 0.9445260 0.9012139 0.8809718 0.7002910 0.5812220 0.4543793 [7] 0.4532511 0.2788804 0.1409139 -2.7322759 Largest eigenvalues: [1] 106348106 102030765 96271945 93779141 93600659 90729851 88830193 [8] 87159364 86641443 85782495 Smallest eigenvalues: [1] 0.715098616 0.603784026 0.534936737 0.524906215 0.492624719 [6] 0.388362880 0.371912083 0.308755573 0.006834966 -0.100082967 Largest eigenvalues: [1] 108238956 104836047 99076862 95388642 95146622 92931486 90134222 [8] 89923436 87911276 87768348 Smallest eigenvalues: [1] 1.0149198 1.0059602 0.8672876 0.7763581 0.7610714 0.7305590 [7] 0.6649024 0.6030967 0.3805226 -0.7769863 Largest eigenvalues: [1] 108091745 103411413 97674256 94206935 93922509 91348762 88889415 [8] 88143305 87328540 86392998 Smallest eigenvalues: [1] 0.9363154 0.8928282 0.8694252 0.7960278 0.6835573 0.6244205 [7] 0.4167354 0.1195476 0.1111607 -0.2391994 Largest eigenvalues: [1] 111119932 102565753 97477410 96667283 93406596 90814147 89402807 [8] 88874007 87762711 87423207 Smallest eigenvalues: [1] 0.9948398 0.8636861 0.7134741 0.6179233 0.6024991 0.4973910 [7] 0.4704489 0.4570190 0.2309826 -0.6427265 Largest eigenvalues: [1] 106053130 101295585 95852877 93766987 92595916 89879398 87954128 [8] 87310051 86850808 85685300
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.334506 | 0.5575056 | 12.40295 | 0.145 | 1.010932 | 0.8306072 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + t + speed
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd,
speed = speed_fd)
path_plot <- 'figures/model_HR_alt_noise_temp_speed_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 80, norder = 4, lambda = 1e2),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 33. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 564 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 1.0260844 0.8850395 0.8527031 0.7607098 0.6484172 0.6220947 [7] 0.5689357 0.5204373 0.4821186 -0.2135256 Largest eigenvalues: [1] 111292628 106391819 99912218 98491447 96219015 93536679 91141423 [8] 90742941 90323719 88660331 Smallest eigenvalues: [1] 0.72480756 0.66212416 0.64015007 0.51878428 0.30657979 0.30349219 [7] 0.05977739 -0.04465672 -0.05489741 -2.59177779 Largest eigenvalues: [1] 111069597 107283939 101037517 98450846 97160601 94742259 91837582 [8] 91750634 91114466 89927348 Smallest eigenvalues: [1] 0.9896444 0.9567728 0.7725702 0.7046511 0.6103521 0.6019973 [7] 0.5425109 0.4490726 -0.3471343 -3.3548327 Largest eigenvalues: [1] 111971226 106306345 100410422 98008927 96709072 93850089 91988684 [8] 91303526 90924326 89900760 Smallest eigenvalues: [1] 0.9950635 0.9368923 0.9173444 0.7566277 0.7159751 0.6610207 [7] 0.6201743 0.5521210 0.5049739 -1.1948875 Largest eigenvalues: [1] 110438519 105460913 99511703 96955325 96373603 93585482 91114736 [8] 89880426 89655335 88132952 Smallest eigenvalues: [1] 0.9138107 0.7388487 0.7257594 0.6922668 0.6873405 0.6527690 [7] 0.5939962 0.5627636 0.3623862 -9.4456780 Largest eigenvalues: [1] 111959090 106495268 99939505 97357324 96505140 94431107 91072984 [8] 90859248 89858603 88832396 Smallest eigenvalues: [1] 0.8453914 0.8245527 0.7799956 0.7175125 0.6794408 0.6790913 [7] 0.6564376 0.5695283 0.5469496 -6.9659224 Largest eigenvalues: [1] 108513693 105519891 99609804 96607707 95886515 93357145 90975607 [8] 90271077 89119314 88215681 Smallest eigenvalues: [1] 1.0591489 0.9908519 0.8512991 0.7022406 0.6480885 0.5905481 [7] 0.4689820 0.4608132 0.4031816 -0.8504813 Largest eigenvalues: [1] 109848300 107622594 100636571 98121131 97406051 94873051 92641225 [8] 91618842 90250749 90027947 Smallest eigenvalues: [1] 1.0113352 0.9536303 0.9119895 0.8274812 0.8210721 0.7474070 [7] 0.6550981 0.5867596 0.4382541 -6.5011028 Largest eigenvalues: [1] 110877385 106418603 100413849 97074814 96974339 94268070 92096816 [8] 90812457 89899473 89152499 Smallest eigenvalues: [1] 0.7630203 0.7117793 0.6974708 0.5821329 0.4940877 0.4416742 [7] 0.3754807 0.3633591 0.3402837 -1.1495654 Largest eigenvalues: [1] 110570292 106116736 100219641 97580343 96601399 94164385 91362909 [8] 90891895 90189757 88915499 Smallest eigenvalues: [1] 1.1059502 1.0683969 0.8071105 0.7856602 0.7493517 0.6975260 [7] 0.6798917 0.5879784 0.5100844 -1.6672398 Largest eigenvalues: [1] 110236997 105851771 99765222 97195790 96549388 93874802 91621234 [8] 90378918 89967770 88737910 Smallest eigenvalues: [1] 1.0560185 1.0083466 0.7872252 0.7453351 0.7309675 0.7263321 [7] 0.6552442 0.5169476 0.5125468 -2.5284843 Largest eigenvalues: [1] 111759423 105943058 99958979 97829738 96810556 93615174 90944910 [8] 90872741 90463838 88924170 Smallest eigenvalues: [1] 1.00628848 0.83676896 0.74353673 0.69981542 0.66294780 0.65849707 [7] 0.56537478 0.39021780 0.15072678 -0.06560649 Largest eigenvalues: [1] 111223048 107493811 100640330 97666189 97612014 94426402 92149132 [8] 90786527 90618194 89064547 Smallest eigenvalues: [1] 0.82888694 0.82486744 0.71224421 0.65278997 0.59096664 0.57302021 [7] 0.53765383 0.42462305 0.19872887 -0.07518924 Largest eigenvalues: [1] 111197003 105726889 100116679 97762711 97464013 94238117 90733479 [8] 90339740 90264015 88405722 Smallest eigenvalues: [1] 0.9116630 0.8184469 0.7042238 0.6559777 0.6436006 0.5267276 [7] 0.4675035 0.3276056 0.3164901 -0.2225504 Largest eigenvalues: [1] 114081538 106110897 101181454 98816706 96608529 94091968 91481729 [8] 91322737 91116411 89795590 Smallest eigenvalues: [1] 0.9980381 0.8910770 0.8857321 0.8394874 0.8091502 0.6951349 [7] 0.6566401 0.6112221 0.5062307 -0.2206848 Largest eigenvalues: [1] 113702811 106149821 100766888 98780009 96906247 93795690 91948460 [8] 91533659 90733578 90239053 Smallest eigenvalues: [1] 0.9402103 0.8589109 0.6467004 0.6399532 0.5898160 0.5737218 [7] 0.5311028 0.4980165 0.4068249 -2.5285333 Largest eigenvalues: [1] 112013032 107484975 101417326 98839748 97832264 95340579 91481803 [8] 91236967 91189333 89202455 Smallest eigenvalues: [1] 0.7933143 0.7494045 0.6984910 0.6391679 0.6329033 0.4975231 [7] 0.3970231 0.3276468 0.2171648 -0.3020071 Largest eigenvalues: [1] 111665500 105992849 100236956 97844674 97005908 94481299 91987821 [8] 90914552 90311839 89343834 Smallest eigenvalues: [1] 0.8985577 0.8549494 0.7844898 0.7343894 0.6354818 0.6076425 [7] 0.4703076 0.4189014 0.3723014 -0.7689090 Largest eigenvalues: [1] 112993537 107346476 101009968 98902961 97269432 94865593 91768924 [8] 91665537 91098885 89626611 Smallest eigenvalues: [1] 0.82546659 0.82276089 0.62292421 0.59010519 0.52630715 0.51336255 [7] 0.40316934 0.30180909 0.03687301 -0.65095018 Largest eigenvalues: [1] 113358585 107886021 101625759 98960875 97895762 95082207 92225915 [8] 92187712 91889422 90448448 Smallest eigenvalues: [1] 0.9122774 0.8732275 0.7813472 0.5744615 0.5255296 0.5130228 [7] 0.4761624 0.3948829 0.3649221 -2.1933804 Largest eigenvalues: [1] 111973718 107468642 101432724 98094667 97905231 94779298 92699059 [8] 91936048 91149962 90875092 Smallest eigenvalues: [1] 0.6815760 0.6254511 0.6243723 0.5997641 0.5230832 0.5161512 [7] 0.4759508 0.4446396 0.2675388 -1.1575794 Largest eigenvalues: [1] 113103702 106038167 100196112 98646220 96898944 94032762 91515073 [8] 91056817 90629761 89255102 Smallest eigenvalues: [1] 0.789897972 0.784382009 0.683992253 0.584833503 0.573968564 [6] 0.508396435 0.421500243 0.242206822 0.088902116 -0.002352464 Largest eigenvalues: [1] 112155723 104808176 99446884 98681943 95408184 92793297 90786592 [8] 90638434 90422962 89077528 Smallest eigenvalues: [1] 1.0463911 0.8171793 0.7386587 0.7029084 0.6625931 0.5797579 [7] 0.5101602 0.4849994 0.4533082 -0.1486453 Largest eigenvalues: [1] 113483630 105509167 99862731 99513876 95618208 92424710 92113388 [8] 90814949 90214303 89044501 Smallest eigenvalues: [1] 0.8601488020 0.6915628779 0.6449047739 0.6296918043 0.5407655949 [6] 0.5182576266 0.4894039867 0.3037491285 0.0273445701 -0.0009680657 Largest eigenvalues: [1] 112598601 106822330 101073674 98667594 97337561 94635741 92086114 [8] 91475405 91266345 90035580 Smallest eigenvalues: [1] 0.8874836 0.8723000 0.8208359 0.7236003 0.6223821 0.5895829 [7] 0.5475264 0.4176873 0.3526485 -0.2878256 Largest eigenvalues: [1] 110490616 104926841 98800527 96984658 95893710 93230474 90507314 [8] 90489775 89798207 88803799 Smallest eigenvalues: [1] 1.05335309 0.99475937 0.82243429 0.80725686 0.73613982 0.71715506 [7] 0.67146915 0.63986518 0.62480456 -0.02430108 Largest eigenvalues: [1] 111302141 106452887 100697659 98331619 97297166 94499320 92364333 [8] 90869486 90450578 89133444 Smallest eigenvalues: [1] 0.8152167 0.6978276 0.6808726 0.6699467 0.6600201 0.5803814 [7] 0.5456787 0.5186091 0.4899459 -0.9435758 Largest eigenvalues: [1] 112810177 106568539 100676372 99503059 96722134 94136193 91604000 [8] 91370231 90984009 89557056 Smallest eigenvalues: [1] 0.87417492 0.78829167 0.65104729 0.58983668 0.57080091 0.56017820 [7] 0.42210846 0.40800803 0.17191411 -0.03490206 Largest eigenvalues: [1] 115228833 106852856 100872305 100612593 96668994 93944870 93133607 [8] 91547886 91099573 89870287 Smallest eigenvalues: [1] 1.0421748 0.9817670 0.8979474 0.7135620 0.6765490 0.6556969 [7] 0.6043825 0.6018187 0.4389780 -0.5168323 Largest eigenvalues: [1] 109488187 108031512 101236633 97874966 96436230 95061262 91791919 [8] 90742249 89733278 89075070 Smallest eigenvalues: [1] 0.66410406 0.63008117 0.44675415 0.44276185 0.43490092 0.36210114 [7] 0.36065442 0.06512088 -0.68429152 -5.46802925 Largest eigenvalues: [1] 111395077 106520544 100813573 98410671 97114953 94708924 91534507 [8] 91129181 90969331 88982751 Smallest eigenvalues: [1] 1.05607197 0.97657931 0.94210397 0.89807917 0.82917942 0.77739581 [7] 0.74458676 0.67188543 0.27173511 -0.01372373 Largest eigenvalues: [1] 112181315 106175825 100114010 98511977 96683015 93941844 91084646 [8] 90688504 90661510 88738164 Smallest eigenvalues: [1] 1.1429093 1.1120269 1.0372100 0.9346440 0.9095105 0.7489668 [7] 0.7312088 0.7108722 0.6998953 -2.7443250 Largest eigenvalues: [1] 110407360 106062556 99698106 96947761 96714957 93805261 91392568 [8] 91116145 89470132 88638925 Smallest eigenvalues: [1] 0.83001031 0.70062883 0.60878181 0.56505925 0.51739158 0.45835171 [7] 0.37423004 0.08768986 -0.22078140 -8.54102379 Largest eigenvalues: [1] 111314821 106422047 100126522 98179475 97317316 94130163 91769598 [8] 91714855 90879757 89852963 Smallest eigenvalues: [1] 1.0256507 0.9123795 0.8720874 0.8595631 0.6163933 0.6050374 [7] 0.5943788 0.4717390 0.2093141 -0.2056350 Largest eigenvalues: [1] 111431510 105446503 99584960 98434487 96181945 93618419 90579169 [8] 90485731 89964174 88201526 Smallest eigenvalues: [1] 0.7844244 0.7480633 0.6155423 0.5491966 0.4699574 0.4126140 [7] 0.2547411 0.1456164 0.1093533 -13.9338254 Largest eigenvalues: [1] 111752712 106734192 100390558 98354552 97565986 94538159 91840314 [8] 91698931 90949547 89868911 Smallest eigenvalues: [1] 0.86448777 0.71902679 0.65863933 0.52573217 0.52028122 0.46881391 [7] 0.44462569 0.43431567 0.38501281 -0.02163295 Largest eigenvalues: [1] 110449945 106456899 100414361 97016898 96844385 94496205 91570406 [8] 90955824 89795802 89515734 Smallest eigenvalues: [1] 0.8077533 0.7210238 0.7046503 0.6085655 0.5154150 0.4638999 [7] 0.4070571 0.4037090 -0.5578822 -2.9755371 Largest eigenvalues: [1] 112973608 106556216 100691312 98152280 96881222 94703967 92021864 [8] 90876640 90683992 89404057 Smallest eigenvalues: [1] 1.0773007 0.9626993 0.9391143 0.7244120 0.6689677 0.6444892 [7] 0.6404767 0.5692663 0.5009240 -1.1511150 Largest eigenvalues: [1] 111311852 105232210 99928039 98265507 96039031 93148420 90556313 [8] 90488658 90308898 88917255 Smallest eigenvalues: [1] 0.7981970 0.7137126 0.5524738 0.5143721 0.4631009 0.4315507 [7] 0.3440508 0.3307966 -0.6640709 -13.6530744 Largest eigenvalues: [1] 112401409 106226143 99606786 98302071 97346257 94324572 91229649 [8] 90974595 90884715 88957844 Smallest eigenvalues: [1] 0.829813872 0.808524245 0.671348323 0.540293260 0.483241813 [6] 0.435728941 0.268804002 -0.007331811 -0.479030577 -9.594758667 Largest eigenvalues: [1] 111347621 106199593 100142393 97726908 97365430 94082117 91829816 [8] 90732757 90601758 89054039 Smallest eigenvalues: [1] 0.9615530 0.8850449 0.7495478 0.6728715 0.5648177 0.5490488 [7] 0.4949402 0.4868193 0.3929350 -2.9092752 Largest eigenvalues: [1] 111631000 107777313 101684344 98172664 98168006 95857725 92842954 [8] 91670704 90774020 90117877 Smallest eigenvalues: [1] 0.8739108 0.8275594 0.7757406 0.7607616 0.6420070 0.6336824 [7] 0.6080127 0.5084099 0.4949343 -0.1608341 Largest eigenvalues: [1] 111466445 106320177 100208899 97248736 97064845 94351587 91498086 [8] 91260856 90024937 89551921 Smallest eigenvalues: [1] 0.9988479 0.9883082 0.7596602 0.7435862 0.6155986 0.5804031 [7] 0.5332565 0.5265821 0.5217056 -1.3656965 Largest eigenvalues: [1] 109425389 104497885 99229765 95947142 95519276 93010176 90788547 [8] 90328333 88918384 88640162 Smallest eigenvalues: [1] 0.9249039 0.8676555 0.7875298 0.6754646 0.6264638 0.5906099 [7] 0.5557671 0.4618144 0.2376553 -1.7922688 Largest eigenvalues: [1] 111799604 106481838 100838188 98745987 97461329 94701464 92312035 [8] 91490629 91128327 89711698 Smallest eigenvalues: [1] 0.8542768 0.8471045 0.8358482 0.8149381 0.7840356 0.7230181 [7] 0.5723058 0.4746535 -0.6272396 -0.7254714 Largest eigenvalues: [1] 112916722 105809923 100571340 99337329 95684253 92882721 91557154 [8] 90806729 90118652 88788615 Smallest eigenvalues: [1] 0.8952134 0.7104466 0.7028589 0.6619203 0.6394758 0.6334800 [7] 0.4738881 0.4188225 0.4144207 -1.6640274 Largest eigenvalues: [1] 109818254 107122122 100135355 97670024 97110970 94890048 92215405 [8] 90651234 89891877 88795194 Smallest eigenvalues: [1] 0.73032461 0.69048295 0.68040785 0.62712556 0.53470399 0.49439651 [7] 0.48178364 0.46440751 0.45518368 -0.06228659 Largest eigenvalues: [1] 113741631 107359730 101493407 99947294 97539029 95205164 92292266 [8] 91682973 91591967 90074837 Smallest eigenvalues: [1] 1.1409923 0.9902209 0.8965798 0.8457491 0.7979157 0.7376543 [7] 0.5407625 0.4906326 0.3232874 -0.1901821 Largest eigenvalues: [1] 113122387 107849352 101228100 99163997 97610249 94451043 92199002 [8] 91649456 91511862 89988175 Smallest eigenvalues: [1] 0.7365103 0.7299214 0.7217137 0.6310214 0.5889902 0.5509948 [7] 0.5200066 0.4028569 0.1723160 -0.2521258 Largest eigenvalues: [1] 112282350 106863390 100634214 98628405 97045471 94335103 91719497 [8] 91339914 91035716 89156143 Smallest eigenvalues: [1] 0.9953283 0.9550616 0.9046692 0.8810875 0.7491354 0.6954332 [7] 0.6133449 0.5778792 0.4657114 -11.5932692 Largest eigenvalues: [1] 115262997 106115067 100363224 100263218 96762338 93914858 93042521 [8] 91098684 90521522 89630432 Smallest eigenvalues: [1] 0.8755228 0.7926383 0.7431564 0.7347429 0.6041977 0.5518729 [7] 0.4817466 0.4594325 0.4559424 -0.5008348 Largest eigenvalues: [1] 111744869 105403438 99730886 98834732 95880066 92957791 90983171 [8] 90840638 90655121 89001006 Smallest eigenvalues: [1] 0.9870905 0.9110886 0.7091675 0.6884389 0.6824216 0.6533060 [7] 0.6234503 0.5830949 0.5056994 -1.5022314 Largest eigenvalues: [1] 111183425 106865713 100001688 97427979 97016915 93682849 91273023 [8] 91100640 90224315 89268923 Smallest eigenvalues: [1] 0.66395357 0.60793105 0.57882042 0.52678373 0.50563976 [6] 0.50326024 0.47520678 0.03497791 -0.38520771 -13.55494233 Largest eigenvalues: [1] 112005687 105771346 99958139 98339602 96475076 93959460 91161788 [8] 90873326 90332974 88527218 Smallest eigenvalues: [1] 8.612330e-01 7.900377e-01 7.213975e-01 6.609407e-01 5.753306e-01 [6] 4.741194e-01 4.497456e-01 3.307483e-01 1.070042e-01 -2.753446e-05 Largest eigenvalues: [1] 114049019 105874335 100464193 99395650 96301079 93511106 92348214 [8] 91402268 90907022 89852610 Smallest eigenvalues: [1] 0.86054413 0.73613501 0.65624374 0.60028953 0.53086601 0.49756083 [7] 0.48957512 0.48883735 0.06621942 -0.58732263 Largest eigenvalues: [1] 112433380 105897861 100790155 98732772 96148610 93674740 91456774 [8] 91265290 91105945 89916993 Smallest eigenvalues: [1] 0.8012861 0.7290541 0.7232635 0.6832502 0.4737090 0.2344541 [7] 0.1750941 0.1655950 -1.1288695 -7.8812476 Largest eigenvalues: [1] 110638199 104722979 100053841 96568931 96511229 93853308 91165033 [8] 90395093 89407024 88855949 Smallest eigenvalues: [1] 0.5730275 0.5275477 0.5120175 0.4519950 0.4352719 0.3681492 [7] 0.1351852 0.1267968 -0.4436056 -7.6377639 Largest eigenvalues: [1] 110469913 105820725 99412132 96832030 96679789 94094500 91461632 [8] 90423132 89457170 88259902 Smallest eigenvalues: [1] 1.0706439 1.0525352 0.8663157 0.8285159 0.7517212 0.7228777 [7] 0.5999208 0.5636557 0.5250552 -1.1117627 Largest eigenvalues: [1] 110844220 106252000 99683618 98070848 96565745 93726388 90722164 [8] 90681828 90548851 88799347 Smallest eigenvalues: [1] 1.1207215 1.0769947 0.9522244 0.8363761 0.7829118 0.7821836 [7] 0.6731551 0.5910142 0.5884217 -0.7990171 Largest eigenvalues: [1] 111822654 105906098 99686805 97954426 96749647 93803503 91546730 [8] 90774389 90605444 88835072 Smallest eigenvalues: [1] 0.8833443 0.8007969 0.7652360 0.6710414 0.5886209 0.5375649 [7] 0.5348174 0.4319573 -0.4827065 -0.7530039 Largest eigenvalues: [1] 113792372 107892590 101206171 99526757 97841155 94945158 92345784 [8] 92291016 91524278 90563002 Smallest eigenvalues: [1] 0.7906509 0.6334079 0.6174079 0.5935930 0.5500160 0.4343821 [7] 0.4083412 0.3817616 0.1963990 -0.3138231 Largest eigenvalues: [1] 111494610 107200857 101227038 97918306 97902035 95052182 92481215 [8] 91533816 90786087 89657430 Smallest eigenvalues: [1] 1.0689002 0.7848512 0.7804397 0.6903064 0.6452717 0.6367489 [7] 0.6143130 0.4779349 0.4564593 -0.5095508 Largest eigenvalues: [1] 111788285 106539667 101261873 97643777 97156546 94560648 91217421 [8] 91075781 90423546 89327671
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.263548 | 0.7573061 | 14.61197 | 0 | 1.078832 | 2.865932 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + t + steps
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd,
steps = steps_fd)
path_plot <- 'figures/model_HR_alt_noise_temp_steps_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 570 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.9348751 0.8093196 0.8040542 0.7777050 0.7055800 0.5354735 [7] 0.4280335 0.3952667 0.3673367 -0.4506395 Largest eigenvalues: [1] 110560798 104438156 98471328 96510822 94369583 91943003 89734160 [8] 89271913 88979213 87500760 Smallest eigenvalues: [1] 0.9148198 0.8080296 0.7935495 0.7855616 0.6945535 0.6615462 [7] 0.6457396 0.5180668 0.4906340 -2.6355302 Largest eigenvalues: [1] 107141197 104661043 99030811 94902669 94330151 92672700 89609511 [8] 89340768 87971457 87278558 Smallest eigenvalues: [1] 0.5842274 0.5086076 0.4276569 0.3914728 0.2094963 0.1706714 [7] 0.1555966 0.1434095 -0.4481483 -1.9866377 Largest eigenvalues: [1] 107717260 103076063 97696149 94584135 94411817 91685513 89632686 [8] 88475584 87476908 86849211 Smallest eigenvalues: [1] 0.9255135 0.9183308 0.7152333 0.5882397 0.5748553 0.5303885 [7] 0.4825541 0.4037417 0.3994518 -0.3085808 Largest eigenvalues: [1] 109857448 103755034 97556038 97168865 93847394 90903460 90038486 [8] 89105322 88709232 87529164 Smallest eigenvalues: [1] 0.8858831 0.8239709 0.6139123 0.5783001 0.5405536 0.4838569 [7] 0.4161177 0.3826504 -0.1580680 -0.1818739 Largest eigenvalues: [1] 109663136 103770360 97920493 97006402 93993462 91034069 89768646 [8] 89496821 89214865 87683496 Smallest eigenvalues: [1] 0.986934769 0.906741179 0.794638082 0.790531278 0.774610658 [6] 0.703182994 0.597410578 0.583205167 0.575475314 -0.009657942 Largest eigenvalues: [1] 109091658 103369129 97840566 95746264 93960993 91035176 88798408 [8] 88737081 88320345 87187357 Smallest eigenvalues: [1] 0.82383862 0.80594310 0.65756364 0.52734114 0.44892800 0.26086729 [7] 0.21487300 0.03755222 -0.10412527 -2.24442264 Largest eigenvalues: [1] 108594474 101307301 96706243 94392361 92917794 90363345 87603931 [8] 87582122 87231534 86366033 Smallest eigenvalues: [1] 1.0097999 0.9277245 0.8833997 0.8709712 0.7470745 0.6625220 [7] 0.5858319 0.5222761 0.3458447 -0.6465332 Largest eigenvalues: [1] 109365157 102797979 96631264 94939915 94117613 91189978 88692480 [8] 88210259 88154308 86698700 Smallest eigenvalues: [1] 0.8821917 0.8566059 0.8546108 0.8477908 0.7738026 0.6348665 [7] 0.5683213 0.4619029 0.3276785 -0.8170213 Largest eigenvalues: [1] 111219897 104266556 98389482 96155883 94940092 92211097 89625330 [8] 89461874 89270509 87912253 Smallest eigenvalues: [1] 0.9519004 0.8774986 0.8714826 0.6573351 0.5987138 0.4794838 [7] 0.4568477 0.4489152 -0.2750028 -6.4406371 Largest eigenvalues: [1] 106176322 101827521 96030586 94085328 93106426 90332269 87754106 [8] 87147891 86805069 85559873 Smallest eigenvalues: [1] 0.70611147 0.63904316 0.59769181 0.56182159 0.46654091 0.38750647 [7] 0.08588930 0.08241867 -0.03336646 -0.83554004 Largest eigenvalues: [1] 108708031 102810434 97851080 95366421 93893256 91481478 88669002 [8] 88456015 87913262 87243465 Smallest eigenvalues: [1] 0.787667992 0.786164541 0.724675825 0.648467100 0.603139918 [6] 0.495925831 0.405797963 0.369148802 -0.005448678 -0.194699930 Largest eigenvalues: [1] 107419741 101992909 96248653 95104978 92745036 90418279 88290100 [8] 87697173 87554001 86302378 Smallest eigenvalues: [1] 1.0425054 0.8836607 0.7949276 0.7516601 0.7330903 0.6955937 [7] 0.5514973 0.5250823 0.4932373 -0.2625946 Largest eigenvalues: [1] 107257342 102287179 96669942 94007831 93932913 90778352 88099904 [8] 87959913 86918076 86421720 Smallest eigenvalues: [1] 0.8449660 0.8358558 0.7799953 0.6674715 0.6550824 0.4692654 [7] 0.4641032 0.4049352 0.3684635 -1.5083540 Largest eigenvalues: [1] 109489098 103049835 97521799 95675749 94178813 91542625 88816175 [8] 88787423 88528986 87287311 Smallest eigenvalues: [1] 0.86402274 0.82285041 0.82047166 0.79914112 0.66068689 0.60334841 [7] 0.57842039 0.50972973 0.27782894 -0.03728339 Largest eigenvalues: [1] 106788677 102523146 96787327 93900386 93887870 91157660 88536411 [8] 87691715 86981931 86125157 Smallest eigenvalues: [1] 0.6902443 0.6887146 0.6476250 0.6437710 0.5685211 0.4726260 [7] 0.4638292 0.3926920 0.3828357 -3.6519680 Largest eigenvalues: [1] 104854669 102225329 96842499 93698710 92400994 91526331 89233891 [8] 87358422 86091170 86034217 Smallest eigenvalues: [1] 0.9595052 0.9399287 0.8237670 0.7804078 0.7151511 0.5967222 [7] 0.5175085 0.4995102 -0.3495336 -0.5565257 Largest eigenvalues: [1] 109909455 102736085 97554445 96406653 94102402 91513439 89284159 [8] 89070005 88956348 87571208 Smallest eigenvalues: [1] 0.9106840 0.8991241 0.7210108 0.6807789 0.6672419 0.5762042 [7] 0.5459487 0.5132373 0.4124881 -0.2897281 Largest eigenvalues: [1] 109459214 104703848 98646210 96377760 94276849 91804835 89392342 [8] 89089093 89054151 87807454 Smallest eigenvalues: [1] 0.9383827 0.9123978 0.7408325 0.7190509 0.6547596 0.5662811 [7] 0.5521328 0.5399948 0.4293418 -0.1883691 Largest eigenvalues: [1] 108526729 102895243 97390691 94579088 93758015 91165300 88226305 [8] 88198559 87639885 86570278 Smallest eigenvalues: [1] 0.9126121 0.8322896 0.7882769 0.7779469 0.6923482 0.5720599 [7] 0.4627222 0.4573269 0.4384198 -1.7239175 Largest eigenvalues: [1] 110753874 103597558 97892843 95900892 94357848 91700757 89265051 [8] 88846774 88722629 87533543 Smallest eigenvalues: [1] 0.98807060 0.92472976 0.88191590 0.76558622 0.75873238 0.58895431 [7] 0.57706534 0.53905494 0.53262966 -0.01002251 Largest eigenvalues: [1] 110933982 104055425 98504863 96799838 94741497 91719515 89651802 [8] 89494385 89248682 87823686 Smallest eigenvalues: [1] 0.9669601 0.8357802 0.7996964 0.7628540 0.6595044 0.5478379 [7] 0.5262466 0.5245446 0.4519131 -0.2540084 Largest eigenvalues: [1] 109899230 103324056 97702827 95839754 94530136 91638618 89350749 [8] 88860696 88750190 87802656 Smallest eigenvalues: [1] 0.9042244 0.8254569 0.8169962 0.7228478 0.7066670 0.6504461 [7] 0.5831069 0.4994867 0.4503487 -0.2249093 Largest eigenvalues: [1] 110835537 105489454 99078364 96641977 95433460 92669628 90021975 [8] 89833432 88940373 87262268 Smallest eigenvalues: [1] 0.8078271 0.7262409 0.6239240 0.5586248 0.5290175 0.4931768 [7] 0.4309517 0.3622649 0.3594863 -0.5018356 Largest eigenvalues: [1] 111273343 103142987 98579238 96744422 93811785 91122572 89526270 [8] 89005590 88413278 87448124 Smallest eigenvalues: [1] 0.7645423 0.6542116 0.6452031 0.6106405 0.4857393 0.4606741 [7] 0.4221937 0.3605441 0.3127330 -0.5698418 Largest eigenvalues: [1] 108912549 103706042 97580975 96304339 93783456 91591109 89108729 [8] 88864949 88580762 87123471 Smallest eigenvalues: [1] 1.0150695 0.9808378 0.9434159 0.8148177 0.8063113 0.7582341 [7] 0.6801490 0.5021209 0.3306220 -1.0327082 Largest eigenvalues: [1] 107578659 102803587 97037622 94823226 93524125 90819146 88582703 [8] 88219136 87628719 86437670 Smallest eigenvalues: [1] 0.8370708 0.8315579 0.7314729 0.6732884 0.6229784 0.5589385 [7] 0.3736938 0.3717455 0.3085594 -1.3044376 Largest eigenvalues: [1] 109609236 103466190 96992804 95965258 94431977 91521651 89162525 [8] 88762898 87970055 86418844 Smallest eigenvalues: [1] 0.80875084 0.75502958 0.72595540 0.65685373 0.59638425 0.54621251 [7] 0.51905116 0.47063072 0.39610270 -0.05887288 Largest eigenvalues: [1] 109354229 104421536 98076640 95163044 93979409 91547264 88624426 [8] 88600186 88071506 87008412 Smallest eigenvalues: [1] 0.26041013 0.20739104 0.10838255 0.01584623 0.01019292 [6] -0.02560742 -0.57417992 -0.66026131 -1.52878029 -40.92491042 Largest eigenvalues: [1] 108164207 101042177 96353509 93164105 93097169 90198547 88092729 [8] 87992806 86405320 85840998 Smallest eigenvalues: [1] 0.48481067 0.45796668 0.35056824 0.34659635 0.29132789 0.21766116 [7] 0.19342659 0.06038247 -0.19053152 -2.02191309 Largest eigenvalues: [1] 107616232 103667421 97110900 95353017 94095340 91431200 89144407 [8] 88586923 87875430 86966556 Smallest eigenvalues: [1] 0.7432947 0.7106206 0.6790812 0.6452983 0.5125927 0.4494981 [7] 0.4363445 0.3188098 0.2902803 -0.4335392 Largest eigenvalues: [1] 108346038 104931074 99182983 95491965 95242805 93033787 90216357 [8] 90017434 88009962 87863187 Smallest eigenvalues: [1] 0.9713218 0.9501582 0.8288115 0.7367016 0.7119248 0.6741525 [7] 0.5509152 0.4596668 0.3893768 -1.3398669 Largest eigenvalues: [1] 110826878 102449973 97311640 96663915 93242202 90686551 89324789 [8] 88323651 88025755 86538732
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.262888 | 0.7368767 | 13.81651 | 0 | 1.107147 | 2.366921 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
temp_body = body_temperature_ENT_fd
)
path_plot <- 'figures/model_HR_alt_temp_body_ENT_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 34. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 204 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.464485 | 0.4787502 | 8.416988 | 0.005 | 0.5999727 | 0.7783512 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd
)
path_plot <- 'figures/model_HR_alt_noise_temp_body_ENT_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 28. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 312 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.539498014 0.481587315 0.466305475 0.437374808 0.423081170 [6] 0.416107218 0.372700653 0.135696735 0.006281957 -0.138226310 Largest eigenvalues: [1] 86591494 79305369 75904835 75903568 73050436 70546791 70340435 69256091 [9] 68852466 68001938 Smallest eigenvalues: [1] 0.7871032 0.7759548 0.7505842 0.7300239 0.7022145 0.6841254 [7] 0.6208750 0.3874420 0.2507688 -0.4148149 Largest eigenvalues: [1] 85316977 81111829 75469702 75196362 73542269 71739741 70842454 69201781 [9] 68697465 67763252 Smallest eigenvalues: [1] 0.80509361 0.62147414 0.60884550 0.51355545 0.50798118 0.46064036 [7] 0.42764667 0.41545691 0.26171675 -0.07306901 Largest eigenvalues: [1] 84593325 80735953 75726240 75647435 73409556 71349813 70057060 69544465 [9] 69193163 68082936
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.399143 | 0.5332019 | 11.20614 | 0.045 | 0.917515 | 0.9335229 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
pollution = pollution25_fd
)
path_plot <- 'figures/model_HR_alt_noise_pollution25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 404 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.68567 | 0.4495668 | 9.376699 | 0.645 | 1.478112 | 0.6997994 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + temp + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
temperature = temperature_fd,
pollution = pollution25_fd
)
path_plot <- 'figures/model_HR_alt_temp_pollution25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 27. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 408 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.68485 | 0.3932684 | 9.166168 | 0.43 | 1.099246 | 0.6483349 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + noise + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
pollution = pollution1_fd
)
path_plot <- 'figures/model_HR_alt_noise_pollution1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 366 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.666164 | 0.4508731 | 9.603953 | 0.625 | 1.40222 | 0.7105318 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + temp + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
temperature = temperature_fd,
pollution = pollution1_fd
)
path_plot <- 'figures/model_HR_alt_temp_pollution1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 27. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 352 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.685915 | 0.3931867 | 9.208156 | 0.445 | 1.140291 | 0.6481669 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + t + acc + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_air = temperature_fd,
acceleration = acceleration_fd,
temp_body = body_temperature_ENT_fd
)
path_plot <- 'figures/model_HR_alt_noise_temp_body_acc_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 60, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 60, norder = 4, lambda = 1e4),
temp_air = list(nbetabasis = 60, norder = 4, lambda = 1e4),
acceleration = list(nbetabasis = 60, norder = 4, lambda = 1e4),
temp_body = list(nbetabasis = 60, norder = 4, lambda = 1e4)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 22. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 572 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.40499922 0.38575140 0.37330254 0.26565527 0.23669670 0.17909644 [7] 0.12022384 0.09929447 0.08027420 -0.11493198 Largest eigenvalues: [1] 100409811 97227921 91487178 86785043 85852388 85144134 83623236 [8] 82165859 81042210 79393144 Smallest eigenvalues: [1] 0.2896454 0.2590102 0.2439697 0.2321240 0.2290729 0.1828896 [7] -0.0313414 -0.1371232 -0.3849387 -0.5804426 Largest eigenvalues: [1] 100808344 96841614 91198062 86431656 85943120 83915587 83387010 [8] 82001826 80104350 78836155 Smallest eigenvalues: [1] 0.34340896 0.31374410 0.30799138 0.30188452 0.16692150 0.10970465 [7] 0.10787023 0.10430705 0.07349305 -0.35782804 Largest eigenvalues: [1] 98998981 97747862 90844333 87274935 85958850 84079228 83692096 81517025 [9] 80656001 78344453 Smallest eigenvalues: [1] 0.4154001 0.3227800 0.2822608 0.2239209 0.1902423 0.1851140 [7] 0.1452747 -0.0386263 -0.5144615 -0.6734427 Largest eigenvalues: [1] 100272007 96658609 90982856 86232050 85414936 83509473 82852874 [8] 80933528 79872321 77840072 Smallest eigenvalues: [1] 0.28349125 0.25350768 0.23627961 0.23420214 0.14783177 0.06159823 [7] -0.22543440 -0.26380441 -0.66641794 -0.80658187 Largest eigenvalues: [1] 99921871 95973474 90119595 85836159 85625488 83783373 82185000 81153194 [9] 79525736 77847237 Smallest eigenvalues: [1] 0.26664951 0.24789935 0.23927021 0.22353279 0.08824512 0.03968938 [7] -0.02912113 -0.03549294 -0.04997009 -0.30938845 Largest eigenvalues: [1] 99858036 96284862 90176795 86150933 84898962 83611760 82670891 81121819 [9] 79803881 77908207 Smallest eigenvalues: [1] 0.3576000 0.2964083 0.2899710 0.2643327 0.2310401 0.2042095 [7] 0.2004565 -0.1296703 -0.3233978 -0.3329375 Largest eigenvalues: [1] 98347651 95861863 89801871 86052759 83374693 82947858 82476556 81049617 [9] 79757305 77507778 Smallest eigenvalues: [1] 0.28357528 0.26952505 0.21067696 0.20116957 0.12406344 0.12300721 [7] 0.11386965 0.11091921 -0.09569219 -0.37868482 Largest eigenvalues: [1] 98350647 97306176 91600206 86753737 85259916 84500186 83997789 82468014 [9] 80710666 79569331 Smallest eigenvalues: [1] 0.263166072 0.237117695 0.208720269 0.143722317 0.120915211 [6] 0.039572040 0.008137819 -0.213259223 -0.518664559 -0.625044333 Largest eigenvalues: [1] 99488573 96535090 90412637 85771308 85272740 83149055 82303012 80166252 [9] 79834294 77076658 Smallest eigenvalues: [1] 0.33087316 0.29332091 0.27808402 0.27482848 0.25179347 0.15599007 [7] 0.14410473 0.10239065 -0.08174326 -0.21962707 Largest eigenvalues: [1] 102186745 97446340 90956431 86962187 86539180 85433882 82809867 [8] 82165291 80491122 79498119 Smallest eigenvalues: [1] 0.32318669 0.32285306 0.30964775 0.29741764 0.25589597 0.19427749 [7] 0.17653953 0.17303152 0.06828234 -0.46645893 Largest eigenvalues: [1] 99040849 97851975 91097719 87526657 85065703 84148649 83722832 81542100 [9] 80103623 78123498 Smallest eigenvalues: [1] 0.35801185 0.30127014 0.22429455 0.20322895 0.18909833 0.14920184 [7] 0.01073892 -0.13422249 -0.51128543 -0.56308417 Largest eigenvalues: [1] 101821747 96632987 90457961 87408137 85869193 84000093 82612171 [8] 81512880 79850050 78532413 Smallest eigenvalues: [1] 0.26128199 0.23391728 0.22453912 0.18306532 0.15426175 0.12829706 [7] 0.10083483 -0.01364102 -0.19001718 -0.82815413 Largest eigenvalues: [1] 101383832 98167018 91742215 87654212 87407813 85339515 84344031 [8] 83007846 81529559 80168045 Smallest eigenvalues: [1] 0.31409117 0.30780545 0.29623860 0.28759548 0.25229695 0.24897994 [7] 0.09010427 0.06366506 -0.16982046 -0.29850493 Largest eigenvalues: [1] 99146203 96817646 90911458 86848025 84581118 83574627 83385542 81185516 [9] 79975257 77685279 Smallest eigenvalues: [1] 0.43664323 0.42304255 0.38684613 0.36953838 0.35607809 0.30589877 [7] 0.26394911 0.23545676 0.08685125 -0.16888413 Largest eigenvalues: [1] 98870968 95686778 89625885 85858336 84157315 82808052 82153344 80306759 [9] 79325757 77124002 Smallest eigenvalues: [1] 0.37760263 0.36183604 0.35465511 0.34773687 0.30503724 0.18599247 [7] 0.12593031 0.09374236 0.02984161 -0.50944468 Largest eigenvalues: [1] 99559108 96302892 89969866 86747295 84890903 84089648 83025149 81769868 [9] 80015468 78514005 Smallest eigenvalues: [1] 0.31249005 0.29108176 0.26181397 0.24792714 0.14131434 0.09839221 [7] 0.08009540 -0.07223220 -0.11408439 -0.16809780 Largest eigenvalues: [1] 100290671 96992885 91168376 86220127 85375749 84346296 83125511 [8] 82075253 80510177 79083207 Smallest eigenvalues: [1] 0.45213367 0.43621775 0.38318628 0.38197710 0.25267327 0.23193849 [7] 0.10383533 0.06100657 0.01787862 -0.49939169 Largest eigenvalues: [1] 98876202 97412122 90817865 86427420 85819873 83917984 83743106 81336712 [9] 80313145 78341465 Smallest eigenvalues: [1] 0.4692218 0.4283286 0.4187500 0.3970100 0.3378676 0.2969187 [7] 0.2932013 0.2397879 0.1354956 -0.2109869 Largest eigenvalues: [1] 100886663 95740984 89824820 86109135 86009369 84042650 82235463 [8] 81442361 79527111 78273939 Smallest eigenvalues: [1] 0.37721892 0.36178260 0.35926790 0.35914786 0.34806129 0.15178651 [7] 0.01312851 -0.20305815 -0.24056860 -0.52847045 Largest eigenvalues: [1] 99889486 97219354 90535407 87016701 86173941 84167110 83585594 81133749 [9] 80391273 77805138 Smallest eigenvalues: [1] 0.44956212 0.43113748 0.34794090 0.30565046 0.24509971 0.21539892 [7] 0.07626997 0.05901595 -0.09107371 -0.47723095 Largest eigenvalues: [1] 98198568 96031354 89701386 85572522 85326996 83119099 82826619 80704813 [9] 79369560 77406174 Smallest eigenvalues: [1] 0.405926625 0.390693620 0.363323656 0.265052771 0.260446920 [6] 0.212611893 0.210829100 0.207717460 -0.006217537 -0.190462800 Largest eigenvalues: [1] 100571932 96218987 89712430 86118059 84899480 83828761 82379222 [8] 81111765 79804814 78306279 Smallest eigenvalues: [1] 0.29379923 0.26671983 0.23145690 0.19418080 0.16178844 0.15327418 [7] 0.09182310 0.06621997 -0.03902393 -0.52312589 Largest eigenvalues: [1] 99708647 97342367 91226684 86766161 85076191 83926140 83336027 81235030 [9] 80382298 77858810 Smallest eigenvalues: [1] 0.4597979 0.4400163 0.3935718 0.3930541 0.2982237 0.2616361 [7] 0.2411777 0.2285961 -0.0936151 -0.1470789 Largest eigenvalues: [1] 100221320 97644767 91205674 86963075 85906252 83946978 83421463 [8] 81224812 80232309 78459953 Smallest eigenvalues: [1] 0.31131033 0.27871188 0.27793978 0.24675938 0.24035070 0.17052164 [7] 0.11874112 0.03552373 0.02022545 -0.37477601 Largest eigenvalues: [1] 99914935 95425913 88887608 85756304 84965721 82859509 82581920 80668768 [9] 78918687 77560808 Smallest eigenvalues: [1] 0.41072865 0.35380235 0.31152920 0.29829745 0.23563424 0.11042764 [7] 0.08595452 0.05026712 -0.15045173 -0.45095803 Largest eigenvalues: [1] 101414690 97422242 91455291 86947924 86485376 85623497 83209668 [8] 82526556 80722420 79643316 Smallest eigenvalues: [1] 0.37661155 0.37492003 0.34053816 0.30530303 0.26060679 0.21956300 [7] 0.11159119 -0.01691463 -0.05754314 -0.35915150 Largest eigenvalues: [1] 100032000 97177861 90538020 87066209 85476424 84061138 83201690 [8] 81225165 80587492 78374163 Smallest eigenvalues: [1] 0.47085305 0.44047079 0.43447665 0.40189831 0.36420557 0.33735926 [7] 0.22780838 0.08806813 0.05957222 -0.13675461 Largest eigenvalues: [1] 101322005 96967969 90697528 86841509 85685407 84402577 82715288 [8] 81463851 80039088 78318791 Smallest eigenvalues: [1] 0.21245253 0.20660722 0.15106556 0.14926415 0.14852636 0.07290937 [7] 0.04075537 -0.03508697 -0.25371986 -1.00928473 Largest eigenvalues: [1] 99377370 97364407 90517905 87248111 85765702 84061761 83485525 81571040 [9] 80306468 77945996 Smallest eigenvalues: [1] 0.45938470 0.45013613 0.43499194 0.40525092 0.30883185 0.30497477 [7] 0.11091883 0.05602612 -0.17371783 -0.35642733 Largest eigenvalues: [1] 100093563 96594256 90858245 86693456 84745672 83656362 83409091 [8] 81165828 80256990 77908107 Smallest eigenvalues: [1] 0.314093203 0.306725501 0.248874030 0.245209039 0.196328915 [6] 0.071010672 0.017277817 0.015906990 -0.006597346 -0.116304159 Largest eigenvalues: [1] 97810937 97059264 90505453 86121661 84460474 83446259 82893943 80476818 [9] 80068860 77597445 Smallest eigenvalues: [1] 0.39031490 0.37796342 0.34930858 0.34212798 0.24005479 0.14761918 [7] 0.14685534 0.14405352 0.03708517 -0.49935565 Largest eigenvalues: [1] 97808153 95028026 89383658 85206158 83530010 83239709 82104279 80491410 [9] 79405177 77566529 Smallest eigenvalues: [1] 0.25923598 0.25236320 0.22232473 0.19899237 0.15081010 0.06844456 [7] 0.06605889 -0.18679572 -0.23041843 -1.71139873 Largest eigenvalues: [1] 99248883 97087692 90240480 86687804 85881591 84761920 82525057 81493474 [9] 79870491 78450471 Smallest eigenvalues: [1] 0.39836078 0.39526171 0.38738993 0.28226396 0.27607376 0.25607851 [7] 0.23984362 0.15642635 0.08866805 -0.31615196 Largest eigenvalues: [1] 97346160 95663274 89495304 86036390 83882987 83232543 82291795 81095326 [9] 79277744 77979753 Smallest eigenvalues: [1] 0.313284458 0.310829996 0.252046172 0.251562527 0.164256148 [6] 0.051978263 0.020428095 -0.001386579 -0.279840232 -0.338049989 Largest eigenvalues: [1] 100228039 97118594 91513487 86092541 85488439 83970107 83272567 [8] 81460678 80637422 78614630 Smallest eigenvalues: [1] 0.41080465 0.38001527 0.34669900 0.27227910 0.25363763 0.22499337 [7] 0.22173489 0.19278159 0.06858431 -0.13090833 Largest eigenvalues: [1] 99784818 96452165 89471537 86187067 85389388 82963293 82590269 80235532 [9] 79325819 76987017 Smallest eigenvalues: [1] 0.458498097 0.456589721 0.420246750 0.388439121 0.378101419 [6] 0.337765963 0.296999919 0.217440473 0.009250704 -0.190879226 Largest eigenvalues: [1] 100691810 95796460 89999010 86217049 85069473 83425480 82333258 [8] 81148756 79405296 78030491 Smallest eigenvalues: [1] 0.403401895 0.396575899 0.339065942 0.205026448 0.169466699 [6] 0.166501472 0.039562486 -0.006456898 -0.259688163 -0.719661342 Largest eigenvalues: [1] 100090304 96358671 90795176 86035637 85179572 83495549 82961045 [8] 81037517 80231164 77902914 Smallest eigenvalues: [1] 0.33489898 0.31948839 0.29983695 0.25278292 0.19677031 0.16581440 [7] 0.13645739 0.11775408 0.06606754 -0.16810145 Largest eigenvalues: [1] 98743753 97532819 90754413 87076455 84323844 83731923 83425970 81180890 [9] 80474875 78012914 Smallest eigenvalues: [1] 0.40085074 0.37300348 0.35643040 0.30709310 0.24466219 0.22871078 [7] 0.17313416 0.09851080 -0.01197968 -0.09208119 Largest eigenvalues: [1] 98984981 96334258 89806810 86920017 84933597 83461642 82764242 80822350 [9] 80074287 77738362 Smallest eigenvalues: [1] 0.3727153070 0.3637305411 0.3104891141 0.3004390483 0.2582798690 [6] 0.2524897325 0.2217216022 0.0590810246 0.0008437753 -0.5295404927 Largest eigenvalues: [1] 102554803 96016389 90802808 85931817 85779304 84139036 82359364 [8] 81643848 79764004 78420441 Smallest eigenvalues: [1] 0.51737863 0.49984632 0.49172217 0.44882690 0.36934854 0.31030308 [7] 0.20670276 0.19453192 0.05975679 -0.17234306 Largest eigenvalues: [1] 100643915 96202406 89708965 86066398 85655332 83543294 82502070 [8] 80890705 79784241 77857469 Smallest eigenvalues: [1] 0.34296124 0.29873743 0.25007675 0.23902385 0.23552444 0.15602640 [7] 0.04632341 0.03537650 -0.18118070 -0.59643524 Largest eigenvalues: [1] 100279656 96075210 90156225 85551588 85335796 83629207 82431881 [8] 81213635 79271178 77872124 Smallest eigenvalues: [1] 0.2680535 0.2304919 0.2177748 0.2030088 0.1828213 0.1433360 [7] -0.1148718 -0.1805616 -0.2355844 -0.4479960 Largest eigenvalues: [1] 100585063 97121171 91481766 86700314 84762150 83679646 83439441 [8] 81317150 80348024 77973821 Smallest eigenvalues: [1] 0.37671217 0.37430604 0.36117745 0.35001678 0.27092440 0.21888527 [7] 0.13756463 0.08396045 -0.13767705 -1.06654921 Largest eigenvalues: [1] 100419108 96840975 90098389 86800322 86181572 84249606 82990260 [8] 81572909 80277651 78647144 Smallest eigenvalues: [1] 0.4074080 0.3967413 0.3701096 0.3528831 0.3421448 0.2849518 [7] 0.2314174 0.2147500 0.1423941 -0.1060413 Largest eigenvalues: [1] 99929547 96218963 89662323 86087950 85504517 83409500 82483543 80675760 [9] 79848095 77632442 Smallest eigenvalues: [1] 0.45419145 0.43425036 0.42495091 0.30142881 0.25420232 0.18762717 [7] 0.17765908 0.08862725 0.05584173 -0.32046316 Largest eigenvalues: [1] 101742773 97032644 90796846 86502784 86468291 84108359 82736303 [8] 81529986 80130655 78987724 Smallest eigenvalues: [1] 0.31431116 0.30401229 0.29482882 0.23339797 0.21266297 0.20039933 [7] 0.10415410 0.08946401 0.08474100 -0.23343580 Largest eigenvalues: [1] 98699953 97228258 90868236 86363864 84901020 83731627 82939562 80978494 [9] 79817840 77912238 Smallest eigenvalues: [1] 0.3240336 0.2967009 0.2927913 0.2874111 0.1889279 0.1860270 [7] 0.1061618 0.0133811 -0.1831504 -0.3977991 Largest eigenvalues: [1] 98365216 96987410 90187599 86346175 84725479 83790222 83591403 81479119 [9] 80228266 78448412 Smallest eigenvalues: [1] 0.26495640 0.26489071 0.22371769 0.21272452 0.21092455 0.13450794 [7] 0.07568175 -0.11308530 -0.25355568 -0.38785730 Largest eigenvalues: [1] 100491773 95592483 89483865 85601483 85489499 82743754 82566395 [8] 80384907 79315528 77336978 Smallest eigenvalues: [1] 0.20849775 0.20253732 0.19351602 0.09609910 -0.05523809 -0.25221580 [7] -0.26257271 -0.34160063 -0.59292528 -0.85442338 Largest eigenvalues: [1] 103198308 95716266 90003891 86909666 85829582 83603974 82528480 [8] 81540857 80021167 78695613 Smallest eigenvalues: [1] 0.27124006 0.22904853 0.22640671 0.19259504 0.17670303 0.11733140 [7] 0.03183786 0.00249886 -0.60376701 -0.80894782 Largest eigenvalues: [1] 100673602 97409450 91515394 87079070 85942614 84881373 84089383 [8] 82481464 81464515 79423696 Smallest eigenvalues: [1] 0.274472616 0.230702312 0.200248548 0.154492050 0.150924328 [6] 0.095856745 0.035929818 0.004475167 -0.145421725 -0.624190552 Largest eigenvalues: [1] 101538431 97484694 91723375 87624019 86213488 84619455 83642029 [8] 81979964 80760794 79012205 Smallest eigenvalues: [1] 0.41310806 0.39554402 0.38618436 0.31271958 0.24652824 0.20700732 [7] 0.20154068 0.12364335 -0.08561735 -0.88749876 Largest eigenvalues: [1] 99271555 97350853 91114716 86844757 85247488 84041997 83368549 81021300 [9] 80452200 77773715 Smallest eigenvalues: [1] 0.4775575 0.4416685 0.4174721 0.3846210 0.3787343 0.2681676 [7] 0.2461911 0.2069391 0.1219360 -0.4126579 Largest eigenvalues: [1] 99493125 97104916 90511072 86636753 85750709 83731296 83284917 81289769 [9] 80087007 78325864 Smallest eigenvalues: [1] 0.321047589 0.256578596 0.246271330 0.241456877 0.233125494 [6] 0.146518835 0.115333127 0.005539807 -0.668371730 -0.792509817 Largest eigenvalues: [1] 101061241 97283880 90959774 87238111 87045290 85133011 83521049 [8] 82210550 80981195 79148486 Smallest eigenvalues: [1] 0.31502864 0.29885731 0.27042688 0.25000756 0.13478598 0.09440181 [7] -0.05863189 -0.18305294 -0.20343206 -0.40745947 Largest eigenvalues: [1] 101666259 96161519 90160730 86162939 86149603 83021845 82876465 [8] 80622416 79911005 77607571 Smallest eigenvalues: [1] 0.32321599 0.29765039 0.28275263 0.23299141 0.20687585 0.14359639 [7] -0.05513066 -0.09088349 -0.13955483 -0.68653307 Largest eigenvalues: [1] 101167422 96969937 91183942 86732446 86210555 84643096 83458690 [8] 82176422 80460081 78838903 Smallest eigenvalues: [1] 0.443018052 0.433213211 0.409304825 0.341968996 0.322748177 [6] 0.272489144 0.269587057 0.061893489 -0.005889398 -0.031154854 Largest eigenvalues: [1] 99387816 96943807 90141891 86317755 85904622 83114595 82768579 80480453 [9] 79807087 77596674 Smallest eigenvalues: [1] 0.46888194 0.44823053 0.43925039 0.43603113 0.24706506 0.17091920 [7] 0.15326666 0.10653323 0.04191861 -0.08799794 Largest eigenvalues: [1] 100689112 96678238 90632215 86676106 85667570 84646780 83016529 [8] 81922957 80678611 79055828 Smallest eigenvalues: [1] 0.44876530 0.42748719 0.40161040 0.37347764 0.30731749 0.26952745 [7] 0.22240745 0.14723311 0.04313528 -0.10656128 Largest eigenvalues: [1] 98249151 96912514 90282710 86542644 84940550 83840127 83274650 81297173 [9] 79972219 78152178 Smallest eigenvalues: [1] 0.31051564 0.28985408 0.21245428 0.19608185 0.06897631 -0.03223848 [7] -0.20209307 -0.29525275 -0.50162766 -0.83945699 Largest eigenvalues: [1] 102471592 95172423 90001053 85932613 84847533 83312912 82309420 [8] 81264859 79268381 78158983 Smallest eigenvalues: [1] 0.3963428 0.3612168 0.3544779 0.3079443 0.2922775 0.2840457 [7] 0.2465732 -0.1109756 -0.3454127 -0.3639729 Largest eigenvalues: [1] 101169130 95860693 90048167 86057373 85187984 83554025 83163367 [8] 81272632 79953091 78011318 Smallest eigenvalues: [1] 0.36818786 0.34443605 0.34330245 0.26352006 0.23837803 0.22697530 [7] 0.14965625 0.13984745 -0.01714207 -0.43932538 Largest eigenvalues: [1] 100897932 97004602 90779091 87101643 85714829 83326501 82823537 [8] 80798358 79924877 77934946 Smallest eigenvalues: [1] 0.339465543 0.328428933 0.313407795 0.286559421 0.285598306 [6] 0.257465199 0.245470759 0.101111314 0.003669218 -0.488906157 Largest eigenvalues: [1] 98608666 97029308 89942148 86443380 85436910 83758391 83302106 81346349 [9] 79992980 78036444 Smallest eigenvalues: [1] 0.37813408 0.34924592 0.31326803 0.30185522 0.29897284 0.18525517 [7] 0.17236735 0.07706857 0.04655103 -0.12091970 Largest eigenvalues: [1] 102004511 97017037 90977195 86504296 86201110 83728273 82671964 [8] 81132065 79690198 78114046 Smallest eigenvalues: [1] 0.38849735 0.37753133 0.35391690 0.31472925 0.28686815 0.27276788 [7] 0.25271352 0.07130709 -0.09001781 -0.17834236 Largest eigenvalues: [1] 102031990 96016037 90345615 86672013 85583433 83557185 82368742 [8] 81169442 79501202 77805902 Smallest eigenvalues: [1] 0.27817447 0.23720392 0.20269332 0.19309593 0.15496230 0.14107932 [7] 0.13863626 0.05970453 -0.08667786 -1.31664468 Largest eigenvalues: [1] 98720336 95742280 89441213 85926938 84031525 82934738 82394779 80367454 [9] 79323556 77139984 Smallest eigenvalues: [1] 0.32259028 0.28718578 0.26595576 0.25182607 0.16949987 0.04819654 [7] -0.01027395 -0.06673669 -0.08626667 -0.36186837 Largest eigenvalues: [1] 99952323 96661136 90322810 86416946 85510766 83445283 82947620 80869633 [9] 80217725 77739396 Smallest eigenvalues: [1] 0.35591690 0.35300928 0.33931493 0.33493348 0.32307042 0.23847879 [7] 0.21540666 0.20364584 0.14205951 -0.06026108 Largest eigenvalues: [1] 99380047 96549841 90846855 86132381 84728796 84440209 83158418 81662943 [9] 80311703 78714208 Smallest eigenvalues: [1] 0.26642410 0.25581797 0.19490048 0.18147550 0.02421292 0.02406712 [7] -0.18875475 -0.37089817 -0.43742610 -0.97236271 Largest eigenvalues: [1] 99596398 97418785 91183505 86463696 86015405 83764300 83372938 81328489 [9] 80340177 78348409 Smallest eigenvalues: [1] 0.50025117 0.39843823 0.39083446 0.38194174 0.34848935 0.32932914 [7] 0.16617195 0.15689723 -0.05260435 -0.24970872 Largest eigenvalues: [1] 100722078 96645060 90070229 86863546 86137152 84310195 82370754 [8] 81308418 79738294 78343637 Smallest eigenvalues: [1] 0.302375575 0.215083527 0.212562528 0.207308069 0.112655653 [6] 0.098919665 0.023181595 0.002992639 -0.343116301 -0.644366724 Largest eigenvalues: [1] 99098176 96956999 90859297 86238772 85401493 83888217 83449735 81208517 [9] 80144778 78045204 Smallest eigenvalues: [1] 0.4588222 0.4267511 0.4176553 0.3883630 0.3876748 0.3333641 [7] 0.2769433 0.1446222 -0.1176175 -0.2994323 Largest eigenvalues: [1] 100619958 95844347 90052100 85989164 85545683 83143355 82574198 [8] 80609272 79758716 77496234 Smallest eigenvalues: [1] 0.33950745 0.33447094 0.28815610 0.28027972 0.27819773 0.25111271 [7] 0.22168267 -0.05237228 -0.40712417 -0.53493874 Largest eigenvalues: [1] 100328398 96955095 90529150 86355623 86257038 84516084 83221751 [8] 81809060 80030567 78563354 Smallest eigenvalues: [1] 0.13205679 0.10842634 0.10184721 0.05648537 0.05537725 0.03935342 [7] -0.04814956 -0.15145606 -0.46596589 -0.51276531 Largest eigenvalues: [1] 98397788 96448275 91300422 87783670 84602707 83604751 83320197 80990146 [9] 80446167 77637415 Smallest eigenvalues: [1] 0.37175172 0.36527311 0.35833299 0.34443991 0.28026019 0.16409954 [7] 0.11544373 0.06779821 0.02316705 -0.07093374 Largest eigenvalues: [1] 99246119 96932624 90886803 86423134 84647982 84472074 83318966 81882594 [9] 80477566 78975551 Smallest eigenvalues: [1] 0.27593798 0.26882660 0.23980222 0.14942382 0.12214058 0.11610548 [7] -0.04505453 -0.13823081 -0.25462989 -0.27196716 Largest eigenvalues: [1] 99125996 96724292 90308229 86466196 85676195 83707786 82898440 81049550 [9] 80025062 78385729 Smallest eigenvalues: [1] 0.46648745 0.44837094 0.44158263 0.38085923 0.37186917 0.36568731 [7] 0.24770157 0.19141239 0.13837776 -0.05683146 Largest eigenvalues: [1] 99184202 95162005 89384377 85143910 84033476 83283302 81551453 80593881 [9] 78864748 77402415 Smallest eigenvalues: [1] 0.4097244 0.3178153 0.2667854 0.2208578 0.2162445 0.2145888 [7] 0.2131585 0.2129423 -0.2270495 -0.3191023 Largest eigenvalues: [1] 98267567 96969484 91068004 86251795 84569527 83941578 82942608 81363583 [9] 79556860 78335908 Smallest eigenvalues: [1] 0.36672967 0.35645687 0.24224017 0.22070704 0.19904944 0.11382517 [7] -0.04024551 -0.47150064 -0.48852963 -1.31912532 Largest eigenvalues: [1] 102767114 97981184 91472173 87761712 87100613 84927348 83899368 [8] 82282737 81009300 79417094 Smallest eigenvalues: [1] 0.23481631 0.21982836 0.21048491 0.20896228 0.17719247 0.16246698 [7] 0.05035253 0.03924741 -0.23450144 -0.53293250 Largest eigenvalues: [1] 99201337 97207139 90949668 86617499 85234546 83954489 83374533 81478305 [9] 80429618 78465224 Smallest eigenvalues: [1] 0.428617258 0.404801171 0.352566605 0.343006154 0.318883414 [6] 0.299959035 0.251958770 0.027442156 0.001942045 -0.021128535 Largest eigenvalues: [1] 99849052 96876335 90948052 86187186 85290238 83852206 83051997 80916079 [9] 80277180 78115014 Smallest eigenvalues: [1] 0.42917812 0.34589424 0.30366688 0.30155517 0.22992807 0.15943113 [7] 0.14776920 0.13517865 0.01593799 -0.05816734 Largest eigenvalues: [1] 97592284 96163709 89712024 86025829 84427021 83327239 82778989 80733220 [9] 79637038 77675034 Smallest eigenvalues: [1] 0.35942367 0.31197655 0.28768258 0.28370090 0.24594165 0.22076058 [7] 0.14438131 0.04239094 -0.28719232 -0.29265377 Largest eigenvalues: [1] 97728963 96755149 89852528 86188725 85089459 84056946 82507876 81235969 [9] 79375947 78028877 Smallest eigenvalues: [1] 0.39862900 0.38488347 0.38423546 0.34398073 0.23361275 0.20624471 [7] 0.17135076 -0.08379514 -0.10908396 -0.29689802 Largest eigenvalues: [1] 100015111 96198242 90135451 86473997 85553230 83700278 82394531 [8] 80882895 79455733 77791560 Smallest eigenvalues: [1] 0.3449952 0.3298586 0.3245529 0.2909400 0.2390100 0.2389493 [7] 0.1978010 0.1556460 0.1414455 -0.4161229 Largest eigenvalues: [1] 98744302 97436351 90896911 87079748 85401945 84653689 83164328 81787636 [9] 79703793 78337059 Smallest eigenvalues: [1] 0.34646422 0.33304773 0.27320820 0.26040558 0.16977101 0.14595103 [7] 0.14507878 0.08576811 -0.29135459 -0.48845203 Largest eigenvalues: [1] 99725346 96755847 90421569 86459429 86073479 85096212 82979874 82401938 [9] 80075619 79147807 Smallest eigenvalues: [1] 0.399628029 0.393430955 0.275768994 0.190936404 0.186153069 [6] 0.090511332 0.086989351 0.032912539 0.006328245 -0.268763860 Largest eigenvalues: [1] 99212951 96764403 90393656 86633321 84308560 83662643 82933602 80904224 [9] 79764997 77515016 Smallest eigenvalues: [1] 0.229245847 0.211035407 0.108199259 0.105259863 0.078437317 [6] 0.005624065 -0.017416658 -0.052969226 -0.091139899 -0.572878304 Largest eigenvalues: [1] 99176070 96365984 90069536 86293296 84661507 83017050 82798501 80657583 [9] 79703400 77576040 Smallest eigenvalues: [1] 0.35344173 0.35169601 0.29651357 0.27540075 0.27252579 0.26509883 [7] 0.20889515 0.05811856 0.02331890 -0.10848214 Largest eigenvalues: [1] 98382937 98063424 91433626 87865870 84661230 84474282 84152148 81791083 [9] 80819320 78358589 Smallest eigenvalues: [1] 0.484711937 0.464397795 0.460029971 0.420550638 0.406648248 [6] 0.400444451 0.359702533 0.084779176 0.004643896 -0.047970685 Largest eigenvalues: [1] 101225338 96972709 90329182 86917538 86420219 84570882 82842403 [8] 81433132 80246810 78521589 Smallest eigenvalues: [1] 0.3223312 0.3133303 0.2807783 0.2803595 0.2403501 0.2273902 [7] 0.2010201 0.1799303 -0.1146300 -0.3789557 Largest eigenvalues: [1] 99949663 96225238 89792217 85646782 85150469 83132908 82070292 80598308 [9] 79427113 77892896 Smallest eigenvalues: [1] 0.47336466 0.46521729 0.36163158 0.33729698 0.28877477 0.27263974 [7] 0.26381791 0.04073367 -0.14707974 -0.39364029 Largest eigenvalues: [1] 103199770 95985428 90592673 86330967 86195579 84203549 82718886 [8] 81858016 80143574 78686127 Smallest eigenvalues: [1] 0.37142294 0.36150721 0.34485164 0.33796501 0.23220514 0.21711344 [7] 0.19104552 0.08555758 -0.01702987 -0.11570236 Largest eigenvalues: [1] 100380630 97297920 90908858 86553787 85991789 84456289 83410405 [8] 81562282 80451831 78390035 Smallest eigenvalues: [1] 0.40325161 0.38671779 0.36522420 0.36169364 0.34129946 0.31401020 [7] 0.15019437 0.07127135 -0.06730594 -0.10579871 Largest eigenvalues: [1] 97958304 96367686 89511740 86404848 84161861 83593581 81725710 79599455 [9] 79326443 76174294 Smallest eigenvalues: [1] 0.3454119 0.3141145 0.2817877 0.2618520 0.2094059 0.1405137 [7] 0.1085651 0.1018783 0.0129301 -0.2010862 Largest eigenvalues: [1] 99092645 96833885 90078243 86563662 85529709 83759886 82688125 80690387 [9] 79903493 77705498 Smallest eigenvalues: [1] 0.35816381 0.32277173 0.28796838 0.27088540 0.26608905 0.21362866 [7] 0.07612091 -0.18094776 -0.36042107 -0.41707999 Largest eigenvalues: [1] 102140772 97459499 91441244 87070662 86537204 84638888 83683507 [8] 82434922 80806133 79590165 Smallest eigenvalues: [1] 0.3900280 0.3794089 0.3408131 0.2658394 0.2499082 0.2268678 [7] 0.1885378 -0.1821073 -0.4017061 -0.4515327 Largest eigenvalues: [1] 101527335 98048617 91368555 87531320 87407152 85608090 83857224 [8] 82691862 81010480 79581223 Smallest eigenvalues: [1] 0.41773987 0.41482266 0.34549022 0.32593907 0.32140120 0.31795387 [7] 0.23161854 0.20562727 0.05054392 -0.04718841 Largest eigenvalues: [1] 97937332 96448687 88911231 86568001 84569052 83264606 83027001 80605480 [9] 79370689 77487846 Smallest eigenvalues: [1] 0.28515622 0.25645770 0.25611474 0.24955606 0.18851065 0.17321769 [7] 0.07821665 0.06115378 -0.22768348 -0.23824025 Largest eigenvalues: [1] 99411744 96361726 90513547 86067230 84638625 83030218 82757730 80648661 [9] 79923228 77621022 Smallest eigenvalues: [1] 0.34563097 0.33164010 0.22131756 0.19967235 0.12474336 0.09391956 [7] 0.07950065 0.07577933 -0.10071544 -0.12849286 Largest eigenvalues: [1] 101275703 97744200 91455978 87027251 85638049 84041800 83247070 [8] 81237680 80171061 78136540 Smallest eigenvalues: [1] 0.27885939 0.26903588 0.24111008 0.15190376 0.14045656 0.06802534 [7] 0.02984304 -0.01374009 -0.10950806 -0.35652718 Largest eigenvalues: [1] 96732182 96008539 90080271 86338523 83744566 83118807 82943695 80824075 [9] 79658306 77262902 Smallest eigenvalues: [1] 0.30063993 0.29631723 0.26422534 0.25198386 0.23796207 0.21666162 [7] 0.16106770 0.07951774 0.07603121 -0.14976514 Largest eigenvalues: [1] 99349475 96807543 89822579 86664030 84745144 84373236 82828176 81678797 [9] 79798081 78380596 Smallest eigenvalues: [1] 0.23714340 0.23196729 0.19928415 0.19618710 0.15868110 0.05805298 [7] 0.02658923 -0.12856663 -0.40083258 -1.09621734 Largest eigenvalues: [1] 102310945 96894070 91732140 86170335 86045650 84815626 83080521 [8] 82608263 80401031 79414190 Smallest eigenvalues: [1] 0.44912469 0.44233099 0.39630960 0.38307006 0.32344334 0.23107470 [7] 0.15981179 0.10479993 0.08017396 -0.16215229 Largest eigenvalues: [1] 99787233 96072598 89631967 86805850 85006367 82995240 82750786 80358447 [9] 79635028 77243902 Smallest eigenvalues: [1] 0.410139102 0.404092112 0.381775714 0.377532893 0.225243378 [6] 0.211265833 0.084522730 0.009718151 0.007250021 -0.276611646 Largest eigenvalues: [1] 99400195 95612316 89754342 85402281 84884448 83279824 81998921 80347792 [9] 79370841 77578389 Smallest eigenvalues: [1] 0.3813101 0.3298211 0.3000051 0.2511375 0.2162794 0.2089192 [7] 0.1479285 0.1032967 -0.1170077 -0.3179301 Largest eigenvalues: [1] 98614134 95976906 89515474 85706928 84880284 82618171 82273691 80062633 [9] 79119409 77137317 Smallest eigenvalues: [1] 0.46342904 0.43755500 0.42007454 0.36745766 0.31590176 0.21377818 [7] 0.20594263 0.16125315 -0.06850554 -0.11062541 Largest eigenvalues: [1] 101107260 96378627 89747632 86250886 85744330 83754362 82451631 [8] 81004998 79924346 78168508 Smallest eigenvalues: [1] 0.42806610 0.35104938 0.34807065 0.33608485 0.32924065 0.32150001 [7] 0.12192950 0.09759104 -0.11167794 -0.12932110 Largest eigenvalues: [1] 101863909 96600821 90460738 86826807 86509823 83840549 82997354 [8] 81126448 80352413 77987962 Smallest eigenvalues: [1] 0.46642828 0.43716392 0.41653242 0.35934138 0.34451162 0.26536333 [7] 0.24551153 0.19147015 -0.03646138 -0.20826431 Largest eigenvalues: [1] 101148232 96209533 90165562 86331613 86262233 83957635 82406434 [8] 81230696 80000994 78540599 Smallest eigenvalues: [1] 0.41867637 0.35632334 0.32348462 0.29727318 0.26370391 0.23843074 [7] 0.05770251 0.01608767 -0.04406826 -0.06623116 Largest eigenvalues: [1] 99067657 97274783 89824284 87491919 84956223 83659899 83041310 80570791 [9] 80228711 77649236 Smallest eigenvalues: [1] 0.40137864 0.38889178 0.32479432 0.28334003 0.23415514 0.21112442 [7] 0.15482432 0.13196442 0.08640855 -0.02693301 Largest eigenvalues: [1] 99225450 97495805 90639545 87379316 84616902 84490204 83031376 81565079 [9] 80564035 78902048 Smallest eigenvalues: [1] 0.37749948 0.32018202 0.25589822 0.23955210 0.20192800 0.19452190 [7] 0.18201782 0.10355985 0.03731818 -0.11208304 Largest eigenvalues: [1] 97979360 97894039 90476967 86722291 84597340 83632611 83166905 80616679 [9] 79966049 77690294 Smallest eigenvalues: [1] 0.41368735 0.39047570 0.37636921 0.31446144 0.28392998 0.23814518 [7] 0.23457630 0.09824392 0.02206441 -0.47102990 Largest eigenvalues: [1] 98477698 96729576 90160366 86031238 85221928 84301004 83022716 81504286 [9] 79789946 78356040 Smallest eigenvalues: [1] 0.4582915 0.4526640 0.4477887 0.3260148 0.2338115 0.2171097 [7] 0.1875100 0.1685598 0.1240071 -0.1775180 Largest eigenvalues: [1] 99537990 95261451 88646861 85289071 85190289 83163762 81449084 80406964 [9] 78673950 77266300 Smallest eigenvalues: [1] 0.29072789 0.25287336 0.20523249 0.14288510 0.13876403 0.10296366 [7] 0.08840748 0.04641719 -0.09422410 -0.11852544 Largest eigenvalues: [1] 97068277 97033652 89758553 86316113 84719321 83697925 83522616 81160675 [9] 79791413 77940896 Smallest eigenvalues: [1] 0.44985814 0.43500943 0.40978109 0.40632485 0.38812908 0.26480478 [7] 0.18500513 0.10175388 -0.01181772 -0.35115980 Largest eigenvalues: [1] 97997905 96678050 89959320 86772646 84430445 83714198 82997980 80678323 [9] 80142563 77525440 Smallest eigenvalues: [1] 0.4681510 0.4376518 0.3697904 0.3582608 0.2599015 0.2271657 [7] 0.2088376 0.1370148 0.0591722 -0.1053801 Largest eigenvalues: [1] 98967244 97296109 91160059 86691282 85550954 84333765 83896686 81614048 [9] 80714976 78781936 Smallest eigenvalues: [1] 0.32957192 0.29182676 0.27535905 0.19788924 0.16317191 0.09712017 [7] 0.03730400 -0.27289352 -0.31904753 -0.43021397 Largest eigenvalues: [1] 98607638 95288019 88621986 85227057 85026377 82546346 82434277 79991302 [9] 79106433 76986539
Warning message in eigchk(Cmat): "Near singularity in coefficient matrix."
Log10 Eigenvalues range from -4.01547907717633 to 8.00597875797177 Smallest eigenvalues: [1] 0.259196756 0.249313642 0.245617617 0.156883606 0.150873072 [6] 0.145698999 0.142372167 0.048984983 -0.001109882 -0.368079432 Largest eigenvalues: [1] 98428021 97154830 90642423 86405619 85353201 83761097 83270055 81105276 [9] 80385156 77886461 Smallest eigenvalues: [1] 0.218090767 0.121425792 0.114296346 0.045727397 0.041379965 [6] -0.003286548 -0.028108202 -0.187746522 -0.562315609 -0.592506110 Largest eigenvalues: [1] 99596110 96981560 90879063 86128246 85879332 83918849 83408812 81133967 [9] 80392608 78211117 Smallest eigenvalues: [1] 0.340409402 0.329469676 0.281608910 0.185865752 0.171685812 [6] 0.051564640 -0.007178453 -0.055688562 -0.056088263 -0.553729613 Largest eigenvalues: [1] 98191868 97711970 90821438 87257403 85301549 84000131 83799543 81620805 [9] 79801215 77950779 Smallest eigenvalues: [1] 0.41901044 0.31445856 0.22145064 0.19501874 0.18265206 0.12606786 [7] 0.08121955 0.04241358 -0.08525668 -0.47532918 Largest eigenvalues: [1] 101452127 96229412 90025195 86563982 85949159 83206074 82698738 [8] 80698715 79814370 77690384 Smallest eigenvalues: [1] 0.36589845 0.31460653 0.30165254 0.26968992 0.18332818 0.18253122 [7] 0.16222568 -0.07051108 -0.10201134 -0.56752033 Largest eigenvalues: [1] 100345586 95951680 89654108 85661932 85616600 83112509 82923643 [8] 80971772 79476273 77533271 Smallest eigenvalues: [1] 0.30367654 0.25207404 0.23254472 0.20109111 0.14811054 0.12419306 [7] 0.11494188 -0.01170954 -0.27181657 -0.41077600 Largest eigenvalues: [1] 99749597 96537618 90289641 86278266 85663294 84271923 82436051 81188901 [9] 79917477 78304015 Smallest eigenvalues: [1] 0.441025453 0.439462083 0.372571162 0.356677027 0.313013594 [6] 0.238547668 0.224046403 0.114471136 -0.009674968 -0.216150694 Largest eigenvalues: [1] 99423634 97126305 90111197 87378814 85234403 84026160 83441953 81183508 [9] 80435248 78147033 Smallest eigenvalues: [1] 0.435486334 0.417198161 0.416554776 0.281058376 0.250670057 [6] 0.221277008 -0.006368029 -0.020031754 -0.057307928 -0.098471958 Largest eigenvalues: [1] 101151130 96454685 90734231 86074600 85779590 83379060 83183615 [8] 80978031 80294962 78070886 Smallest eigenvalues: [1] 0.3868220 0.3789579 0.3492270 0.3008169 0.2778945 0.1397108 [7] 0.1292415 0.1276767 -0.1417223 -0.1463796 Largest eigenvalues: [1] 98537937 96762464 90757702 86031794 84791344 83451552 82980380 80702426 [9] 80039246 77768034 Smallest eigenvalues: [1] 0.29351778 0.27087740 0.26718787 0.26605354 0.22760828 0.20951933 [7] 0.19888023 -0.05679158 -0.30420524 -0.44577242 Largest eigenvalues: [1] 100159453 96992049 90676823 86239631 85490874 83871612 83486783 [8] 81140006 80405209 77949290 Smallest eigenvalues: [1] 0.31210121 0.29676468 0.25489653 0.23534481 0.17556597 0.16176963 [7] 0.03296527 0.01299031 -0.18791658 -0.35607091 Largest eigenvalues: [1] 99397434 97293203 90616232 86721129 85171874 83821442 83595709 81165285 [9] 80439179 77802061 Smallest eigenvalues: [1] 0.44224582 0.42063060 0.34986328 0.28829221 0.26456858 0.17754717 [7] 0.06869811 -0.02368882 -0.05822343 -0.18000631 Largest eigenvalues: [1] 100176069 96083635 90083969 86154758 85814355 84081751 83145709 [8] 81473333 79964269 78332991 Smallest eigenvalues: [1] 0.39516742 0.39346730 0.32435771 0.32200876 0.25218728 0.21258067 [7] 0.20579027 0.17422558 0.14710203 -0.07944606 Largest eigenvalues: [1] 100089600 96755063 90572390 86365563 85497599 84368517 82957708 [8] 81793504 80565545 78988086 Smallest eigenvalues: [1] 0.40028543 0.38825149 0.38467744 0.33513049 0.23741795 0.16506795 [7] 0.15223137 0.06039350 -0.08664239 -0.63461905 Largest eigenvalues: [1] 100974040 95560400 90147006 85332818 85197571 83739983 82137404 [8] 81294257 79754662 78118248 Smallest eigenvalues: [1] 0.35454367 0.33639411 0.32766083 0.21714687 0.21073165 0.16153351 [7] 0.12030570 -0.02118556 -0.32053854 -0.70574110 Largest eigenvalues: [1] 102797605 96038489 90289079 86135019 85528318 83840614 82470316 [8] 81482985 79839376 78382400 Smallest eigenvalues: [1] 0.42505074 0.41775639 0.38500489 0.34631109 0.30725052 0.28323056 [7] 0.27981238 0.01403913 -0.08137273 -0.19322242 Largest eigenvalues: [1] 101146142 97185577 90824185 86915344 86135074 85141001 83529662 [8] 82569490 80712207 79505298 Smallest eigenvalues: [1] 0.36993710 0.33028816 0.32731964 0.30314400 0.29631073 0.23479809 [7] 0.22525067 0.17854997 -0.02560994 -0.33201960 Largest eigenvalues: [1] 101537599 96759784 90779334 86691465 85695453 83566135 82399410 [8] 80841092 79787019 77824691 Smallest eigenvalues: [1] 0.39317939 0.38106219 0.35141570 0.31858379 0.30698009 0.29446393 [7] 0.18572891 -0.08385814 -0.37576226 -0.81780937 Largest eigenvalues: [1] 101632568 97059712 91065745 86937685 86578448 84346382 83291725 [8] 82065876 80466212 79022467 Smallest eigenvalues: [1] 0.274190097 0.273652479 0.269222208 0.221017930 0.198924658 [6] 0.075026662 0.027345104 -0.007483765 -0.100049567 -0.497888488 Largest eigenvalues: [1] 98584708 97446450 90632336 86973782 84999799 84589347 83649732 81868079 [9] 80368028 78672134 Smallest eigenvalues: [1] 0.3101156 0.2812338 0.2456275 0.1587053 0.1463317 0.1416373 [7] 0.1080058 -0.1902076 -0.2473457 -0.4326882 Largest eigenvalues: [1] 99429831 97094677 90262642 87200701 85896901 84955079 83849676 82164157 [9] 80679518 79107106 Smallest eigenvalues: [1] 0.3768285 0.3357103 0.3141694 0.2925934 0.2366395 0.2290650 [7] 0.2248386 -0.1920549 -0.6268244 -1.1577079 Largest eigenvalues: [1] 100698618 98277135 91954786 87682044 86362721 84821749 84195523 [8] 82018964 81399394 78944049 Smallest eigenvalues: [1] 0.27115226 0.26225686 0.23556787 0.21404877 0.21369164 0.19097448 [7] 0.09825333 -0.17105229 -0.19535816 -0.31331510 Largest eigenvalues: [1] 98839831 96840745 90272247 86289392 85331896 83712982 83259072 81305740 [9] 79824444 77964753 Smallest eigenvalues: [1] 0.43994736 0.41874154 0.41299847 0.37380041 0.36380660 0.27293547 [7] 0.21963153 0.03603612 0.01513694 -0.14864908 Largest eigenvalues: [1] 100534921 95727116 89930214 85946800 85176071 82924403 82643602 [8] 80475202 79670474 77212527 Smallest eigenvalues: [1] 0.37339401 0.31331646 0.30025620 0.26233953 0.19805133 0.19268086 [7] 0.16568904 0.16402035 0.15988226 -0.02653874 Largest eigenvalues: [1] 99876619 96975475 90615390 86793615 85588170 85155821 82839841 81981010 [9] 80144016 78950471 Smallest eigenvalues: [1] 0.45169361 0.42740031 0.40597492 0.30450009 0.25938436 0.25381492 [7] 0.19369093 0.09081850 -0.01894558 -0.20198622 Largest eigenvalues: [1] 99522168 97166023 91031916 86468292 85417465 83634230 83324316 81009755 [9] 80189476 78008132 Smallest eigenvalues: [1] 0.39817549 0.39519547 0.39221453 0.38811775 0.36246929 0.32616827 [7] 0.25142713 -0.02559785 -0.06004750 -0.23770886 Largest eigenvalues: [1] 99744542 95693085 89581587 85256937 84939759 83143348 82386383 80688494 [9] 79278589 77590351 Smallest eigenvalues: [1] 0.359905443 0.325037405 0.291494018 0.281458375 0.217112446 [6] 0.171013565 0.128861815 0.002151916 -0.337760144 -0.844361298 Largest eigenvalues: [1] 100414942 96298376 90398512 86556588 85386919 83363472 82773181 [8] 80511355 80129484 77506910 Smallest eigenvalues: [1] 0.42442600 0.41862708 0.39623058 0.30843689 0.29572071 0.28974822 [7] 0.26471727 0.21085550 -0.06701425 -0.11128117 Largest eigenvalues: [1] 99411075 97052472 90548873 86640969 85210319 84162671 83359419 81251740 [9] 80423633 78252416 Smallest eigenvalues: [1] 0.37204263 0.31101989 0.30180413 0.29831277 0.27741850 0.22178133 [7] 0.19367054 0.05446480 0.02483204 -0.15069950 Largest eigenvalues: [1] 99681516 96245110 89766699 85887664 85290315 83825828 83287701 81642721 [9] 79680228 78333747 Smallest eigenvalues: [1] 0.20700142 0.20185063 0.16721312 0.13012804 0.12607157 0.07549707 [7] 0.06044686 -0.03663962 -0.45028358 -0.46509576 Largest eigenvalues: [1] 99224611 98412673 91950906 88898837 85056550 84291883 84032718 81732058 [9] 81246291 78230725 Smallest eigenvalues: [1] 0.41415410 0.41070569 0.38841230 0.35190471 0.34318967 0.33497720 [7] 0.31396779 0.13813861 0.06721334 -0.40984924 Largest eigenvalues: [1] 102480511 96341023 90656572 86504746 85769980 84498323 82468282 [8] 81431207 80231301 78591154 Smallest eigenvalues: [1] 0.19026154 0.18460442 0.16440288 0.08446663 0.07973830 0.04368909 [7] -0.20650268 -0.50374943 -0.97668665 -1.34700643 Largest eigenvalues: [1] 99419544 96974443 90713130 86659997 86041423 84914576 83379350 82146695 [9] 80870567 78976427 Smallest eigenvalues: [1] 0.35283779 0.33383613 0.28385606 0.22260731 0.21650760 0.20013846 [7] 0.11291193 0.08583090 0.03724823 -0.17760326 Largest eigenvalues: [1] 100467844 96447283 90985143 85734951 85578596 83458516 82948051 [8] 80929081 80098863 78261205 Smallest eigenvalues: [1] 0.236674925 0.196333432 0.161101419 0.154485210 0.148593147 [6] 0.001363579 -0.054575175 -0.218659529 -0.239224331 -0.319684180 Largest eigenvalues: [1] 98654472 96511516 90432937 86989104 83578022 83519580 83344136 81134569 [9] 80482244 77798489 Smallest eigenvalues: [1] 0.27084644 0.26036264 0.25183650 0.18144729 0.17232211 0.06987502 [7] -0.05134286 -0.14784944 -0.31974606 -0.88826172 Largest eigenvalues: [1] 100830801 96525537 90347329 86367571 86343278 83334634 83048460 [8] 80617674 79981559 77431122 Smallest eigenvalues: [1] 0.26597564 0.25545233 0.25422201 0.20097502 0.19228524 0.06237084 [7] 0.02574948 -0.04988070 -0.16662011 -0.30599645 Largest eigenvalues: [1] 100387250 97974410 92176227 86913227 86051673 84896058 84166721 [8] 82300726 81108437 79282069 Smallest eigenvalues: [1] 0.12090349 0.12038161 0.05659220 0.04976744 0.04688604 -0.06617030 [7] -0.08217257 -0.08786815 -0.36310615 -0.46025389 Largest eigenvalues: [1] 98481114 97609636 91229827 87477480 84689035 84265687 83322298 80827046 [9] 80386709 77432665 Smallest eigenvalues: [1] 0.38647404 0.37604123 0.35281657 0.33201684 0.26623796 0.25973318 [7] 0.22703667 0.11396106 0.05159202 -0.47088056 Largest eigenvalues: [1] 99501508 96328063 90155692 86246068 85579232 83976769 82560282 81227234 [9] 79607062 78104189 Smallest eigenvalues: [1] 0.29119720 0.26434436 0.25256430 0.22992220 0.22007386 -0.01779067 [7] -0.10912288 -0.17256624 -0.94253995 -1.05241811 Largest eigenvalues: [1] 100415818 96706330 91068024 86237538 85585364 83614060 83399271 [8] 81319682 80282550 78011859 Smallest eigenvalues: [1] 0.423685212 0.358641430 0.343763630 0.319606363 0.312285656 [6] 0.296451951 0.207879709 0.200301236 0.055839325 -0.003057454 Largest eigenvalues: [1] 100288672 97451207 90624361 86487833 86480907 84075663 82663891 [8] 81065809 79917246 78404547 Smallest eigenvalues: [1] 0.48887791 0.47736292 0.47717636 0.40620722 0.38931696 0.30925282 [7] 0.30522812 0.26944861 0.22118918 -0.05669037 Largest eigenvalues: [1] 99604403 96612206 89782802 86549668 85355365 83377167 82826510 80954125 [9] 79594004 77735367 Smallest eigenvalues: [1] 0.31091702 0.20454303 0.19548475 0.16798131 0.14324054 0.13499058 [7] 0.11177758 0.06977989 0.03012750 -1.05817888 Largest eigenvalues: [1] 98664826 95220723 89134537 84799410 84293536 82256106 81908737 79854974 [9] 78989336 76987559 Smallest eigenvalues: [1] 0.47139123 0.44564922 0.34291217 0.31928703 0.26539900 0.25404080 [7] 0.19000088 -0.06733429 -0.08730505 -0.08809411 Largest eigenvalues: [1] 101154751 96193456 90300361 85892165 84743259 83525548 82228703 [8] 80938436 79551917 77625983 Smallest eigenvalues: [1] 0.4165684 0.3753378 0.3727181 0.3675855 0.3445250 0.3163810 [7] 0.2568659 0.1335433 -0.1439579 -0.1823380 Largest eigenvalues: [1] 100459529 97326496 90649900 86870869 86290559 84135404 83321036 [8] 81284806 80583012 78344475 Smallest eigenvalues: [1] 0.3751088 0.3082582 0.2846152 0.2792904 0.2686102 0.2338961 [7] 0.1976973 0.1067882 -0.1758633 -0.2869967 Largest eigenvalues: [1] 100841028 96342942 90384275 86756271 86021714 84386337 82714464 [8] 81519286 79566105 78210183 Smallest eigenvalues: [1] 0.2829990 0.2522599 0.2184583 0.1879066 0.1744687 0.1448572 [7] -0.0211150 -0.2006961 -0.6272395 -0.9162553 Largest eigenvalues: [1] 100977867 95839336 89392211 85839543 85769670 84015581 81990927 [8] 81001702 79528786 77551917 Smallest eigenvalues: [1] 0.475675549 0.467663150 0.456874355 0.370401681 0.235164824 [6] 0.230000107 0.219340425 0.179321869 -0.002527997 -0.085619389 Largest eigenvalues: [1] 99617461 96208817 90199621 86034682 84857763 83693803 82693278 81082954 [9] 79805478 78084052 Smallest eigenvalues: [1] 0.39890223 0.37849095 0.33083518 0.28708106 0.27494527 0.21151717 [7] 0.21115159 0.04594424 -0.05599630 -0.18966230 Largest eigenvalues: [1] 100807540 96351997 89994850 86798510 84867925 83644332 82571762 [8] 80854733 79935247 78008363 Smallest eigenvalues: [1] 0.5398797 0.5119049 0.4910498 0.4553929 0.4285348 0.2442247 [7] 0.2236218 0.2174147 0.1126432 -0.3077161 Largest eigenvalues: [1] 101200087 95790897 90034271 85986469 85847795 83187038 82401688 [8] 80625825 79780671 77577992 Smallest eigenvalues: [1] 0.362285239 0.256392152 0.255136133 0.245801268 0.207630656 [6] 0.195891292 0.181043293 0.138143577 -0.008728413 -0.117895179 Largest eigenvalues: [1] 98470545 96261078 89847389 85761141 83907744 83296823 82809204 80816730 [9] 79469960 77323357 Smallest eigenvalues: [1] 0.34336671 0.28823191 0.28575239 0.19940711 0.17702827 0.10689894 [7] 0.04083368 -0.02516718 -0.33429302 -0.37126126 Largest eigenvalues: [1] 100816047 97275356 90641160 86584665 86227590 83461191 83278439 [8] 80850998 80070177 77714746 Smallest eigenvalues: [1] 0.41378131 0.36194406 0.35018541 0.28551934 0.23192564 0.22591458 [7] 0.11763455 0.09582884 0.00310396 -0.01600872 Largest eigenvalues: [1] 98708699 95775077 89480775 85942675 84075112 83085320 82173690 80247674 [9] 79422784 77203818 Smallest eigenvalues: [1] 0.27804713 0.26595776 0.19451082 0.14815892 0.05245555 -0.02131120 [7] -0.25594283 -0.29253821 -0.67270772 -1.02913831 Largest eigenvalues: [1] 101592160 97387017 91371384 87529858 86632848 85122233 84170164 [8] 82426578 80882461 79414976 Smallest eigenvalues: [1] 0.42846211 0.42494961 0.34954212 0.34437638 0.32930869 0.26364152 [7] 0.17359267 0.03940581 -0.19278295 -0.22221333 Largest eigenvalues: [1] 99367496 96556598 90188138 86356102 84729359 83219631 82956413 80639491 [9] 80087819 77638602 Smallest eigenvalues: [1] 0.38347536 0.35627308 0.29812688 0.27801859 0.27726729 0.23347794 [7] 0.14519985 0.11876596 -0.05414279 -0.37327979 Largest eigenvalues: [1] 98662275 95949085 89943937 85899151 83978626 83047907 82738688 80351334 [9] 79685022 76946097 Smallest eigenvalues: [1] 0.36760940 0.35120392 0.29705876 0.26535126 0.26328126 0.21654292 [7] 0.10906304 0.08295381 0.06830809 -0.40073066 Largest eigenvalues: [1] 100180406 96550872 90443392 86362852 85413691 83688184 82578241 [8] 80817413 79731402 77872326 Smallest eigenvalues: [1] 0.38170315 0.37559237 0.36337744 0.32469500 0.29244703 0.24883401 [7] 0.21256052 0.05151235 -0.03317623 -0.59633988 Largest eigenvalues: [1] 98931766 95469050 88882223 85298399 84134462 83206474 82250343 80501442 [9] 79144870 77529246 Smallest eigenvalues: [1] 0.38711372 0.37310976 0.36558909 0.33357093 0.26801582 0.20142193 [7] 0.16883399 0.14218216 -0.03222853 -0.13851576 Largest eigenvalues: [1] 99850233 96314294 90129294 86497378 84695458 84464230 82792624 81811295 [9] 80161330 78718575 Smallest eigenvalues: [1] 0.36374899 0.34638654 0.33119650 0.32025008 0.28654127 0.22596740 [7] 0.16369697 0.04255003 0.04026850 -0.25951160 Largest eigenvalues: [1] 101080853 97264752 91372453 86560250 86456136 84456539 83286847 [8] 81890568 80527971 78804341 Smallest eigenvalues: [1] 0.40008244 0.38841572 0.37563787 0.34217453 0.23345082 0.21731559 [7] 0.20292146 0.18104199 0.04963511 -0.10371434 Largest eigenvalues: [1] 99949754 96065104 89948613 85835089 85632412 84052498 82515558 81440915 [9] 79544129 78206953 Smallest eigenvalues: [1] 0.39189412 0.38527035 0.34313987 0.23559510 0.21788875 0.14420221 [7] 0.13312286 -0.02473703 -0.18785820 -0.93056149 Largest eigenvalues: [1] 101790662 96728218 90819899 87261941 86637686 83852840 83254602 [8] 81599388 80311863 78417057 Smallest eigenvalues: [1] 0.22945440 0.22142444 0.21661571 0.16272737 0.10505681 0.04489440 [7] -0.02834395 -0.11923691 -0.17255477 -0.62328909 Largest eigenvalues: [1] 100371869 97800458 91808555 87087175 85993068 84630821 83914020 [8] 82150836 80805313 78848494 Smallest eigenvalues: [1] 0.43512981 0.40665327 0.39082725 0.36193407 0.35078444 0.32496774 [7] 0.15677982 0.14423356 0.01115005 -0.08789770 Largest eigenvalues: [1] 98701410 96935267 90284678 86701902 84186580 82993401 82806822 80113616 [9] 79753318 76824208 Smallest eigenvalues: [1] 0.26578445 0.25326925 0.23449873 0.19144536 0.15726074 0.09172629 [7] 0.08388444 0.02972164 -0.05190195 -0.26329349 Largest eigenvalues: [1] 99349327 97548308 90339028 87245524 85546253 84704440 83350332 81904533 [9] 80563672 79247307 Smallest eigenvalues: [1] 0.3291675 0.3003846 0.2786729 0.2738109 0.2270862 0.2182747 [7] 0.1610270 0.1142171 -0.8554455 -1.0663738 Largest eigenvalues: [1] 99969800 97443247 91385442 86977193 86457271 85121186 83831034 82599073 [9] 80601561 79283089 Smallest eigenvalues: [1] 0.23199575 0.18891530 0.15278536 0.07700010 0.06983587 0.01985868 [7] -0.07025673 -0.15438599 -0.17489595 -0.27130823 Largest eigenvalues: [1] 98781228 95791103 88722173 86296463 84588981 82609053 82165344 79994644 [9] 79162039 76743440 Smallest eigenvalues: [1] 0.21003141 0.18659366 0.17602103 0.16742998 0.10466265 0.09722515 [7] 0.08369750 -0.07968870 -0.12272959 -0.59606422 Largest eigenvalues: [1] 101553756 97654027 91221148 87325615 85964083 84750796 82765272 [8] 81837507 80152298 78869539 Smallest eigenvalues: [1] 0.39666680 0.37590317 0.28062674 0.26315180 0.26131842 0.25456757 [7] 0.21612607 0.21070172 0.09646027 -0.22958180 Largest eigenvalues: [1] 100726104 97266231 91184593 86351371 86295989 84103027 82942359 [8] 81510741 80175890 78702522 Smallest eigenvalues: [1] 0.31633471 0.25496171 0.24492725 0.21529846 0.21337277 0.16928994 [7] 0.13148027 0.11199629 -0.01804806 -0.62813112 Largest eigenvalues: [1] 99136049 97697681 90943238 87284800 85083236 84497460 83812058 81765659 [9] 80812411 78596535 Smallest eigenvalues: [1] 0.4161065 0.3966191 0.3665883 0.3600131 0.3499192 0.3053255 [7] 0.3043102 0.2941767 0.2515397 -0.3789164 Largest eigenvalues: [1] 100225901 95869246 90078775 85976774 85191818 82808699 82631040 [8] 80208728 79722232 77482020 Smallest eigenvalues: [1] 0.29922866 0.29013662 0.28053669 0.27181468 0.22721597 0.19815085 [7] 0.17241151 -0.01949369 -0.03403402 -0.21495175 Largest eigenvalues: [1] 97967019 96156356 90067926 85552537 83862494 82888748 82723462 80291827 [9] 79835304 77292909 Smallest eigenvalues: [1] 0.3216793 0.3192788 0.3079577 0.2921470 0.2861906 0.2628851 [7] 0.2381517 0.2088655 -0.2276861 -0.4686292 Largest eigenvalues: [1] 101213840 96885018 90111947 86731120 85309532 84599300 83318794 [8] 81808539 80349690 78703592 Smallest eigenvalues: [1] 0.3214139 0.3023930 0.2834594 0.2475218 0.2466521 0.2261063 [7] 0.1787387 0.1585157 0.1222383 -0.4262098 Largest eigenvalues: [1] 98712233 96508625 90052198 86634799 84837275 82949584 82842958 80425813 [9] 79494438 77104164 Smallest eigenvalues: [1] 0.46254130 0.32133495 0.31749391 0.30695002 0.29268884 0.17404896 [7] 0.14812832 0.06587111 0.03210534 -0.18469517 Largest eigenvalues: [1] 99331776 97827517 91298883 87693021 84989739 84289132 83429365 81092415 [9] 80644269 77499566 Smallest eigenvalues: [1] 0.412889258 0.347453092 0.340124119 0.300958369 0.275975566 [6] 0.220822725 -0.007434993 -0.022930492 -0.104674844 -0.307833345 Largest eigenvalues: [1] 99985361 96023806 90046714 86387080 85146789 83105020 82882379 80671102 [9] 79934272 77514683 Smallest eigenvalues: [1] 0.375020467 0.358525063 0.341763082 0.306006194 0.283169903 [6] 0.231242161 0.198312888 0.007256288 -0.003244579 -0.243174567 Largest eigenvalues: [1] 100021546 96563865 90699336 85919483 85901413 84166078 83033402 [8] 81395802 80027518 78306189 Smallest eigenvalues: [1] 0.36530870 0.33538903 0.32586180 0.31922281 0.21224283 0.21145359 [7] 0.18008291 0.11365012 -0.09954352 -0.15536536 Largest eigenvalues: [1] 98316566 96213754 89640733 85782453 84929365 83379526 83229353 80727682 [9] 79676267 77648032 Smallest eigenvalues: [1] 0.4582382 0.4200222 0.4082777 0.3439409 0.2634010 0.2533368 [7] 0.2293562 0.1810232 -0.1092063 -0.2340864 Largest eigenvalues: [1] 98306494 95589119 89318153 85821222 83663165 82947160 82602594 80421398 [9] 79366316 76901517 Smallest eigenvalues: [1] 0.35144551 0.33198170 0.33065923 0.31326850 0.28276695 0.24514249 [7] -0.03281605 -0.19137565 -0.61688945 -0.77482055 Largest eigenvalues: [1] 99480227 97025066 90620121 86676811 85963513 83899927 83289270 80862336 [9] 80393081 77619514 Smallest eigenvalues: [1] 0.4154858 0.3815868 0.3220493 0.3179277 0.3162152 0.2845961 [7] 0.2263959 0.2205937 0.1136755 -0.1710908 Largest eigenvalues: [1] 99186859 95532602 89395318 85300467 85247838 82941904 82012811 80628258 [9] 78706338 77203631 Smallest eigenvalues: [1] 0.41615203 0.37707605 0.36047194 0.17221318 0.13724036 0.13582418 [7] 0.13023637 0.05293728 -0.20113903 -0.34785317 Largest eigenvalues: [1] 102162469 95735566 89517891 87269639 85280794 83235676 82276005 [8] 80936718 79204643 77679853 Smallest eigenvalues: [1] 0.3994863 0.3992282 0.3642533 0.3290305 0.2579752 0.2373379 [7] 0.1683926 -0.0420832 -0.1039533 -0.2572223 Largest eigenvalues: [1] 99896820 96181368 89932593 86502697 84685950 83506049 82521069 80730113 [9] 79562650 77390813 Smallest eigenvalues: [1] 0.41035983 0.40646410 0.40512550 0.39692791 0.26199456 0.24860087 [7] 0.24139778 0.14702915 0.08478759 -0.07098513 Largest eigenvalues: [1] 99670481 96506224 90148483 86043237 85840803 83214937 82918402 80858999 [9] 79858880 77971787 Smallest eigenvalues: [1] 0.347000202 0.344199181 0.315087619 0.287693909 0.175687813 [6] 0.127912868 0.120181757 0.057190081 -0.009006519 -0.141100665 Largest eigenvalues: [1] 98056011 96404770 90156944 85741641 84533230 83469045 82514584 80344616 [9] 79861539 77319905 Smallest eigenvalues: [1] 0.31306558 0.27892713 0.23333162 0.20461735 0.18944369 0.10929574 [7] 0.09386942 -0.13956659 -0.36082364 -1.11787213 Largest eigenvalues: [1] 101336268 97049279 90810913 86534350 86338783 84178218 82927568 [8] 81514715 79989224 78269626 Smallest eigenvalues: [1] 0.29307189 0.28111630 0.25421351 0.18754356 0.16336131 0.11358028 [7] 0.03905137 -0.19453378 -0.31177664 -0.52945666 Largest eigenvalues: [1] 100129472 96260617 90483092 86668798 85442631 84209223 82697721 [8] 81488669 79925814 78107352 Smallest eigenvalues: [1] 0.12702860 0.11906627 0.08365494 0.08265123 0.07673187 0.03975713 [7] -0.07808367 -0.14527752 -0.24044438 -0.63567854 Largest eigenvalues: [1] 97405243 96542842 89786693 85994773 85030976 83597721 82781746 81193204 [9] 79635487 77884657 Smallest eigenvalues: [1] 0.3464688 0.3064337 0.3051792 0.3027974 0.2934510 0.1808576 [7] -0.1113322 -0.1985794 -0.2103916 -0.5316172 Largest eigenvalues: [1] 100551761 96781814 91111007 87277807 84836640 83959345 83532685 [8] 81139180 80360906 77501914 Smallest eigenvalues: [1] 0.40292058 0.38526621 0.34944115 0.31246299 0.25810781 0.22784548 [7] 0.01719268 -0.10578526 -0.13236859 -0.59616293 Largest eigenvalues: [1] 99766137 96347587 89281445 86198011 85278772 83212801 82098563 80289897 [9] 79291361 77373958 Smallest eigenvalues: [1] 0.4633765 0.4075929 0.3790127 0.3535581 0.3509942 0.3017647 [7] 0.2565188 0.1332860 -0.0841150 -0.5273491 Largest eigenvalues: [1] 99816949 97961584 91446978 87484876 86076947 84188029 83727238 81372019 [9] 80799387 78436985 Smallest eigenvalues: [1] 0.3430210 0.3274314 0.3257035 0.2857321 0.2264250 0.1830879 [7] 0.1517858 0.1189842 -0.1129485 -0.9711132 Largest eigenvalues: [1] 99093127 95963978 89295297 86406245 84452192 82898741 82685217 80324336 [9] 79401800 77338301 Smallest eigenvalues: [1] 0.39527790 0.39127607 0.35387400 0.32317101 0.30054978 0.27751045 [7] 0.09715711 -0.05053430 -0.26776845 -0.52062774 Largest eigenvalues: [1] 100985826 96692954 90375031 86720491 85948056 84166287 82543037 [8] 81420569 79537640 78079147 Smallest eigenvalues: [1] 0.38343967 0.38081924 0.30055663 0.27027364 0.24150702 0.23782706 [7] 0.21326696 0.20748606 0.08765733 -0.25564405 Largest eigenvalues: [1] 100057447 95800009 89786180 85461927 85227780 83446327 81931125 [8] 80734533 78966587 77246303 Smallest eigenvalues: [1] 0.29652574 0.27203556 0.26606878 0.23413065 0.19355386 0.16757500 [7] 0.01158197 -0.05636534 -0.22215475 -0.38362701 Largest eigenvalues: [1] 100044039 96356941 90534604 85767011 84999943 83245877 82593581 [8] 80656660 79778857 78028632 Smallest eigenvalues: [1] 0.23204359 0.22067409 0.18011525 0.16345270 0.08028338 0.03076562 [7] -0.03719673 -0.12609204 -0.57744191 -1.81682630 Largest eigenvalues: [1] 102582074 95820926 90097921 87423487 85379266 84413103 82028258 [8] 81566760 79575945 78671542 Smallest eigenvalues: [1] 0.45166991 0.44745100 0.43423239 0.40267643 0.38558276 0.24018359 [7] 0.22463824 -0.01382489 -0.29946988 -0.43337923 Largest eigenvalues: [1] 100865946 96222523 90016155 86248985 86103043 84243666 83022249 [8] 81614466 79919868 78312241 Smallest eigenvalues: [1] 0.32315683 0.31532212 0.27120714 0.26565123 0.26446407 0.21746149 [7] 0.04901346 -0.16134939 -0.36713728 -0.36755138 Largest eigenvalues: [1] 99122458 97898161 90597533 87795502 85159682 84444572 84005362 81662863 [9] 80808099 78553285 Smallest eigenvalues: [1] 0.37597041 0.36286674 0.30386485 0.29827873 0.17702349 0.11301322 [7] 0.08094356 -0.03107875 -0.14068952 -0.49460175 Largest eigenvalues: [1] 98952864 95477958 89887667 86038188 84013230 82761700 82233153 80023278 [9] 79582295 76982833 Smallest eigenvalues: [1] 0.12597992 0.04513590 -0.04890039 -0.07213219 -0.07627277 -0.21394939 [7] -0.39549316 -0.50071926 -0.56298682 -0.57471745 Largest eigenvalues: [1] 98654871 97201999 91283342 86479210 85523715 83925555 83567606 81273903 [9] 80350222 78201328 Smallest eigenvalues: [1] 0.276598608 0.268721294 0.260447405 0.254317941 0.241952773 [6] 0.190143882 0.042452456 0.006071576 -0.157321816 -0.251843010 Largest eigenvalues: [1] 100982306 97198985 90669919 86973672 85562286 84500116 83090845 [8] 81501087 80542988 78154396 Smallest eigenvalues: [1] 0.33265075 0.32885275 0.30730838 0.29423247 0.22585955 0.19838492 [7] 0.16117098 0.04974100 -0.05149819 -0.22451260 Largest eigenvalues: [1] 97773615 96777235 90475121 86783846 83539049 83400043 83184414 81056386 [9] 80036050 77505075 Smallest eigenvalues: [1] 0.312718937 0.309681053 0.274937486 0.253273059 0.231690334 [6] 0.099959658 0.025005146 0.008546921 -0.579522682 -0.638603196 Largest eigenvalues: [1] 100743080 96248332 90677644 86420883 85693059 84088221 82836185 [8] 81819577 79915828 78735807 Smallest eigenvalues: [1] 0.33645592 0.32279225 0.31011952 0.30446195 0.24947690 0.24943856 [7] 0.11788043 0.11695098 -0.07846772 -0.21012461 Largest eigenvalues: [1] 100684971 96506237 90482217 86683652 85273124 84073020 83134120 [8] 81621384 80353984 78557262 Smallest eigenvalues: [1] 0.38911709 0.37430428 0.37238149 0.27852723 0.23606819 0.19665507 [7] 0.14232562 0.09086630 0.08897772 -0.33328594 Largest eigenvalues: [1] 99916481 95907757 89808516 85649656 85422060 84125523 82258463 81293861 [9] 79413200 78152823 Smallest eigenvalues: [1] 0.40634823 0.39723192 0.34518860 0.26826902 0.25036844 0.22548455 [7] 0.20119042 0.09338915 -0.17348603 -0.21030668 Largest eigenvalues: [1] 100401077 95287422 88853380 85512380 85504708 82619420 81710725 [8] 80272625 78783452 77129602 Smallest eigenvalues: [1] 0.48430968 0.47001574 0.44787245 0.43601338 0.32911416 0.28596273 [7] 0.26200361 0.22016720 -0.06379419 -0.25833025 Largest eigenvalues: [1] 100523266 97015137 90532238 86498341 85973553 84258108 82872745 [8] 81394134 80432957 78564814 Smallest eigenvalues: [1] 0.38837923 0.37896130 0.36430759 0.35988917 0.34127659 0.19751969 [7] 0.12653637 0.08903336 -0.01695984 -0.47896245 Largest eigenvalues: [1] 100988971 96588351 90552384 86392669 86124013 84129894 82169323 [8] 81320872 79299660 78116178 Smallest eigenvalues: [1] 0.49024449 0.46949091 0.45607350 0.35711434 0.28386645 0.27041847 [7] 0.24752663 0.18342243 -0.05472445 -0.06261830 Largest eigenvalues: [1] 100779844 95627929 89129689 86094974 85420246 83303611 81896062 [8] 80823683 79232247 77819223 Smallest eigenvalues: [1] 0.42321529 0.41695157 0.39216309 0.37831099 0.36799435 0.30300748 [7] 0.25156678 0.24275763 0.07992087 -0.40432720 Largest eigenvalues: [1] 99644241 95286206 89316966 85658165 84302091 83003838 81704517 80506349 [9] 79056627 77356619 Smallest eigenvalues: [1] 0.34817834 0.31605088 0.30693275 0.27688276 0.18149851 0.15739872 [7] 0.02158334 -0.02329128 -0.17513328 -0.23148561 Largest eigenvalues: [1] 101527880 96250593 90049642 86264788 85919822 84457432 82359297 [8] 81683126 79658802 78554537 Smallest eigenvalues: [1] 0.18485307 0.16092170 0.15001711 0.07913802 0.06921725 0.03837940 [7] 0.02570691 -0.02465212 -0.20237358 -0.35648977 Largest eigenvalues: [1] 100966335 97179506 91315744 86418678 85564814 84540465 83211789 [8] 82285852 80862447 79578609 Smallest eigenvalues: [1] 0.42165929 0.40243210 0.40210420 0.34802547 0.32175317 0.25084766 [7] 0.21593482 0.17089007 0.11645095 -0.09180467 Largest eigenvalues: [1] 97748372 96499858 89552987 86799718 84467937 83176536 83044897 80156333 [9] 79702516 77055607 Smallest eigenvalues: [1] 0.38827180 0.34251530 0.28184131 0.23947784 0.23227511 0.18386221 [7] 0.05640226 0.02499066 -0.21741532 -0.32025736 Largest eigenvalues: [1] 99164812 96240231 89923484 85809514 84395231 82860020 82524677 80336784 [9] 79514470 77410770 Smallest eigenvalues: [1] 0.34302947 0.34182981 0.27248100 0.27091306 0.23122997 0.20878231 [7] 0.04227076 -0.10340108 -0.13087240 -0.39114792 Largest eigenvalues: [1] 100878133 96885799 90612183 86659998 86032280 85771515 82964210 [8] 82593016 80631635 79812794 Smallest eigenvalues: [1] 0.25356761 0.23879392 0.23383386 0.19953623 0.15848870 0.14271905 [7] 0.12571647 0.01224474 -0.15947641 -0.36363778 Largest eigenvalues: [1] 98749497 96377162 90369128 86146041 84176250 83223259 83093620 80831556 [9] 80177213 77625852 Smallest eigenvalues: [1] 0.44456767 0.44060360 0.36394276 0.35768201 0.32643542 0.31010307 [7] 0.23970755 0.12808537 -0.05697475 -0.16550292 Largest eigenvalues: [1] 101129234 97157152 90903101 86757191 85766315 84195084 83058121 [8] 81725134 80187907 78767996 Smallest eigenvalues: [1] 0.26540925 0.23451510 0.20078053 0.18543693 0.16725291 0.11197229 [7] 0.02752947 -0.06868394 -0.50617854 -0.81610439 Largest eigenvalues: [1] 98324543 96604115 89711853 87178362 84150428 83960289 82990706 80756794 [9] 80285305 77445213 Smallest eigenvalues: [1] 0.28568151 0.27754011 0.25707438 0.21941157 0.20828855 -0.00013390 [7] -0.05049161 -0.14676752 -0.27230607 -0.39985837 Largest eigenvalues: [1] 100966031 95013983 89634586 85862208 84378557 83301361 82065638 [8] 81063682 79112131 78252387 Smallest eigenvalues: [1] 0.184691033 0.167621781 0.155796873 0.130384275 0.051403602 [6] 0.049759081 0.009072942 -0.151557707 -0.179620903 -0.209282656 Largest eigenvalues: [1] 99753956 97386549 90544820 86895287 86385577 84584446 83591887 81712832 [9] 80603307 78768247 Smallest eigenvalues: [1] 0.36778600 0.35469351 0.30069769 0.25321614 0.20809725 0.18065364 [7] 0.17235986 0.10710076 -0.03079384 -0.43534888 Largest eigenvalues: [1] 99182524 96402230 90195937 86273320 84383283 83501295 83272060 81306825 [9] 80253629 77975324 Smallest eigenvalues: [1] 0.33399926 0.31968902 0.31505493 0.31260416 0.24586000 0.23678295 [7] 0.13240147 0.07774475 0.06793222 -0.06856036 Largest eigenvalues: [1] 100180468 97528473 91604134 86135933 85974659 84680703 83048059 [8] 82121960 80107418 79139710 Smallest eigenvalues: [1] 0.4757747 0.4553701 0.4355483 0.4095840 0.3916077 0.3192264 [7] 0.2416094 0.2020688 0.1798108 -0.2692753 Largest eigenvalues: [1] 100804652 96065601 89941508 85973485 85945694 83595498 81942275 [8] 80809735 79604926 77815113 Smallest eigenvalues: [1] 0.47734364 0.45145534 0.40431510 0.38796143 0.34586134 0.29092103 [7] 0.19974862 0.19255734 0.17288024 -0.02851935 Largest eigenvalues: [1] 100976341 97085559 91131335 86845517 86186179 84430567 83195337 [8] 81622364 80288516 78512993 Smallest eigenvalues: [1] 0.31632760 0.31370086 0.28511324 0.20507800 0.18430051 -0.00899935 [7] -0.06563834 -0.10539771 -0.13831195 -0.36272954 Largest eigenvalues: [1] 100430831 96092760 90665985 85611370 84632059 83116926 82881536 [8] 80824651 79915380 77723653 Smallest eigenvalues: [1] 0.3862668 0.3653550 0.3439284 0.3406631 0.2856466 0.1922455 [7] 0.1519309 0.1110390 0.1104294 -0.3500123 Largest eigenvalues: [1] 98002826 97171820 90023107 86745494 84755559 83796250 82851972 80975122 [9] 79907200 77969997 Smallest eigenvalues: [1] 0.41514096 0.39727186 0.34381708 0.25630818 0.23747529 0.20419885 [7] 0.10078711 0.04913593 -0.09320301 -0.10057764 Largest eigenvalues: [1] 99371099 95118565 89424908 85202852 84011995 83033972 82573671 80536753 [9] 79391444 77652182 Smallest eigenvalues: [1] 0.34398659 0.32952786 0.27196761 0.23300557 0.23115483 0.15432715 [7] 0.03740143 -0.08096112 -0.11260029 -0.20871787 Largest eigenvalues: [1] 99538440 97528581 91529951 86979673 84783102 84372574 83579216 81327616 [9] 80947081 77999215 Smallest eigenvalues: [1] 0.45518257 0.40756718 0.39072914 0.36554424 0.35428706 0.29156589 [7] 0.22963038 0.15111965 0.05115811 -0.01631632 Largest eigenvalues: [1] 100663844 96382675 90696751 86225390 84957666 83995236 82738361 [8] 81317435 80103751 78040351 Smallest eigenvalues: [1] 0.195197717 0.161341218 0.146352698 0.134936413 0.098163546 [6] 0.041424516 0.007805326 -0.003949245 -0.189198555 -1.181700339 Largest eigenvalues: [1] 98924237 95332461 89430368 85254513 83958235 82985119 81534868 80408470 [9] 78827224 77510514 Smallest eigenvalues: [1] 0.47796652 0.45684969 0.37908885 0.31055869 0.27846235 0.20940000 [7] 0.20330266 0.20070581 0.02639600 -0.02833537 Largest eigenvalues: [1] 100304472 96987869 90575756 87251576 85419424 85179391 82857770 [8] 82308672 80406475 79251323 Smallest eigenvalues: [1] 0.46403123 0.35692262 0.34718261 0.32525475 0.32240378 0.26540520 [7] 0.23531617 0.15888102 -0.07622361 -0.74325361 Largest eigenvalues: [1] 100874296 96869032 90512209 86478389 86361265 83590610 83435132 [8] 81265617 80408758 78116568 Smallest eigenvalues: [1] 0.54342496 0.49489343 0.45629783 0.41508670 0.36114282 0.35119942 [7] 0.27038261 0.24277144 0.20562848 -0.03024015 Largest eigenvalues: [1] 101127527 96957381 90952912 86762119 85889780 83925428 83345599 [8] 81498859 80118835 78466631 Smallest eigenvalues: [1] 0.42728072 0.33455752 0.32416050 0.32056341 0.31809632 0.29698017 [7] 0.26466078 0.13199857 -0.01440903 -0.39626377 Largest eigenvalues: [1] 100781381 97135407 91476641 86545224 85908812 83545136 83318852 [8] 81217749 80464180 78242871 Smallest eigenvalues: [1] 0.41384263 0.39694174 0.32630602 0.31443622 0.27198068 0.26303314 [7] 0.14563044 0.08390344 -0.05887081 -0.32927068 Largest eigenvalues: [1] 99985856 96420730 89496861 86276708 85888583 83463933 82125367 80593602 [9] 79556926 77284291 Smallest eigenvalues: [1] 0.48409846 0.46047950 0.33809180 0.32802802 0.30923408 0.30740876 [7] 0.30633482 0.21646520 0.05395513 -0.26058177 Largest eigenvalues: [1] 102086890 96633745 90799643 87215985 86681506 85125504 82646759 [8] 82115853 80314791 79166057 Smallest eigenvalues: [1] 0.26115641 0.25706897 0.22502930 0.21352187 0.20397583 0.19166852 [7] 0.15771685 -0.03954547 -0.21332860 -0.45011978 Largest eigenvalues: [1] 103103219 96799581 91056879 87855379 86003186 85290215 82589807 [8] 82353851 80264176 79434237 Smallest eigenvalues: [1] 0.35309845 0.35156979 0.32990841 0.31272979 0.23141193 0.17749904 [7] 0.09621083 -0.36626742 -0.53864449 -0.58900444 Largest eigenvalues: [1] 101060562 97105503 90689879 87663794 85832575 84416876 83287501 [8] 81692048 80685160 78628708 Smallest eigenvalues: [1] 0.20550306 0.12757887 0.11987698 0.06587969 0.01296513 -0.03522072 [7] -0.20410615 -0.39973943 -0.55665765 -1.15107614 Largest eigenvalues: [1] 98746734 95848128 89338104 85889286 84553559 83485920 81930213 80373130 [9] 79284084 76920870 Smallest eigenvalues: [1] 0.52594425 0.52459640 0.42908248 0.41049870 0.38887935 0.38005278 [7] 0.30121354 0.22013713 0.04129827 -0.20977980 Largest eigenvalues: [1] 100140965 96502505 89994264 86821378 84988537 83605599 82487290 [8] 81068985 79908957 78266658 Smallest eigenvalues: [1] 0.25983446 0.23987920 0.21500647 0.18577541 0.13195431 0.12474848 [7] 0.01810365 -0.24138122 -0.30334257 -0.61039975 Largest eigenvalues: [1] 102005547 96229923 90290784 86780741 85736703 84329573 82784464 [8] 81924336 79630278 78661342 Smallest eigenvalues: [1] 0.206061583 0.158825275 0.094685515 0.081105260 0.062276448 [6] -0.006946356 -0.022011346 -0.200217184 -0.736750012 -3.023532963 Largest eigenvalues: [1] 99954394 96932845 90266678 86752148 86025662 83543424 83425671 80857339 [9] 80238196 77634283 Smallest eigenvalues: [1] 0.29338960 0.28336088 0.25608377 0.21405189 0.13789354 0.12774976 [7] 0.02917010 -0.05477915 -0.14952020 -0.50239001 Largest eigenvalues: [1] 99283271 97712234 90788034 87033988 85743062 84241021 83867345 81565549 [9] 80480758 78539430 Smallest eigenvalues: [1] 0.41191743 0.38831819 0.37829724 0.37110462 0.36234026 0.24324395 [7] 0.13000044 -0.02806658 -0.25825507 -0.29734829 Largest eigenvalues: [1] 100227988 96605618 90159287 86664578 86016001 83667416 83126864 [8] 80836934 80229073 77553358 Smallest eigenvalues: [1] 0.36683396 0.32329157 0.27255923 0.24039080 0.22197503 0.12106564 [7] 0.07198629 0.06427798 -0.03542347 -0.25320037 Largest eigenvalues: [1] 97437351 96474726 89269088 86407381 84627558 83091606 82622272 80078310 [9] 79606860 76899444 Smallest eigenvalues: [1] 0.41900098 0.41552782 0.39187334 0.37908836 0.31411864 0.29556530 [7] 0.24607098 0.15354364 0.13832788 -0.09514892 Largest eigenvalues: [1] 99262601 96319546 90756712 86038776 83983571 83423710 82997385 81009837 [9] 80113669 78014063 Smallest eigenvalues: [1] 0.13542078 0.10838830 0.06527687 0.05114663 0.01252765 -0.06218801 [7] -0.11624063 -0.18233019 -0.53721818 -1.59057088 Largest eigenvalues: [1] 101744806 96061144 90408327 86327842 85589343 82837228 82520269 [8] 80629715 79519545 77581417 Smallest eigenvalues: [1] 0.26264187 0.25289521 0.23944124 0.14147780 0.07836688 0.04588163 [7] 0.02809017 -0.08795779 -0.22751067 -0.96404681 Largest eigenvalues: [1] 98672707 96043462 89456281 85892452 85052371 83244846 82845759 80602218 [9] 79749573 77295342 Smallest eigenvalues: [1] 0.18224151 0.14056577 0.11811042 0.11541480 0.06551399 -0.01665821 [7] -0.02569742 -0.17271294 -0.42953448 -0.86161600 Largest eigenvalues: [1] 100000715 97335765 91457644 87027396 85387482 83896507 83542443 [8] 81354508 80409750 77989654 Smallest eigenvalues: [1] 0.410941368 0.409940961 0.405765945 0.385677498 0.342102471 [6] 0.313067301 0.312958457 0.075523265 -0.009503385 -0.201398076 Largest eigenvalues: [1] 101150566 97406295 90944200 86609898 86173769 84395456 83151267 [8] 81596691 80215055 78405763 Smallest eigenvalues: [1] 0.35954504 0.28806519 0.28761561 0.28271469 0.25442688 0.25098268 [7] 0.20826564 0.09919214 0.07259341 -0.17158757 Largest eigenvalues: [1] 98632646 96261604 90381823 85830639 84958640 83141248 82971083 80827585 [9] 79754962 77800286 Smallest eigenvalues: [1] 0.315504265 0.274150049 0.268798153 0.209765688 0.209184680 [6] 0.188387185 0.152342979 0.044360849 0.007999525 -0.525304287 Largest eigenvalues: [1] 98106401 96467204 90396168 86345511 84421316 83625563 82728924 81555621 [9] 79754767 78263900 Smallest eigenvalues: [1] 0.37551098 0.35717644 0.35277251 0.32769410 0.29684679 0.27673303 [7] 0.22555497 0.06252272 -0.06303788 -0.07195551 Largest eigenvalues: [1] 100010490 95942987 89527235 86555914 85229991 83526427 82277213 [8] 80863939 79324185 77766156 Smallest eigenvalues: [1] 0.40153764 0.38666062 0.37916862 0.35086708 0.34914564 0.26515184 [7] 0.25919527 0.01648512 -0.04849692 -0.39697202 Largest eigenvalues: [1] 100757118 96270989 90264260 86087865 85795869 83069813 82889792 [8] 80830857 79909826 77967908 Smallest eigenvalues: [1] 0.41332623 0.40486474 0.39324460 0.30204771 0.29149568 0.20254791 [7] 0.18401483 0.17777057 -0.03826471 -0.05574242 Largest eigenvalues: [1] 101410146 96193191 89909644 85880860 85735157 83811789 81995320 [8] 81150716 79327795 78002431 Smallest eigenvalues: [1] 0.31893150 0.31403269 0.23936019 0.22614173 0.14741564 0.13344797 [7] 0.05984539 0.05161561 -0.26951289 -0.38600859 Largest eigenvalues: [1] 98660803 96840884 91246244 85828325 85202653 83691319 83420177 81310383 [9] 80311052 78199052 Smallest eigenvalues: [1] 0.31598378 0.28386395 0.28300100 0.18478046 0.16167060 0.07340897 [7] 0.06000512 -0.02818990 -0.14806082 -0.82313271 Largest eigenvalues: [1] 98773590 96734859 90721688 86895328 84122017 83531472 82822036 80224378 [9] 79975781 76877540 Smallest eigenvalues: [1] 0.45672443 0.45356768 0.39039613 0.34271179 0.25906281 0.23425985 [7] 0.20916326 0.09867012 0.09498200 -0.10650875 Largest eigenvalues: [1] 100265857 96006411 90012619 86101666 85801491 83050926 82870980 [8] 80470182 79739230 77154832 Smallest eigenvalues: [1] 0.4349221 0.3508096 0.3462192 0.3059278 0.2991485 0.2473554 [7] 0.2446368 0.2129678 0.1354859 -0.4905267 Largest eigenvalues: [1] 99702994 96658287 90098762 86479827 85919310 84410845 82890449 81676708 [9] 79925750 78589519 Smallest eigenvalues: [1] 0.4483314 0.4392232 0.4204877 0.3603856 0.3368610 0.2981903 [7] 0.2778506 0.2059360 -0.1309537 -0.3970985 Largest eigenvalues: [1] 101884490 97141146 90672508 86832776 86370776 84071061 83300409 [8] 81545253 80460380 78464208 Smallest eigenvalues: [1] 0.17426344 0.17182520 0.06169208 0.04080552 -0.01846709 -0.03059209 [7] -0.05756674 -0.06531979 -0.24535768 -0.31927827 Largest eigenvalues: [1] 98164402 96834498 90215328 86760997 84854385 83763509 83457659 81138065 [9] 80413185 78323703 Smallest eigenvalues: [1] 0.24773276 0.19715515 0.19417415 0.16131015 0.15673156 0.12630187 [7] 0.11154260 -0.08043828 -0.13345107 -0.21355205 Largest eigenvalues: [1] 98525865 97307835 90281369 87651881 84674919 83889058 83773781 81062503 [9] 80430124 78176983 Smallest eigenvalues: [1] 0.383493163 0.305957818 0.296519640 0.252084573 0.207161299 [6] 0.182602334 0.061461769 0.055282320 0.008604677 -0.393837281 Largest eigenvalues: [1] 100214054 96641137 90655279 86611317 85789325 84284459 82997968 [8] 81904539 80069893 78620632 Smallest eigenvalues: [1] 0.34880471 0.32342149 0.31956390 0.23700840 0.15967854 0.13329146 [7] 0.10890479 -0.05317232 -0.19427275 -0.27206121 Largest eigenvalues: [1] 99188999 96356940 89534720 86159698 85180630 83343807 83027984 80902550 [9] 79612682 77756380 Smallest eigenvalues: [1] 0.155172861 0.072894172 0.070185773 0.042781184 0.007175571 [6] -0.011342685 -0.055372512 -0.237398157 -0.278440018 -0.729851642 Largest eigenvalues: [1] 98579765 97357353 90474112 86556469 86092710 84108259 83883713 81411180 [9] 80326220 78455355 Smallest eigenvalues: [1] 0.35499943 0.30073602 0.29654105 0.28200510 0.28023086 0.21120569 [7] 0.19460628 0.13342011 0.09231254 -0.28238577 Largest eigenvalues: [1] 100071901 97915129 91381873 86890165 86032251 84372367 83601445 [8] 82035776 80798180 79240387 Smallest eigenvalues: [1] 0.31370045 0.28063132 0.25919905 0.23262713 0.18478666 0.15085317 [7] 0.06557096 0.01305432 -0.49264782 -1.30855319 Largest eigenvalues: [1] 98890768 96930549 90867894 86413382 85427615 83619758 83285159 81172121 [9] 80346484 78097818 Smallest eigenvalues: [1] 0.3341142 0.2732187 0.2540869 0.1814860 0.1404521 0.1303099 [7] 0.1123285 -0.2187510 -0.2642946 -0.2714035 Largest eigenvalues: [1] 101524689 96943838 91075925 86159889 86090680 84276758 82832115 [8] 81712116 80008882 78851804 Smallest eigenvalues: [1] 0.16416788 0.11323524 0.11172799 0.08739572 0.08640761 0.03301722 [7] -0.09981504 -0.46938898 -0.59052810 -0.97609004 Largest eigenvalues: [1] 99538329 97036720 91197781 86703210 85755467 84034430 83918077 81716019 [9] 80472962 78344259 Smallest eigenvalues: [1] 0.404661666 0.281517763 0.234899294 0.231735637 0.191571480 [6] 0.186306537 0.070013474 0.005452714 -0.130371006 -0.300630757 Largest eigenvalues: [1] 100297171 95820536 90053142 85548104 85337359 82927690 82630018 [8] 80913319 79282005 77517226 Smallest eigenvalues: [1] 0.41817883 0.37422092 0.32052509 0.30414643 0.25334850 0.23362959 [7] 0.19075144 0.12417547 -0.03599612 -0.11118505 Largest eigenvalues: [1] 99195220 96853467 90133959 87282673 84243851 83731022 83448442 80571997 [9] 80289891 77316377 Smallest eigenvalues: [1] 0.24381848 0.21576391 0.15856428 0.15297957 0.12383629 0.08160785 [7] -0.02978785 -0.03411285 -0.49109867 -0.53033102 Largest eigenvalues: [1] 97374265 96245480 89769362 86196965 83572612 83031385 82947342 80458351 [9] 79745645 77130126 Smallest eigenvalues: [1] 0.37636672 0.34651860 0.31825845 0.29080076 0.25412362 0.20325746 [7] 0.19303854 0.13944486 -0.06950515 -0.39647607 Largest eigenvalues: [1] 99787091 96169701 90316717 85960516 84925264 84616436 82216521 81565751 [9] 79570393 78408758 Smallest eigenvalues: [1] 0.38931753 0.37298295 0.32462657 0.30245460 0.27467859 0.21651127 [7] 0.14413236 -0.09411993 -0.28685808 -0.50445883 Largest eigenvalues: [1] 100861031 96338902 90484974 85901975 85816310 83892440 82976856 [8] 81548980 80045823 78543482 Smallest eigenvalues: [1] 0.4887759 0.4815089 0.4502573 0.3780822 0.3772039 0.3284920 [7] 0.3059593 0.2677716 0.2492140 -0.1546292 Largest eigenvalues: [1] 103028995 95626709 90134434 85487588 84538959 83695095 82111537 [8] 81347664 79726460 78018679 Smallest eigenvalues: [1] 0.3955029 0.3321981 0.2870831 0.2598618 0.2188692 0.1578309 [7] 0.1182783 0.0156418 -0.1830077 -0.3999441 Largest eigenvalues: [1] 99164822 96028027 89548319 86260963 84525203 82956121 82461608 79559365 [9] 79319510 76464971 Smallest eigenvalues: [1] 0.4767262 0.4288105 0.4025991 0.3216745 0.3013755 0.2578659 [7] 0.1778260 0.1586763 0.1203154 -0.1112833 Largest eigenvalues: [1] 98826409 96164071 89843520 86252132 83782243 82941004 82571985 80084052 [9] 79648614 76869632 Smallest eigenvalues: [1] 0.24572210 0.21248467 0.20320529 0.18133973 0.17477387 0.10298381 [7] 0.04049493 0.02598455 -0.01957025 -0.37745505 Largest eigenvalues: [1] 98807663 97636162 90802080 86811761 85667643 84833666 83392098 81894952 [9] 80572539 79070644 Smallest eigenvalues: [1] 0.32494936 0.31935302 0.27318597 0.24954817 0.15855708 0.14960057 [7] 0.02209010 0.01375357 -0.21325186 -0.31215670 Largest eigenvalues: [1] 100028598 96441595 90465666 86321915 85438548 84163956 83130278 [8] 81447596 79989596 78466583 Smallest eigenvalues: [1] 0.34567278 0.28676210 0.26351511 0.23673034 0.17568903 0.14907552 [7] 0.10940699 0.05997607 0.03050480 -0.56494643 Largest eigenvalues: [1] 97790513 97122436 90361271 87294246 84908647 84037562 83889604 81416654 [9] 80701826 78579237 Smallest eigenvalues: [1] 0.225675692 0.224534885 0.223187572 0.192975157 0.177508897 [6] 0.064045867 0.003930736 -0.029519605 -0.690876052 -0.807599075 Largest eigenvalues: [1] 98214376 97297919 90913947 87104103 84276072 83953672 83659715 81491935 [9] 80449460 77972423 Smallest eigenvalues: [1] 0.35635727 0.24931975 0.22581877 0.22029411 0.19380178 0.12955552 [7] 0.09527798 -0.01053746 -0.18503495 -0.26920432 Largest eigenvalues: [1] 98946111 97700658 90436022 87331809 85390543 83918246 83747778 81359762 [9] 80122272 77835803 Smallest eigenvalues: [1] 0.352636399 0.309437125 0.188931288 0.152171506 0.123511249 [6] 0.119057268 0.002721336 -0.033698373 -0.331834582 -0.601425136 Largest eigenvalues: [1] 99220690 95404759 89111125 85728780 85124875 82477878 82367181 80113924 [9] 79208241 77065560 Smallest eigenvalues: [1] 0.36444915 0.33907555 0.30108956 0.23492446 0.19642916 0.18340258 [7] 0.15510708 0.07184936 0.06246827 -0.02636197 Largest eigenvalues: [1] 97435793 97320473 90256545 86733478 84231669 83997244 82751496 81103309 [9] 79900040 78104654 Smallest eigenvalues: [1] 0.35122388 0.34557985 0.30998011 0.28319674 0.20932128 0.15284063 [7] 0.12640085 0.07735302 0.04032326 -0.36850674 Largest eigenvalues: [1] 99089984 96571109 90448137 86144777 85195778 84020013 82728350 81384573 [9] 79376220 77965833 Smallest eigenvalues: [1] 0.23413280 0.22593062 0.22097383 0.19490262 0.19345159 0.13760096 [7] 0.09268230 -0.02113823 -0.22935054 -0.37182262 Largest eigenvalues: [1] 99936841 97365938 90531516 87328719 86059545 84691220 83536088 82021526 [9] 80724664 78982079 Smallest eigenvalues: [1] 0.35646864 0.35621668 0.29771233 0.29643406 0.27201901 0.13566842 [7] 0.09330052 -0.02555616 -0.21489309 -0.22480430 Largest eigenvalues: [1] 99167909 96541992 90049428 86443603 85420910 83276437 83129470 80720455 [9] 79789533 77592789 Smallest eigenvalues: [1] 0.247444786 0.214292469 0.153425737 0.145757214 0.093414648 [6] -0.009802122 -0.067461703 -0.108966820 -0.339967754 -0.396803033 Largest eigenvalues: [1] 101424742 96537063 90979045 86264026 85760795 83647672 83273439 [8] 81695723 80247054 78748891 Smallest eigenvalues: [1] 0.3995752 0.3861944 0.3075573 0.2533182 0.2446386 0.2191666 [7] 0.1809214 0.1350172 0.1206828 -0.3011655 Largest eigenvalues: [1] 100054099 96704878 89861304 87109115 85641628 84456229 82561769 [8] 81570723 80013130 78485529 Smallest eigenvalues: [1] 0.4487522 0.3998189 0.3990713 0.3423149 0.2793767 0.2749401 [7] 0.2258511 0.2122147 0.1636149 -0.5377268 Largest eigenvalues: [1] 100832596 96332060 90310555 86132986 85122182 83965089 82844240 [8] 81246800 80281138 78356070 Smallest eigenvalues: [1] 0.30606598 0.29634342 0.19580032 0.12110825 0.08078618 0.02462287 [7] -0.07258641 -0.31355326 -0.63209106 -0.99620054 Largest eigenvalues: [1] 101666791 95637852 90518568 85796548 85140430 82990903 82224391 [8] 80700831 79326895 77669289 Smallest eigenvalues: [1] 0.23860159 0.23141815 0.21786662 0.19348013 0.17394407 0.10782237 [7] 0.05769664 0.01355850 -0.11474222 -0.68447938 Largest eigenvalues: [1] 99922061 96789637 90487505 85928853 85874345 83426514 82904950 80937600 [9] 79999634 78006305 Smallest eigenvalues: [1] 0.40182759 0.39254129 0.36799233 0.32131141 0.30188519 0.27435449 [7] 0.22546005 0.16863591 -0.02489685 -0.16173751 Largest eigenvalues: [1] 99126871 96126802 89665415 85750911 85428668 83062713 82732692 80643224 [9] 79386018 77206279 Smallest eigenvalues: [1] 0.46461053 0.43554796 0.42727741 0.33542841 0.33402817 0.30740964 [7] 0.27541710 0.16406832 0.14915552 -0.05658413 Largest eigenvalues: [1] 99971209 95848538 89354237 86126572 85143954 83353723 82113431 80570020 [9] 79439388 77552732 Smallest eigenvalues: [1] 0.36784686 0.32877916 0.32689721 0.31985606 0.26491347 0.25552511 [7] 0.14644696 0.10677458 0.05207215 -0.12488462 Largest eigenvalues: [1] 99791474 96884615 90205769 86546904 85090598 83992796 83036552 81330975 [9] 80009793 77866120 Smallest eigenvalues: [1] 0.31953712 0.31181272 0.28402580 0.26550021 0.23532333 0.23112261 [7] 0.15466897 0.07155424 -0.31226557 -0.88993360 Largest eigenvalues: [1] 101740918 96462602 90608158 87351928 85365844 83932442 82082490 [8] 81287498 79475034 78420145 Smallest eigenvalues: [1] 0.4524914 0.4459416 0.4104251 0.3606343 0.3117717 0.2796908 [7] 0.1669751 0.1528316 0.1308103 -0.1546491 Largest eigenvalues: [1] 98983496 96770048 89958279 86900654 84912629 83189107 82689406 80057690 [9] 79811730 76898757 Smallest eigenvalues: [1] 0.40133594 0.38063107 0.34122381 0.30931897 0.25246874 0.16867394 [7] 0.10477144 0.05625151 -0.04545561 -0.15253094 Largest eigenvalues: [1] 99502697 97137231 91167685 86344911 85381320 83962773 83728185 81488974 [9] 80593049 78703830 Smallest eigenvalues: [1] 0.377478867 0.374785142 0.300490170 0.263067050 0.256155320 [6] 0.255597417 0.156797013 0.054077637 -0.009283969 -0.646392121 Largest eigenvalues: [1] 99879632 98554075 91819072 88012136 86231621 85670492 84088259 82913136 [9] 80796756 79751815 Smallest eigenvalues: [1] 0.38684892 0.35256063 0.35027141 0.29815667 0.26069783 0.20290028 [7] 0.12866846 0.10752501 -0.07398599 -0.20880520 Largest eigenvalues: [1] 99381133 95450959 89098007 85677282 84647521 83208743 82526926 80909876 [9] 79058676 77605546 Smallest eigenvalues: [1] 0.40017253 0.37063367 0.35164918 0.33259087 0.27451587 0.17724248 [7] 0.13739204 0.11806899 -0.09707913 -0.33473433 Largest eigenvalues: [1] 100919432 95591550 89262516 86531864 85420744 83464754 82003665 [8] 80762835 79043355 77403950 Smallest eigenvalues: [1] 0.36476280 0.29011148 0.24984857 0.20427609 0.17491026 0.16963265 [7] 0.16540353 0.12071118 -0.05522887 -0.41669961 Largest eigenvalues: [1] 101310264 97055975 91110423 86605304 86584859 84950632 83128303 [8] 82262817 80842449 79357356 Smallest eigenvalues: [1] 0.3296075 0.2728563 0.2615494 0.2492401 0.2311479 0.1625284 [7] 0.1509390 -0.1630511 -0.4244158 -0.7234031 Largest eigenvalues: [1] 100218216 96588281 90816829 86475103 86339803 84558363 83276740 [8] 82111448 80008258 78705989 Smallest eigenvalues: [1] 0.27569481 0.26903723 0.24113019 0.19816557 0.14926897 0.11453316 [7] 0.08413974 0.04647350 -0.19379624 -0.38530425 Largest eigenvalues: [1] 101157073 96832411 90572813 86709485 85697109 84516436 83067507 [8] 81764743 80606752 78465484 Smallest eigenvalues: [1] 0.38431598 0.36340146 0.30762859 0.29361553 0.27656759 0.26409070 [7] 0.17356957 0.17311955 -0.01481429 -0.34806793 Largest eigenvalues: [1] 99209191 97104441 90970782 86596695 85378808 83950158 83459398 81804383 [9] 79953565 78377505 Smallest eigenvalues: [1] 0.24551377 0.23186245 0.22558035 0.20370132 0.14953925 0.08285052 [7] -0.00369371 -0.09445282 -0.10480596 -0.22987720 Largest eigenvalues: [1] 97155034 96372654 90731211 86074369 84373642 84027325 83538678 81370072 [9] 80430557 78537128 Smallest eigenvalues: [1] 0.40600543 0.30358233 0.29694394 0.28271463 0.26384152 0.07228635 [7] 0.01886570 0.01639374 -0.02469746 -0.28751733 Largest eigenvalues: [1] 101695624 96223097 90643108 86366063 85793687 83603564 83103101 [8] 81157538 80143913 78104443 Smallest eigenvalues: [1] 0.41391815 0.31796303 0.28691679 0.28262731 0.25734193 0.17927178 [7] 0.16979021 0.05924129 -0.05302641 -0.15750450 Largest eigenvalues: [1] 100364415 96408296 89974809 86373465 85643452 83526106 82471721 [8] 80983524 79245995 77669790 Smallest eigenvalues: [1] 0.17432864 0.16916192 0.16035653 0.15674914 0.07422896 -0.13277239 [7] -0.22666780 -0.39543984 -0.54018638 -0.86850116 Largest eigenvalues: [1] 101688281 97517104 92062024 86738585 86452671 84380580 83988759 [8] 82485602 81067288 79520143 Smallest eigenvalues: [1] 0.44329224 0.42913610 0.41652505 0.34661711 0.31057302 0.29445932 [7] 0.28106263 0.08765684 -0.08221495 -0.65419945 Largest eigenvalues: [1] 102397805 96824677 91415476 86573144 86433616 84236501 83170403 [8] 81923231 80468675 78970242 Smallest eigenvalues: [1] 0.44850073 0.36970957 0.36374926 0.35857882 0.29862854 0.24408555 [7] 0.14465521 0.04634988 -0.04085345 -0.19452264 Largest eigenvalues: [1] 101642708 96098377 90673083 85995790 85909638 82964052 82671795 [8] 80667869 80014578 77771767 Smallest eigenvalues: [1] 0.22625762 0.18733332 0.18073175 0.14164846 0.08719953 0.07226312 [7] -0.06683011 -0.07138373 -0.27896282 -0.30504011 Largest eigenvalues: [1] 98098374 96377253 90231038 85616629 84814079 84185687 83273781 82123934 [9] 79688359 78424671 Smallest eigenvalues: [1] 0.26228933 0.25516369 0.20127234 0.19251817 0.18656578 0.13696064 [7] 0.07152340 -0.04973992 -0.19924104 -0.53310386 Largest eigenvalues: [1] 101144359 96572544 90895970 86566300 85322799 85023336 82885762 [8] 82335552 80258291 78946044 Smallest eigenvalues: [1] 0.31425472 0.29232665 0.29075440 0.21315227 0.19541121 0.12096287 [7] 0.10495014 0.03156166 -0.09900187 -0.56218498 Largest eigenvalues: [1] 99622731 97436697 90892607 87405121 85757009 84020041 83803027 81371208 [9] 80354054 77885160 Smallest eigenvalues: [1] 0.4465739 0.4193418 0.4051978 0.3187929 0.3119098 0.2671968 [7] 0.1688253 -0.1336306 -0.1804687 -0.2749556 Largest eigenvalues: [1] 100381539 96660805 90605672 86253895 86158424 83631946 83530252 [8] 81099220 80189865 78040963 Smallest eigenvalues: [1] 0.39008753 0.38160474 0.36413128 0.34316733 0.30699135 0.28512160 [7] 0.25444969 -0.01322824 -0.01544472 -0.16627302 Largest eigenvalues: [1] 100162096 96473592 90180263 86733724 85540054 84059328 83101169 [8] 81531313 80092393 78119442 Smallest eigenvalues: [1] 0.41861967 0.39262556 0.38049540 0.33515061 0.26838976 0.23596506 [7] 0.12945188 0.09761897 -0.06329057 -0.23699486 Largest eigenvalues: [1] 100374704 96103018 89791830 85923019 85266917 83171212 82136710 [8] 80295545 79215579 77147460 Smallest eigenvalues: [1] 0.28738449 0.24913151 0.24652734 0.18475134 0.17914336 0.14902647 [7] 0.12668149 0.07205256 0.03869582 -0.16388367 Largest eigenvalues: [1] 99232217 96327823 89835456 85651361 85587322 83597217 82559834 81079558 [9] 79303218 77895041 Smallest eigenvalues: [1] 0.48928234 0.46392669 0.42913993 0.40900368 0.31466784 0.31025645 [7] 0.19904872 0.02996629 -0.10909826 -0.30305982 Largest eigenvalues: [1] 101245356 96956479 90547754 86728756 86132677 84187650 83422985 [8] 81614638 80404206 78615373 Smallest eigenvalues: [1] 0.48683616 0.40605442 0.39315705 0.38228399 0.30552375 0.26655492 [7] 0.22389781 0.19634832 0.10197018 -0.01158128 Largest eigenvalues: [1] 99989298 95692157 89377903 86219262 85180256 83889768 81867681 80859266 [9] 79414338 77970261 Smallest eigenvalues: [1] 0.32579221 0.31422255 0.30954782 0.30603726 0.28792185 0.25651022 [7] 0.25000196 0.16151739 0.08090955 -0.27462201 Largest eigenvalues: [1] 98873143 96744610 90674457 85669109 84743710 83576046 82891876 80578961 [9] 80070338 77711055 Smallest eigenvalues: [1] 0.22526279 0.17317759 0.10599801 0.05908499 0.03306539 0.02518277 [7] -0.03273921 -0.07240640 -0.34068194 -1.21983101 Largest eigenvalues: [1] 99112819 96381256 90515844 86556055 84394800 83413816 83269114 80998778 [9] 80171892 77411919 Smallest eigenvalues: [1] 0.40259340 0.39362327 0.34444887 0.33384453 0.24983615 0.20863125 [7] 0.09461222 0.07240370 0.01613215 -0.13904183 Largest eigenvalues: [1] 98892184 96958354 90007214 87212967 84424141 83813097 82858974 80421131 [9] 80061215 77213586 Smallest eigenvalues: [1] 0.43057434 0.36382332 0.30067717 0.29230871 0.27096904 0.23761812 [7] 0.22916630 0.15295642 -0.01816134 -0.59872798 Largest eigenvalues: [1] 99877461 97352596 90918817 86801097 85585995 84453827 83259039 82024081 [9] 80310399 78913063 Smallest eigenvalues: [1] 0.34739348 0.30659360 0.29108482 0.23788418 0.16880245 0.15659054 [7] 0.14583203 0.09183633 -0.01252479 -0.60626167 Largest eigenvalues: [1] 99553497 97122614 91168791 86879778 85778748 84820483 83091831 82105560 [9] 80151687 78942715 Smallest eigenvalues: [1] 0.450956053 0.442523383 0.427279110 0.412650720 0.338030639 [6] 0.298041333 0.260460946 0.148424385 0.002344365 -0.271899040 Largest eigenvalues: [1] 101520316 96516418 90605210 86880818 86064790 83535332 83123199 [8] 81269675 79963993 78193027 Smallest eigenvalues: [1] 0.34018108 0.29864039 0.27460988 0.26176493 0.19859976 0.19573599 [7] 0.14219140 0.09380002 -0.12350303 -0.42591160 Largest eigenvalues: [1] 101278509 96487122 90574845 86014869 84022823 83781279 82470949 [8] 80986426 79915223 77815519 Smallest eigenvalues: [1] 0.22495882 0.20455576 0.20245823 0.19698026 0.13884342 0.02618067 [7] -0.12289622 -0.23587343 -0.27023480 -0.27352964 Largest eigenvalues: [1] 100358750 95466105 90014201 85278854 84937147 83239576 82768721 [8] 81162770 79677906 78053183 Smallest eigenvalues: [1] 0.38823012 0.38712569 0.37378028 0.36105341 0.32477152 0.30614659 [7] 0.28048654 0.09945887 -0.06009152 -0.08498040 Largest eigenvalues: [1] 100709733 97151207 90792849 86596243 85640497 84254894 83145570 [8] 81462551 80292895 78331537 Smallest eigenvalues: [1] 0.45027281 0.44817929 0.43074911 0.37958881 0.33360187 0.24300297 [7] 0.15577164 0.10935828 -0.01744099 -0.59285194 Largest eigenvalues: [1] 98907222 95621812 90119568 85517997 84303424 83649226 82453253 81064251 [9] 79473062 77934888 Smallest eigenvalues: [1] 0.21604247 0.16766568 0.14039010 0.09394209 0.09072088 0.08102785 [7] 0.07933263 -0.06598817 -0.08301799 -0.66654315 Largest eigenvalues: [1] 99648748 96213718 90744505 86177607 85513596 84631061 82664140 81893909 [9] 80078251 79301089 Smallest eigenvalues: [1] 0.223231799 0.215173801 0.213164127 0.185839058 0.080812111 [6] 0.032679906 -0.002710683 -0.195506878 -0.379178233 -0.407147630 Largest eigenvalues: [1] 99285888 96369196 89730201 86284418 85154246 82719495 82594682 80097223 [9] 79580125 77037997 Smallest eigenvalues: [1] 0.38210214 0.33330334 0.32887680 0.29342782 0.28370784 0.21505827 [7] 0.19067972 0.10801247 -0.08479556 -0.24816456 Largest eigenvalues: [1] 98035128 97140450 90120027 86959673 84674544 84008355 83053190 81279098 [9] 79866359 78092984 Smallest eigenvalues: [1] 0.42095191 0.40586310 0.39196811 0.32951223 0.27188078 0.25067862 [7] 0.24427800 0.22358717 0.12756453 -0.01524738 Largest eigenvalues: [1] 100272784 95602079 89441475 85961379 84149784 83627979 81827737 [8] 80735630 79391403 77237907 Smallest eigenvalues: [1] 0.337518850 0.313931226 0.310652171 0.293687131 0.232552235 [6] 0.148557061 0.002684596 -0.039277516 -0.145194806 -0.397152129 Largest eigenvalues: [1] 100543735 96721070 90651002 86316689 85461133 83968735 83146689 [8] 81549110 80094928 78466743 Smallest eigenvalues: [1] 0.51708467 0.47575527 0.43004257 0.40503028 0.37028150 0.33466927 [7] 0.28618749 0.24838679 -0.01219082 -0.22384564 Largest eigenvalues: [1] 100908170 97928412 91218783 87472626 86591219 84754166 83816093 [8] 82011116 80900929 79106800 Smallest eigenvalues: [1] 0.4170582 0.3849799 0.3615875 0.3249693 0.3052663 0.2800357 [7] 0.2492211 0.1430776 -0.2622172 -0.5314545 Largest eigenvalues: [1] 100529120 96762162 90523829 86396672 86019035 84130099 82613911 [8] 81486187 80096608 78692339 Smallest eigenvalues: [1] 0.2882131581 0.2507007011 0.2461772948 0.2136708819 0.1739795803 [6] 0.1320590895 0.0006083194 -0.0426102072 -0.3553098171 -0.8678625185 Largest eigenvalues: [1] 100702551 96868425 90858529 87003845 84265959 84104150 83730697 [8] 81669663 80483022 78280670 Smallest eigenvalues: [1] 0.389565927 0.382001945 0.343533618 0.334162226 0.333193126 [6] 0.271996440 0.219229834 -0.008580813 -0.095131886 -0.307370850 Largest eigenvalues: [1] 100996903 96197731 90071617 86640032 85248194 83804839 82419325 [8] 80875394 79593832 77906293 Smallest eigenvalues: [1] 0.45406298 0.41596934 0.35874272 0.30455855 0.25275811 0.24717082 [7] 0.21060864 0.07776984 -0.14985800 -0.63722932 Largest eigenvalues: [1] 100712713 95027493 89219612 85556197 85017605 82228151 82021609 [8] 79935306 79062798 76944379 Smallest eigenvalues: [1] 0.3567306 0.3235459 0.2525263 0.2378950 0.2295788 0.1737657 [7] 0.1403549 0.1017452 -0.1588549 -0.2259587 Largest eigenvalues: [1] 98520110 97389215 90984757 87058738 84481405 84054224 83694725 81143519 [9] 80416261 78261546 Smallest eigenvalues: [1] 0.10512725 0.03501004 0.02448124 0.02104269 -0.25180588 -0.38267106 [7] -0.45106993 -0.65973958 -0.68814195 -0.78222381 Largest eigenvalues: [1] 98226777 97829734 91460341 86985686 84636698 84011445 83893764 81112292 [9] 80458439 77848076 Smallest eigenvalues: [1] 0.42229072 0.41364868 0.38231237 0.31810273 0.26337545 0.23998662 [7] 0.17490495 0.08922615 0.06088044 -0.25937998 Largest eigenvalues: [1] 99180563 95629957 89445454 85908698 84553340 83003197 82523376 80558981 [9] 79516431 77566614 Smallest eigenvalues: [1] 0.34633722 0.32758718 0.31749913 0.30171195 0.25463636 0.22123821 [7] 0.15995147 0.08587602 -0.39927322 -0.59175271 Largest eigenvalues: [1] 99451051 96628302 90729090 86307868 85890907 84149444 83659432 81668002 [9] 80386894 78603134 Smallest eigenvalues: [1] 0.25140056 0.24398003 0.17889252 0.13288612 0.11690513 0.06701467 [7] -0.01931691 -0.17686512 -0.40370415 -0.56734953 Largest eigenvalues: [1] 100276625 96841263 90031187 86445723 86294272 84433987 82882410 [8] 81557008 79874566 78323875 Smallest eigenvalues: [1] 0.4000925 0.3464329 0.3342947 0.3292621 0.2904134 0.2646720 [7] 0.2529778 0.1890054 0.1072928 -0.2506938 Largest eigenvalues: [1] 100185053 96984280 90562612 86741563 84868734 83791909 82769729 [8] 80937645 79880551 78168111 Smallest eigenvalues: [1] 0.4655190 0.4286237 0.4004332 0.3814505 0.3480695 0.3312053 [7] 0.1973777 0.1847620 0.1483448 -0.2754437 Largest eigenvalues: [1] 99641537 95720650 89569075 86080477 85003635 83896115 82250269 81024622 [9] 79673390 78140749 Smallest eigenvalues: [1] 0.28487984 0.25965614 0.25928171 0.25114519 0.20739786 0.14697560 [7] -0.02552457 -0.03067389 -0.04248938 -0.21548912 Largest eigenvalues: [1] 98360930 97956436 91609113 88006856 84966266 84043688 83448733 81147691 [9] 80489249 77453931 Smallest eigenvalues: [1] 0.40348231 0.35871517 0.34439924 0.29462767 0.26835584 0.20248058 [7] 0.12035211 0.04711807 -0.34253262 -0.40355534 Largest eigenvalues: [1] 99081992 96498225 90036295 86414576 85165714 83608951 83022245 80754922 [9] 79880628 77650349 Smallest eigenvalues: [1] 0.36973058 0.24558072 0.24354208 0.24295108 0.19838105 0.18505031 [7] 0.11492212 -0.02736849 -0.06631418 -0.60687569 Largest eigenvalues: [1] 101088625 97651330 91415090 87150853 86296308 84867018 83534621 [8] 82075352 80577420 78873691 Smallest eigenvalues: [1] 0.4323251 0.4260857 0.4184527 0.3205421 0.2541329 0.1927956 [7] 0.1756116 0.1575012 -0.1320411 -0.2270379 Largest eigenvalues: [1] 100847129 96282092 89986380 86306721 84818229 83418770 82852103 [8] 80960585 80119646 77782715 Smallest eigenvalues: [1] 0.41561646 0.38364172 0.32530082 0.30007041 0.26910228 0.23647945 [7] 0.16373446 -0.02968727 -0.03596532 -0.33166659 Largest eigenvalues: [1] 101109639 96199594 90185777 86434782 86163396 84327425 83227996 [8] 82004246 80072649 78654393 Smallest eigenvalues: [1] 0.30779216 0.30414069 0.28797484 0.27439569 0.18072347 0.15884774 [7] 0.06233294 -0.38741537 -0.74679006 -0.77220231 Largest eigenvalues: [1] 100203915 96386324 89936975 86142450 86058216 83523760 83228908 [8] 80938425 80043933 77885025 Smallest eigenvalues: [1] 0.3640130 0.3437144 0.3151329 0.2875822 0.2788707 0.2564149 [7] 0.2229312 0.1026802 -0.3913795 -0.3935394 Largest eigenvalues: [1] 100008977 97577321 91078401 87390210 85498138 83986670 83597054 [8] 81080537 80661441 77915508 Smallest eigenvalues: [1] 0.38173382 0.35580841 0.31893826 0.28715904 0.25146163 0.09758433 [7] 0.05960150 -0.03232801 -0.15323409 -0.25395670 Largest eigenvalues: [1] 100994317 95801696 90178177 85603291 85241789 83495794 82012156 [8] 80766914 79585798 77905954 Smallest eigenvalues: [1] 0.422539908 0.368664441 0.335734760 0.319807536 0.279513037 [6] 0.271428306 0.242369693 -0.004495994 -0.014857761 -0.534931724 Largest eigenvalues: [1] 101518806 96172589 90132744 86531284 85415544 83882602 82175895 [8] 81147573 79861314 78120511 Smallest eigenvalues: [1] 0.4046639 0.3546784 0.3531929 0.3237723 0.2742388 0.1953243 [7] 0.1188659 0.1017503 -0.1840807 -0.2361507 Largest eigenvalues: [1] 100910634 95601076 89484175 85795414 85596304 83010294 82187040 [8] 80373637 79364889 77456641 Smallest eigenvalues: [1] 0.37565698 0.30643723 0.29395285 0.26265620 0.23216807 0.20760756 [7] 0.16162055 0.09730921 -0.05464493 -0.32412276 Largest eigenvalues: [1] 98791412 95603540 89533656 85425404 84200588 83988961 81895810 81192265 [9] 79105974 77852984 Smallest eigenvalues: [1] 0.35053932 0.31988756 0.30457879 0.28305635 0.23601211 0.22062125 [7] 0.17952252 0.05293524 -0.01422083 -0.12139775 Largest eigenvalues: [1] 98716373 97089248 90042200 86716488 84753165 83612065 82902253 80975747 [9] 79591971 77440248 Smallest eigenvalues: [1] 0.4315482 0.3212320 0.2775270 0.2635595 0.2525289 0.2318917 [7] 0.2225824 0.1866442 0.1580802 -0.1838012 Largest eigenvalues: [1] 99867989 97783772 90737901 87262105 85916826 84599054 83539407 81861719 [9] 80637532 79225262 Smallest eigenvalues: [1] 0.41778702 0.37188209 0.33111567 0.29305827 0.29200653 0.28780413 [7] 0.26014597 0.19363434 0.14132096 -0.03054311 Largest eigenvalues: [1] 98697255 96039709 89476168 85930693 85071462 83277755 82979098 80838213 [9] 79802189 77856048 Smallest eigenvalues: [1] 0.31735061 0.31204173 0.29569054 0.28252792 0.26950029 0.19944601 [7] 0.16057404 0.12080352 0.05726589 -0.16960427 Largest eigenvalues: [1] 97089410 97018751 90793359 86874936 83828849 83081839 82701049 80444433 [9] 80118783 77165167 Smallest eigenvalues: [1] 0.26672444 0.25123775 0.23719834 0.21283683 0.19948307 0.16346010 [7] 0.08639443 0.03927285 -0.02403168 -0.40746805 Largest eigenvalues: [1] 98627691 96571191 89636254 86587376 84739535 83371775 83161558 81119893 [9] 79683786 77965882 Smallest eigenvalues: [1] 0.21531951 0.20729704 0.17897215 0.16221977 0.15645348 0.13183488 [7] 0.07069141 0.05819838 -0.10136669 -0.81570001 Largest eigenvalues: [1] 101462852 97445671 91591733 86918663 86721773 85216150 83597053 [8] 82716586 80722430 79377115 Smallest eigenvalues: [1] 0.4138523 0.4124753 0.3941361 0.3765952 0.3673656 0.3013338 [7] 0.2884123 0.2693577 0.2671783 -0.2159696 Largest eigenvalues: [1] 100416910 95405210 89187089 85717638 84766989 83592314 82829357 [8] 81264930 79519038 77868719 Smallest eigenvalues: [1] 0.4803736 0.4648956 0.4130571 0.4060590 0.3918486 0.3636475 [7] 0.3342313 0.2763485 0.1966139 -0.2143531 Largest eigenvalues: [1] 99591361 96294388 90208650 86173062 85513287 83634110 82663206 81076684 [9] 79999366 78150311 Smallest eigenvalues: [1] 0.43162536 0.39235037 0.33362075 0.30794097 0.30098441 0.29714699 [7] 0.10115827 0.07900846 0.05870488 -0.36593480 Largest eigenvalues: [1] 99295479 96819116 90310691 86604233 85942191 83757742 83521595 81247519 [9] 80259111 77994443 Smallest eigenvalues: [1] 0.26752533 0.25597285 0.24233937 0.23143638 0.15439079 0.06197901 [7] 0.04931553 0.01421427 -0.07378400 -0.51012329 Largest eigenvalues: [1] 99887657 96427297 90747635 86198826 85968456 84904778 82850402 82039778 [9] 80146214 78997904 Smallest eigenvalues: [1] 0.280689378 0.249771292 0.247927707 0.203628403 0.193103932 [6] 0.111617560 0.049305170 0.007692562 0.001829109 -0.477047265 Largest eigenvalues: [1] 100975994 97875139 91711351 87148814 85853602 84821558 83387261 [8] 82087265 80061380 78704714 Smallest eigenvalues: [1] 0.35031501 0.30057697 0.29749850 0.23742719 0.22917048 0.14593471 [7] 0.13998219 -0.01573393 -0.02939857 -0.82813323 Largest eigenvalues: [1] 102346028 96512219 91000331 86588224 86368776 83578359 82898729 [8] 80976793 80155377 77808097 Smallest eigenvalues: [1] 0.23953005 0.18574767 0.15495206 0.12693522 0.10872901 0.10675879 [7] 0.02511950 -0.05398068 -0.18715285 -0.19360303 Largest eigenvalues: [1] 99176755 97227996 90114528 86530746 85707485 83190764 82920750 80482543 [9] 79877246 77633915 Smallest eigenvalues: [1] 0.39586305 0.38929281 0.34561935 0.29629986 0.28342246 0.12108434 [7] 0.04130694 0.03658649 -0.10510365 -0.48165769 Largest eigenvalues: [1] 99847994 96329765 89809365 86621724 84554900 83644057 82313680 80706031 [9] 79504729 77240011 Smallest eigenvalues: [1] 0.24959236 0.23573055 0.21193732 0.16333859 0.15469907 0.11834565 [7] 0.11208011 0.07893102 -0.51020532 -1.01657483 Largest eigenvalues: [1] 98756900 97588085 91229250 86935560 85423134 84837303 83834838 82014312 [9] 80833715 78960086 Smallest eigenvalues: [1] 0.23049271 0.17259789 0.15795286 0.13370686 0.11952944 0.10526978 [7] 0.09780656 -0.03463285 -0.43738020 -0.57699751 Largest eigenvalues: [1] 99700823 98708148 91657957 88164539 86179600 85871006 84235209 82489902 [9] 81433598 79722391 Smallest eigenvalues: [1] 0.1926638704 0.1886783332 0.1684652738 0.0820769670 0.0577678044 [6] 0.0007470578 -0.0735877005 -0.0882565391 -0.3116061119 -0.5334949285 Largest eigenvalues: [1] 98668223 97421074 90954417 86675651 84998913 84057689 83454829 81164469 [9] 80379879 77965271 Smallest eigenvalues: [1] 0.38508090 0.37205729 0.36358650 0.27906184 0.19664225 0.14815868 [7] 0.02223784 -0.03584776 -0.20877023 -0.34899210 Largest eigenvalues: [1] 101059165 96041245 90435313 86129629 85847844 84144114 83149862 [8] 81650237 79942263 78460162 Smallest eigenvalues: [1] 0.33306914 0.32589570 0.27336716 0.26575993 0.23635918 0.19886799 [7] 0.17934528 0.12390215 -0.03895463 -0.45555546 Largest eigenvalues: [1] 97763597 96975526 90323189 86804237 84631726 83883732 82781668 81750044 [9] 79492959 78230699 Smallest eigenvalues: [1] 0.39937269 0.35969961 0.35222583 0.34500986 0.25150033 0.23377614 [7] 0.18107403 0.03753776 -0.34911042 -0.38920895 Largest eigenvalues: [1] 100021071 95952913 90002151 85974665 85512004 83270178 83152051 [8] 80935016 79803354 77730536 Smallest eigenvalues: [1] 0.27011731 0.24859072 0.24796274 0.19995566 0.17175407 0.10208083 [7] -0.01935700 -0.02458107 -0.13557538 -0.81492607 Largest eigenvalues: [1] 101264022 96610525 91186401 86179287 86173355 84398976 83380485 [8] 82201158 80321313 78890433 Smallest eigenvalues: [1] 0.44034696 0.36036845 0.32329327 0.31905050 0.31463437 0.29631225 [7] 0.21948459 0.09859459 -0.04423912 -0.04614522 Largest eigenvalues: [1] 100440536 96170997 90439181 86300042 84716190 83778400 82770122 [8] 81048288 79994776 78133742 Smallest eigenvalues: [1] 0.37421110 0.32599877 0.31509411 0.28505454 0.24147991 0.20826107 [7] 0.19516552 0.04896781 0.04807424 -0.02752855 Largest eigenvalues: [1] 99485811 96744465 90006993 86261064 84845184 83167826 82890605 80369329 [9] 79773275 77202238 Smallest eigenvalues: [1] 0.30151903 0.20625776 0.15434672 0.11963654 0.04986176 -0.04840008 [7] -0.08866457 -0.14978759 -0.41278671 -0.81969876 Largest eigenvalues: [1] 100792195 97025816 91052751 86886736 85770543 83508886 83310820 [8] 81218164 80196053 78150179 Smallest eigenvalues: [1] 0.3938262 0.3835030 0.3444733 0.3411253 0.3067322 0.2080827 [7] 0.1721212 0.1465819 -0.1001295 -0.1662654 Largest eigenvalues: [1] 98976366 96230683 89700439 86337712 84710462 83362802 82981616 80898480 [9] 79979825 77804298 Smallest eigenvalues: [1] 0.40418773 0.39475125 0.31551012 0.25216223 0.22927721 0.16817612 [7] 0.09901924 0.09239385 -0.02714463 -0.10646846 Largest eigenvalues: [1] 98985422 96639401 90708870 85759168 84828584 83674609 83109352 81056603 [9] 80017481 78215784 Smallest eigenvalues: [1] 0.23550919 0.22882326 0.15052621 0.08568235 0.04739304 0.02480883 [7] -0.02468985 -0.04299996 -0.15974593 -0.60927196 Largest eigenvalues: [1] 99068265 96186320 90658330 85907951 84085032 83389443 82626820 80907600 [9] 79856025 77478548 Smallest eigenvalues: [1] 0.27108994 0.24439420 0.20530583 0.17430710 0.14953447 0.09561237 [7] 0.09486943 0.02209804 -0.15089026 -0.57755486 Largest eigenvalues: [1] 99632845 95398855 89633377 85624057 84483144 83886155 82463862 81437498 [9] 79505550 78295345 Smallest eigenvalues: [1] 0.449113802 0.448274072 0.420258724 0.385066194 0.358959415 [6] 0.215238348 0.202719945 0.008369484 -0.002545651 -0.097033668 Largest eigenvalues: [1] 99231445 96222466 90028811 86520658 84519227 83776852 83223562 81333433 [9] 79880390 78015307 Smallest eigenvalues: [1] 0.22310133 0.18785070 0.13420682 0.12730033 0.08039525 0.06986402 [7] 0.05962369 -0.13627781 -0.42258206 -0.62618678 Largest eigenvalues: [1] 98113994 97355537 90524497 87172360 84680906 84144215 83458597 81307262 [9] 80429975 77906986 Smallest eigenvalues: [1] 0.36070889 0.35466051 0.26676820 0.25474898 0.25318535 0.21290835 [7] 0.18446632 0.18154968 0.02585697 -0.06153801 Largest eigenvalues: [1] 97903130 96615910 89430511 86482607 84381989 83426775 82497828 80530382 [9] 79669045 77122707 Smallest eigenvalues: [1] 0.3409468 0.3021379 0.2999484 0.2304528 0.2035924 0.1838266 [7] 0.1702454 0.1604355 -0.2597936 -0.4075668 Largest eigenvalues: [1] 99324699 98540922 91806746 87474548 85990939 84518205 84100426 81618580 [9] 81099155 78675610 Smallest eigenvalues: [1] 0.37735259 0.31294602 0.24329095 0.14005362 0.13819981 0.02840671 [7] -0.05518334 -0.07977283 -0.13087838 -0.38907929 Largest eigenvalues: [1] 99513594 97056602 90214599 86546127 85633018 83697804 83263246 80798172 [9] 80256301 77898612 Smallest eigenvalues: [1] 0.4542761 0.4138827 0.4075287 0.2999736 0.2009530 0.1558497 [7] 0.1531053 0.1388860 -0.1646449 -0.3706835 Largest eigenvalues: [1] 101135774 96617585 90338240 86791460 85724094 84494789 82876909 [8] 81500129 80144316 78268364 Smallest eigenvalues: [1] 0.4376275229 0.4219747376 0.3913908038 0.2947092078 0.2862341011 [6] 0.2703908297 0.2296939039 0.0839935492 -0.0003486296 -0.0994138395 Largest eigenvalues: [1] 98989603 96615496 90788490 86067778 84646760 83460049 83274542 81099423 [9] 80232567 78018947 Smallest eigenvalues: [1] 0.31125821 0.30756006 0.30001058 0.28426259 0.22086590 0.16831740 [7] 0.13492852 0.13217185 -0.07676006 -0.30992984 Largest eigenvalues: [1] 99752773 95835715 90006065 85722744 85382725 83267947 82363813 80566495 [9] 79683650 77477526 Smallest eigenvalues: [1] 0.39018705 0.37096744 0.34210719 0.29877313 0.28561771 0.23928139 [7] 0.22306082 0.03063135 -0.01285469 -0.19431874 Largest eigenvalues: [1] 99876531 97622510 91157293 87292598 85513137 84238900 83503917 81701967 [9] 80452736 78306467 Smallest eigenvalues: [1] 0.33373436 0.31788416 0.31095196 0.29292469 0.24197851 0.22653076 [7] 0.11741449 0.07935776 0.01182836 -0.46686532 Largest eigenvalues: [1] 99136468 96570847 90324217 87144056 84291429 84014020 83102242 81481736 [9] 80249748 78075517 Smallest eigenvalues: [1] 0.3492333 0.3183674 0.2999183 0.2751889 0.2748991 0.2381646 [7] 0.2198520 0.1731930 0.1133202 -0.2993485 Largest eigenvalues: [1] 99964134 96006905 90738075 85711013 85335832 84775810 82444194 82113944 [9] 79722442 78831376 Smallest eigenvalues: [1] 0.43907095 0.34541057 0.33726545 0.29386774 0.29145759 0.27812008 [7] 0.15318857 0.12422081 0.08260224 -0.10733687 Largest eigenvalues: [1] 100622931 97541656 91370427 86903309 85774861 85508313 83084135 [8] 82253946 80571532 79629639 Smallest eigenvalues: [1] 0.3206931 0.3144289 0.3140894 0.2889132 0.2602198 0.2175505 [7] 0.2028738 0.1096424 -0.2766387 -0.3634534 Largest eigenvalues: [1] 101138909 96942098 91218154 86157699 85275534 83543985 83204662 [8] 81130508 80508769 78041763 Smallest eigenvalues: [1] 0.42738273 0.41166329 0.39525201 0.27552693 0.26959841 0.24230490 [7] 0.20538706 0.15522210 -0.09870404 -0.31463964 Largest eigenvalues: [1] 101888679 96133533 90035557 87071150 85429035 83603039 82113817 [8] 80958188 79715092 78146017 Smallest eigenvalues: [1] 0.39669429 0.37847748 0.37782070 0.27519668 0.26374311 0.21415789 [7] 0.20797428 0.15556163 0.01250644 -0.11256888 Largest eigenvalues: [1] 98548420 95384392 89245605 85337467 82990884 82731878 82343105 80381749 [9] 79255826 76925433 Smallest eigenvalues: [1] 0.4689156166 0.4554242251 0.4320563565 0.3449777003 0.2625576859 [6] 0.2120052072 0.2031850588 0.1483157421 0.0005732822 -0.0479211227 Largest eigenvalues: [1] 100218560 96480542 90479396 86909834 85130397 84280259 82946339 [8] 81350251 80554946 78585002 Smallest eigenvalues: [1] 0.22816545 0.17283149 0.15660339 0.14095849 0.11119365 0.04680411 [7] 0.04017759 -0.27807809 -0.37721787 -0.44670587 Largest eigenvalues: [1] 100296305 97186698 91196691 86915922 84940356 83904032 83658723 [8] 80980332 80492975 77860742 Smallest eigenvalues: [1] 0.3578494 0.3318037 0.3162512 0.3105722 0.3089050 0.2521968 [7] 0.2267988 0.1347732 0.1240214 -0.0144601 Largest eigenvalues: [1] 99457311 98069142 91533684 87616419 84692653 84613349 83240662 81203132 [9] 80634439 78131058 Smallest eigenvalues: [1] 0.44454474 0.38368426 0.35360068 0.30528310 0.27886134 0.26433023 [7] 0.24853326 0.15108415 0.05328573 -0.29308998 Largest eigenvalues: [1] 98802357 95386421 89339547 85520124 84181553 83010458 81738468 80442613 [9] 78942457 77090234 Smallest eigenvalues: [1] 0.4634143 0.3941080 0.3496938 0.3015902 0.2704276 0.2588945 [7] 0.2486256 0.2196774 0.0755789 -0.5539918 Largest eigenvalues: [1] 100953149 97048901 90866016 86374013 86305230 84092679 82841758 [8] 81497632 80257455 78503913 Smallest eigenvalues: [1] 0.304397732 0.261754626 0.253640653 0.222707844 0.197160573 [6] 0.139352309 0.135077492 0.041905552 0.001260181 -0.365215168 Largest eigenvalues: [1] 99179909 97134107 91029016 86824209 84608984 83880464 83068343 81308878 [9] 80063611 78001902 Smallest eigenvalues: [1] 0.39036382 0.38814500 0.32118717 0.28249365 0.26706930 0.23092764 [7] 0.15663242 0.07084688 -0.09617200 -0.48041005 Largest eigenvalues: [1] 102831748 96588186 90609969 87578399 86207711 84675827 82558034 [8] 81939453 79826894 78774727 Smallest eigenvalues: [1] 0.44533986 0.42877758 0.40946613 0.39609396 0.37742077 0.31375589 [7] 0.24210320 0.15528385 0.05655215 -0.20191647 Largest eigenvalues: [1] 99487182 96677476 90458017 87210612 84393553 83519497 82900985 80868716 [9] 79890787 77546962 Smallest eigenvalues: [1] 0.118010818 0.076144054 0.057050369 0.014531861 0.007574394 [6] -0.070783322 -0.173814969 -0.359602087 -0.551051105 -0.944043629 Largest eigenvalues: [1] 98544517 96573762 90471337 86863437 84517827 83930449 83749691 81513812 [9] 80177523 78328041 Smallest eigenvalues: [1] 0.3733985 0.3636938 0.3539554 0.3240115 0.3210622 0.2401722 [7] 0.1522610 0.1407973 0.1331477 -0.5066377 Largest eigenvalues: [1] 101144776 97357336 91101274 86640136 86113996 84975844 82970432 [8] 82211823 80365497 79169163 Smallest eigenvalues: [1] 0.42194630 0.36643540 0.30849887 0.29495970 0.18556692 0.14946758 [7] 0.08895793 0.07119086 -0.32794784 -0.36333182 Largest eigenvalues: [1] 101290411 96570051 90344413 86498084 86264317 84975927 82205111 [8] 81800160 79699262 78675675 Smallest eigenvalues: [1] 0.463517033 0.427795954 0.396663602 0.324266657 0.321517994 [6] 0.294482232 0.177336549 0.045929547 0.005135486 -0.107882241 Largest eigenvalues: [1] 99757105 96264813 89901609 86284396 84826118 83209415 82811075 80340764 [9] 79813229 77158752 Smallest eigenvalues: [1] 0.13763711 0.11744402 0.03383973 -0.09361435 -0.17177170 -0.23744794 [7] -0.30895757 -0.39655814 -0.88606288 -1.00357106 Largest eigenvalues: [1] 101159724 94758652 88489718 85676057 85378605 82998513 81429547 [8] 80128194 78605823 77110950 Smallest eigenvalues: [1] 0.39836413 0.38816964 0.35950824 0.35574254 0.34229493 0.25651961 [7] 0.19019463 0.18419021 0.05260736 -0.35659083 Largest eigenvalues: [1] 100085244 97735354 91472440 87104303 86051268 85127331 83499348 [8] 82499517 80418803 79279001 Smallest eigenvalues: [1] 0.31754143 0.29906450 0.28651197 0.25754892 0.21770808 0.21063717 [7] 0.14253485 0.10340743 -0.01625338 -0.11601395 Largest eigenvalues: [1] 97601372 97230764 91004793 86860837 84169476 83746789 83640481 81654338 [9] 80318818 78525039 Smallest eigenvalues: [1] 0.34445024 0.32043208 0.30597717 0.23314078 0.22107962 0.16928771 [7] 0.08206912 0.05399807 -0.27254118 -0.99980294 Largest eigenvalues: [1] 97983187 95012557 89382975 85404738 83510979 82521898 82260044 80093153 [9] 79255467 77302231 Smallest eigenvalues: [1] 0.35640603 0.32531971 0.23836030 0.18078362 0.15318344 0.12505446 [7] 0.10760883 -0.06218987 -0.18915834 -0.26120759 Largest eigenvalues: [1] 102126616 96256080 90558052 86950230 85451714 84259059 82769964 [8] 81598687 80334404 79002354 Smallest eigenvalues: [1] 0.34708835 0.34284117 0.26071459 0.24445478 0.21504923 0.19387273 [7] 0.14720569 -0.05828855 -0.18398081 -0.35060766 Largest eigenvalues: [1] 100090153 97319417 90522292 87302095 85661284 84423359 83743176 [8] 81336722 80577103 78290675 Smallest eigenvalues: [1] 0.33243466 0.31689379 0.27451006 0.26389887 0.21991949 0.11776743 [7] 0.07909847 0.05716138 0.05633957 -0.17631125 Largest eigenvalues: [1] 98698435 96353425 90118551 85997130 85061451 83820509 82730846 80689341 [9] 80106444 77694374 Smallest eigenvalues: [1] 0.27108158 0.25878729 0.25383143 0.22965802 0.14378848 0.08547422 [7] 0.02281610 0.02165068 -0.07151370 -0.26469923 Largest eigenvalues: [1] 98267799 96766553 90464609 85615434 85167333 83671075 83255380 81231873 [9] 80027464 78412721 Smallest eigenvalues: [1] 0.40739037 0.40297082 0.37039658 0.34531499 0.28885457 0.23115028 [7] 0.21801250 0.20091496 0.01010609 -0.20407532 Largest eigenvalues: [1] 100859675 96140646 90010993 86636553 85396301 84632570 82225618 [8] 81567740 79975414 78561177 Smallest eigenvalues: [1] 0.36153185 0.35263144 0.34359855 0.34176053 0.24570836 0.21139960 [7] 0.19190760 0.12164975 0.07469133 -0.05388423 Largest eigenvalues: [1] 97781326 96178115 89850755 85389126 84489496 82954034 82799225 80355126 [9] 79614703 77560920 Smallest eigenvalues: [1] 0.370120289 0.364771342 0.346577410 0.304753132 0.296859094 [6] 0.163146158 0.096873328 0.031080391 0.009492749 -0.625070383 Largest eigenvalues: [1] 99342844 96076435 90367556 86383141 84528461 83335996 83110458 80729534 [9] 80132964 77386873 Smallest eigenvalues: [1] 0.39181350 0.38373232 0.33429629 0.28292813 0.27653197 0.26483503 [7] 0.18200635 0.17685264 -0.05443421 -0.13852630 Largest eigenvalues: [1] 100953955 97211231 91011546 86769461 86223204 85066524 82953790 [8] 81943442 80157711 78912494 Smallest eigenvalues: [1] 0.35549314 0.34385815 0.34203176 0.32588590 0.02205661 0.01722075 [7] -0.01454430 -0.23008843 -0.31394841 -0.39610048 Largest eigenvalues: [1] 99702420 96581917 90329176 86153787 85283814 84022335 83059505 81237630 [9] 80148723 78088218 Smallest eigenvalues: [1] 0.39574475 0.38690746 0.37161963 0.35791519 0.32649832 0.32647130 [7] 0.30877303 0.23639015 -0.04260909 -0.13348769 Largest eigenvalues: [1] 99413493 97472799 90630126 86902027 85302150 83856854 83476993 81212258 [9] 80347437 78286521 Smallest eigenvalues: [1] 0.43707474 0.37342799 0.35335179 0.33287168 0.28823153 0.22765054 [7] 0.19577074 0.16938743 0.13989620 -0.03962136 Largest eigenvalues: [1] 98856420 96852163 90350029 86601524 84550863 83978947 82702317 81112294 [9] 80032112 77907788 Smallest eigenvalues: [1] 0.34429309 0.28980578 0.26433521 0.24939250 0.15785677 0.14481161 [7] 0.06367226 -0.16941722 -0.29621078 -0.35527919 Largest eigenvalues: [1] 101097984 97652515 91516624 86847647 86036786 84796862 83551164 [8] 82100781 80939333 79433297 Smallest eigenvalues: [1] 0.38765615 0.33113480 0.32208901 0.29174656 0.28967414 0.26968406 [7] 0.25091721 0.11253298 0.08109373 -0.06002116 Largest eigenvalues: [1] 100964601 97208429 90662132 86907512 85818321 84285424 82425000 [8] 81096460 80062632 78262584 Smallest eigenvalues: [1] 0.3676270 0.2664219 0.2479153 0.2466358 0.2283154 0.2155199 [7] 0.1766076 0.1135760 -0.0178251 -0.5790804 Largest eigenvalues: [1] 97747191 96058790 89718279 85797684 83807856 82929869 82454151 80385163 [9] 79163229 76911361 Smallest eigenvalues: [1] 0.4166852 0.3694587 0.3627989 0.2695094 0.2666033 0.1207934 [7] -0.2451575 -0.3191504 -0.4614576 -1.2888291 Largest eigenvalues: [1] 101978532 96283555 90792960 86701656 86071691 84420093 82982429 [8] 81824887 80305554 78978541 Smallest eigenvalues: [1] 0.34430764 0.30309128 0.24474618 0.22964111 0.12496146 0.09400842 [7] 0.08674272 0.05373652 -0.17392909 -0.61076441 Largest eigenvalues: [1] 100508186 95946811 89856940 86426764 85022283 83727163 82260063 [8] 80867761 79806600 78205625 Smallest eigenvalues: [1] 0.3712703 0.3406365 0.3290207 0.3225666 0.2161522 0.1695865 [7] 0.0734146 -0.2901562 -0.3214343 -0.4076146 Largest eigenvalues: [1] 100937365 96746227 90461548 86710095 85157652 83798163 82888118 [8] 80885111 79848012 77537719 Smallest eigenvalues: [1] 0.3878788 0.3801770 0.3214060 0.2949996 0.2694249 0.2398643 [7] 0.2284926 0.1284223 -0.1234032 -0.3112984 Largest eigenvalues: [1] 98636176 96682916 89806236 86601063 85098097 83922890 83500637 81097789 [9] 79843689 77645868 Smallest eigenvalues: [1] 0.3241729733 0.3115427612 0.3014599295 0.2695526028 0.2231204055 [6] 0.0308982248 0.0113911885 0.0003479822 -0.2314885175 -0.9148584589 Largest eigenvalues: [1] 100740455 96258273 90864222 85974469 85687490 84241898 82916836 [8] 81782719 80044210 78684461 Smallest eigenvalues: [1] 0.30007003 0.29104257 0.27013914 0.26686089 0.25958276 0.16606629 [7] 0.12700005 0.10862977 0.05919622 -0.98114946 Largest eigenvalues: [1] 98703080 96814323 90306020 86394761 85406938 83618090 83302743 81174032 [9] 79996759 77857167 Smallest eigenvalues: [1] 0.40025262 0.36846199 0.36287890 0.34600333 0.31688411 0.31107306 [7] 0.23995088 0.16284988 0.15259396 -0.09884837 Largest eigenvalues: [1] 98633237 95623443 89457089 85562300 83976992 82556768 82398596 80188985 [9] 79283667 76923215 Smallest eigenvalues: [1] 0.33388794 0.30209265 0.29591901 0.25304083 0.22680882 0.12645044 [7] 0.11219459 0.10285303 0.00966683 -0.33590339 Largest eigenvalues: [1] 98082746 96997856 90761132 86473092 84726099 83875588 83561247 81170043 [9] 80431276 77811189 Smallest eigenvalues: [1] 0.31123053 0.26049558 0.25405609 0.25324440 0.18694500 0.13857176 [7] 0.09704981 -0.10138859 -0.31468305 -0.53202822 Largest eigenvalues: [1] 99411750 97441034 90315099 87152475 85774286 84309084 83222317 81309676 [9] 80332733 78451171 Smallest eigenvalues: [1] 0.3753334 0.2634897 0.2588335 0.2410766 0.2332993 0.2246530 [7] 0.2184609 0.1172257 -0.2176387 -0.2239272 Largest eigenvalues: [1] 100399856 97555392 91191325 87347504 85571653 85058091 83595414 [8] 82275814 81086629 79713132 Smallest eigenvalues: [1] 0.38741653 0.38370448 0.37525905 0.37318332 0.27706767 0.20593097 [7] 0.05590575 0.02377025 -0.06203291 -0.13339107 Largest eigenvalues: [1] 100663081 96981526 90548509 86338172 86284908 84156315 82937900 [8] 81154449 80079177 78381154 Smallest eigenvalues: [1] 0.30879773 0.29781915 0.24994595 0.24066122 0.23308781 0.20513364 [7] 0.16985581 0.15584044 0.09696983 -0.11819995 Largest eigenvalues: [1] 101046211 96003885 89963409 85860551 85731885 83624311 81858372 [8] 80948789 79732490 77756975 Smallest eigenvalues: [1] 0.4271959 0.4002332 0.3904296 0.3903091 0.3785927 0.2463006 [7] 0.1798466 0.1640075 0.1218662 -0.3006366 Largest eigenvalues: [1] 98590081 97057204 90208731 87370173 84370904 83480790 83201959 80696706 [9] 80170677 77536368 Smallest eigenvalues: [1] 0.30296087 0.21429638 0.20016446 0.19828833 0.19465761 0.15978757 [7] 0.15446267 0.03500772 -0.06108077 -0.42671351 Largest eigenvalues: [1] 100510727 96503035 90688969 85990047 84868299 83615351 83157202 [8] 81047763 80330202 78128504 Smallest eigenvalues: [1] 0.348695042 0.337564143 0.281479485 0.177135988 0.142988303 [6] 0.029398012 0.011129277 -0.008415165 -0.743042352 -0.833540453 Largest eigenvalues: [1] 101982494 95703977 90503058 85977231 85643654 83661654 82357253 [8] 81357618 79868481 78403165 Smallest eigenvalues: [1] 0.45671648 0.41165927 0.40249679 0.33846605 0.22319678 0.21497284 [7] 0.15765044 0.07886118 0.03730287 -0.08667760 Largest eigenvalues: [1] 100285640 96718821 90148183 86447098 85417992 83564620 82507627 [8] 80634430 79975668 77724542 Smallest eigenvalues: [1] 0.228541447 0.227063607 0.221173417 0.154167774 0.071543494 [6] -0.001522917 -0.188033620 -0.194962143 -0.244090342 -0.590038148 Largest eigenvalues: [1] 101528831 95719596 90556762 85764367 84838753 83934358 82125818 [8] 81475583 79874321 78847358 Smallest eigenvalues: [1] 0.38392711 0.37686344 0.34237811 0.33672498 0.28698969 0.16325425 [7] 0.03551562 -0.01511404 -0.02935671 -0.05721715 Largest eigenvalues: [1] 99671282 95847824 90017591 85403772 85202862 83615256 82609529 80891207 [9] 79699671 77883010 Smallest eigenvalues: [1] 0.36413909 0.36187706 0.32672426 0.27982996 0.25610037 0.19266826 [7] 0.18818113 0.07963762 0.07320753 -0.45621319 Largest eigenvalues: [1] 98956070 96295260 90274372 85726087 84916247 82907470 82773324 80569358 [9] 79743566 77448320 Smallest eigenvalues: [1] 0.272452752 0.268093112 0.233269719 0.221057581 0.099897359 [6] 0.077135881 -0.008974206 -0.152999573 -0.409153890 -0.786816028 Largest eigenvalues: [1] 99835657 96930201 90290150 86547782 85571775 83981321 83303663 81425771 [9] 80039813 78010161 Smallest eigenvalues: [1] 0.38470796 0.34961126 0.31197878 0.22413131 0.21462432 0.17429218 [7] 0.16704220 0.05242967 -0.01362830 -0.51049669 Largest eigenvalues: [1] 100575003 96798507 90488934 87109534 85388331 84524575 83476270 [8] 81833050 80669382 78577768 Smallest eigenvalues: [1] 0.48168969 0.48063126 0.42853678 0.38863011 0.34302813 0.26067613 [7] 0.22760373 0.03906630 0.01561523 -0.17975349 Largest eigenvalues: [1] 101548885 95906017 89918625 85850754 85423537 83681532 82268306 [8] 80950093 79617825 77881376 Smallest eigenvalues: [1] 0.36801243 0.31612583 0.30568380 0.30311802 0.27669096 0.18039616 [7] 0.14550022 0.10414646 -0.05708747 -0.41127360 Largest eigenvalues: [1] 99195211 95135297 89205131 85035639 83656068 83236589 82362740 80709965 [9] 79407447 77568013 Smallest eigenvalues: [1] 0.3630558 0.3552533 0.2788957 0.2157778 0.2140177 0.1891380 [7] 0.1706367 0.1163342 0.0427792 -0.8699088 Largest eigenvalues: [1] 98132246 96452716 89997706 86088919 84177904 83288053 83053140 80971923 [9] 79924560 78119995 Smallest eigenvalues: [1] 0.44210401 0.43596528 0.38314672 0.34376226 0.34208626 0.29392120 [7] 0.25062822 0.23417909 0.14346429 -0.06698027 Largest eigenvalues: [1] 100588362 96848137 90676689 86421278 85451337 83733043 83141376 [8] 81303894 80472746 78474060 Smallest eigenvalues: [1] 0.24608415 0.12301252 0.11425315 0.08439212 0.02875445 -0.03239082 [7] -0.13014552 -0.14691597 -0.24464442 -0.30533046 Largest eigenvalues: [1] 96951152 96658835 89772218 86225000 84400714 83040963 82856794 80279190 [9] 79196044 76986566 Smallest eigenvalues: [1] 0.30971552 0.26663164 0.25016579 0.22264682 0.19538359 0.15502151 [7] 0.11417466 0.06639802 0.06342260 -0.77227511 Largest eigenvalues: [1] 100521470 95542785 89887270 85125396 85032344 82663969 81733479 [8] 80229544 79069333 77375327 Smallest eigenvalues: [1] 0.37261245 0.31810526 0.29554204 0.25251230 0.20639885 0.17947953 [7] 0.05152177 0.01526193 -0.12796109 -0.19750224 Largest eigenvalues: [1] 99478784 96441494 90163582 85793140 85161265 83797013 82439933 81009093 [9] 79588749 77820312 Smallest eigenvalues: [1] 0.54628650 0.49356860 0.47864726 0.42718756 0.41245972 0.37671630 [7] 0.32817865 0.17343919 0.07379411 -0.02165498 Largest eigenvalues: [1] 100093914 96780531 90486255 87226384 85409093 83704813 83316878 [8] 80914446 80263471 77726184 Smallest eigenvalues: [1] 0.37093775 0.36395958 0.32819322 0.29290160 0.19931767 0.18901128 [7] 0.16802766 0.07071485 -0.03583926 -0.49426202 Largest eigenvalues: [1] 101186816 96130766 90466651 85743035 85226720 83928363 82559008 [8] 81470684 79656057 78205768 Smallest eigenvalues: [1] 0.28492384 0.21090119 0.19604934 0.18954266 0.14050079 0.13812079 [7] 0.12776229 -0.06964428 -0.37194664 -0.46445000 Largest eigenvalues: [1] 100025122 97352387 90222962 87153482 85470228 85025177 82822855 [8] 81986114 80266759 79090436 Smallest eigenvalues: [1] 0.411993004 0.409709787 0.391715183 0.367397629 0.318052164 [6] 0.304488174 0.248749069 0.226122460 0.006895722 -0.160416584 Largest eigenvalues: [1] 101006864 96814507 91040875 86284502 85397228 84197222 82871980 [8] 81301505 80273266 78635324 Smallest eigenvalues: [1] 0.4566624 0.4466032 0.4247940 0.4007810 0.3823345 0.3261750 [7] 0.2313097 0.1291146 -0.1605673 -0.1820893 Largest eigenvalues: [1] 100680907 96348762 89993856 86262287 85534866 83859967 83017513 [8] 81328067 80044789 78181806 Smallest eigenvalues: [1] 0.34482383 0.29991965 0.29282460 0.24273262 0.18534238 0.15430959 [7] 0.05373261 0.04469854 -0.07354668 -0.16024261 Largest eigenvalues: [1] 99841020 96727836 90060725 86519018 85337827 83718913 83094694 81091010 [9] 80371329 78055516 Smallest eigenvalues: [1] 0.354283470 0.294617263 0.260464994 0.245314008 0.216354223 [6] 0.170487939 0.131768582 0.104071752 -0.006006261 -0.070503264 Largest eigenvalues: [1] 99697980 98087148 91278574 87220021 86028957 84760132 83390133 81760204 [9] 80382114 78795805 Smallest eigenvalues: [1] 0.26009382 0.25825686 0.23073219 0.14848904 0.11808849 0.11397764 [7] 0.10083738 0.02216616 0.01815838 -0.85852118 Largest eigenvalues: [1] 97645229 95758734 89720401 86525329 84453644 83602088 82737544 81084832 [9] 79560621 77753369 Smallest eigenvalues: [1] 0.36215334 0.33200552 0.32354317 0.28822947 0.28443315 0.25354143 [7] 0.16765527 0.01306040 -0.02126239 -0.24619437 Largest eigenvalues: [1] 97817880 94978679 89086698 85477604 82523695 82021733 81468917 79380357 [9] 78669947 76345007 Smallest eigenvalues: [1] 0.54287051 0.49056861 0.43077711 0.39718352 0.39610485 0.38419621 [7] 0.31519397 0.27934390 0.07812666 -0.12855651 Largest eigenvalues: [1] 102191832 95909261 90375557 86247877 85666205 84086668 82148600 [8] 81463063 79758393 78434092 Smallest eigenvalues: [1] 0.29684947 0.26154647 0.25173220 0.24769201 0.23990333 0.21592635 [7] 0.09245003 0.05114277 -0.00888879 -0.09204184 Largest eigenvalues: [1] 100579681 97261462 90938698 86866813 85781427 84944154 83139873 [8] 82377581 80063928 78966255 Smallest eigenvalues: [1] 0.48837812 0.46538074 0.39483984 0.36812518 0.36293155 0.36089380 [7] 0.29982250 0.23608839 0.14942120 -0.08436834 Largest eigenvalues: [1] 99783275 97211044 90207119 86764491 85692849 83288019 83071112 80632100 [9] 80002648 77621999 Smallest eigenvalues: [1] 0.328762978 0.279383006 0.239245073 0.228611371 0.218796356 [6] 0.216969040 0.066138058 -0.008804448 -0.101897702 -0.345301606 Largest eigenvalues: [1] 99566549 96006192 90226234 86324257 84357264 83397317 83175515 80979997 [9] 80360049 77609028 Smallest eigenvalues: [1] 0.42760836 0.39695539 0.37799744 0.37448479 0.35124914 0.22765205 [7] 0.18707256 0.15156045 -0.09179962 -0.37689368 Largest eigenvalues: [1] 100770756 97227655 91021203 86728108 85990028 84159791 83550042 [8] 81948538 80446341 78912480 Smallest eigenvalues: [1] 0.33278368 0.33175610 0.22649417 0.19076022 0.17700991 0.11279682 [7] 0.09700239 0.04099863 -0.23462927 -0.23610921 Largest eigenvalues: [1] 98273947 97180455 90709358 86814452 84815039 83901773 82910927 80768144 [9] 80199051 77855863 Smallest eigenvalues: [1] 0.42691156 0.38715787 0.37500290 0.37055189 0.35284878 0.23669577 [7] 0.21510769 0.16668320 -0.02719969 -0.05248460 Largest eigenvalues: [1] 99114594 96041449 89662641 86149405 85387719 84558115 82663378 81616155 [9] 79833867 78434825 Smallest eigenvalues: [1] 0.42290109 0.38039727 0.33927692 0.31964401 0.30431695 0.20422458 [7] 0.19405433 0.09168327 0.02855149 -0.17863149 Largest eigenvalues: [1] 100172270 97788595 91608112 86802119 85909058 83969881 83669569 [8] 81574411 80473886 78684329 Smallest eigenvalues: [1] 0.37791803 0.34551114 0.34166535 0.30159110 0.27940815 0.21942159 [7] 0.14642246 0.07762277 0.06817518 -0.28825981 Largest eigenvalues: [1] 97863998 96532893 89684855 86034569 84816578 83626743 82787056 80769365 [9] 79728096 77838767 Smallest eigenvalues: [1] 0.43475421 0.42663472 0.42619223 0.34561639 0.32651875 0.31021487 [7] 0.25307035 0.12156014 0.07994455 -0.06094652 Largest eigenvalues: [1] 98423803 95139108 89158878 84706367 83648604 82339988 81853719 79891260 [9] 78989200 76960403 Smallest eigenvalues: [1] 0.33792263 0.28148467 0.26673520 0.25492677 0.22208890 0.20700823 [7] 0.15722524 0.07982529 0.04877991 -0.64969001 Largest eigenvalues: [1] 98880222 96535454 90433446 86232730 85508353 83706478 83049555 81112742 [9] 79705227 77837725 Smallest eigenvalues: [1] 0.34743019 0.33400505 0.27868723 0.20866929 0.20359728 0.18888553 [7] 0.14531753 0.05805121 0.02947548 -0.12448300 Largest eigenvalues: [1] 99757453 98065596 91994620 87161858 86035173 85570370 84044304 82403752 [9] 80988756 79362791 Smallest eigenvalues: [1] 0.26697761 0.26664204 0.25371362 0.24444707 0.01305265 -0.17989474 [7] -0.24634201 -0.46320660 -0.74346493 -0.93219520 Largest eigenvalues: [1] 101189337 95929023 90244969 86814011 85326241 82956353 82810194 [8] 80605059 79801258 77712274 Smallest eigenvalues: [1] 0.32697845 0.31177554 0.30709096 0.22379773 0.21125860 0.02467064 [7] -0.03566370 -0.12183877 -0.31410091 -0.34614835 Largest eigenvalues: [1] 97337540 94851179 88622049 85133697 83125050 82297215 81502706 79590325 [9] 78595728 76357052 Smallest eigenvalues: [1] 0.23420983 0.22626169 0.21599331 0.20910381 0.16391971 0.09933557 [7] 0.01949609 -0.05158341 -0.10881832 -0.49407252 Largest eigenvalues: [1] 98166023 95009308 89036809 85125818 82721599 82268312 82091384 79730734 [9] 79007585 76455425 Smallest eigenvalues: [1] 0.28286345 0.26949619 0.24007289 0.22154884 0.20570567 0.14487649 [7] 0.07398656 -0.05284925 -0.35967355 -0.50310239 Largest eigenvalues: [1] 101690482 97211345 91764085 87133390 86535925 85359389 83533148 [8] 82632572 80680912 79497692 Smallest eigenvalues: [1] 0.393795338 0.385298235 0.369522021 0.334718406 0.329348797 [6] 0.312995348 0.209513696 0.104409429 -0.008657202 -0.010730160 Largest eigenvalues: [1] 100586027 97698195 91042561 86719949 86180074 83989552 83037952 [8] 80818679 80417390 78278361 Smallest eigenvalues: [1] 0.44682124 0.42928444 0.38548750 0.32385364 0.30566305 0.29532295 [7] 0.27387176 0.27097945 0.26918173 -0.06675064 Largest eigenvalues: [1] 99156445 96301342 90227937 85720301 85345997 83463121 82943076 81004706 [9] 79764650 77899106 Smallest eigenvalues: [1] 0.2869746 0.2707422 0.2591637 0.2569717 0.2203477 0.2191196 [7] 0.1102222 0.1012788 -0.4479487 -0.7359944 Largest eigenvalues: [1] 101082558 97469395 91774426 86844929 86557415 85016807 83327756 [8] 82044638 80376471 78936290 Smallest eigenvalues: [1] 0.36154435 0.35528275 0.34745181 0.26154884 0.22116694 0.19556946 [7] 0.11044037 0.08842001 -0.16344848 -0.17419351 Largest eigenvalues: [1] 99924018 97152557 91031842 86080018 85692379 84078667 82779338 81246448 [9] 80111426 78656759 Smallest eigenvalues: [1] 0.46645225 0.33452829 0.32861863 0.30407173 0.29472933 0.25607429 [7] 0.20206810 0.19231033 0.07086878 -0.04548917 Largest eigenvalues: [1] 101548791 96684790 90796081 86946336 85655549 85267532 82696523 [8] 82220609 80324964 79244341 Smallest eigenvalues: [1] 0.154858576 0.105073449 0.088844204 -0.007575988 -0.175607434 [6] -0.229360824 -0.290800719 -0.298618821 -0.416415107 -0.979371346 Largest eigenvalues: [1] 101878771 95677861 89940214 86005765 85418313 83936187 82734301 [8] 81629792 79542898 78329694 Smallest eigenvalues: [1] 0.37961553 0.34225829 0.27415639 0.23696539 0.17896868 0.11815653 [7] 0.09066802 0.03963638 -0.07176412 -0.17937928 Largest eigenvalues: [1] 97971950 95660599 89876090 85393122 84332558 83631724 82662159 80974591 [9] 79491563 78058423 Smallest eigenvalues: [1] 0.29624273 0.28305774 0.26130040 0.23707974 0.22337609 0.17175739 [7] 0.16179654 0.07259951 -0.02515440 -0.05012574 Largest eigenvalues: [1] 98563368 96330194 89639280 86027206 85169767 82699435 82560795 80203400 [9] 79481521 77224119 Smallest eigenvalues: [1] 0.38963566 0.38886048 0.33183788 0.29017331 0.26915344 0.24032852 [7] 0.21138502 0.21111700 0.06538584 -0.02814864 Largest eigenvalues: [1] 97739869 95506995 89293852 85084973 84346385 83391217 82341959 80975478 [9] 79017813 77670699 Smallest eigenvalues: [1] 0.39340653 0.36962752 0.34932305 0.33285840 0.29052747 0.21464714 [7] 0.18992228 0.11901901 0.08937024 -0.52085392 Largest eigenvalues: [1] 99966174 95955485 89944989 86096419 84766547 83166533 82602511 80770613 [9] 79758673 77686966 Smallest eigenvalues: [1] 0.3826192 0.3622961 0.3372793 0.3198039 0.2721926 0.1954268 [7] 0.1704835 -0.1181644 -0.2327284 -0.4010284 Largest eigenvalues: [1] 101633322 96742106 90421358 86601572 85801057 84145303 82665742 [8] 81566379 80427781 78311276 Smallest eigenvalues: [1] 0.32710056 0.28571297 0.22112551 0.19843754 0.19092330 0.15505902 [7] 0.11570371 0.07036709 -0.01677417 -0.08125318 Largest eigenvalues: [1] 97047801 96570505 89996693 86243752 83613364 83454293 83121887 80804134 [9] 80087335 77521134 Smallest eigenvalues: [1] 0.358422211 0.354652747 0.342115403 0.310069088 0.189125892 [6] 0.167548832 0.081846922 0.009986815 -0.151345758 -0.280494041 Largest eigenvalues: [1] 99199436 96950750 90026852 86426929 85187488 83782829 82490859 80613274 [9] 79618461 77348242 Smallest eigenvalues: [1] 0.335086534 0.298815068 0.271147149 0.253947734 0.241306794 [6] 0.183991248 0.158177142 0.087580542 0.079893715 -0.007231212 Largest eigenvalues: [1] 100228624 97955122 91603622 86822549 85604723 84804199 83542040 [8] 81807890 80627316 78844511 Smallest eigenvalues: [1] 0.3708371568 0.3653915566 0.3269298229 0.3205833194 0.2931298639 [6] 0.2266393519 0.1844310085 0.0624871614 -0.0005274267 -0.4571866048 Largest eigenvalues: [1] 97654679 95726247 89603926 86043276 83316912 82931962 82816333 80321103 [9] 79589577 77248469 Smallest eigenvalues: [1] 0.41543063 0.32164773 0.24228880 0.21285122 0.20985308 0.13772626 [7] 0.08647726 -0.14076971 -0.17953838 -0.51983491 Largest eigenvalues: [1] 99525655 97638460 90475833 87488974 85952898 84215473 84059048 81750571 [9] 80908513 78578469 Smallest eigenvalues: [1] 0.43131297 0.37442354 0.34046640 0.33561261 0.31970827 0.31955520 [7] 0.29485693 -0.08118299 -0.17679021 -0.23402752 Largest eigenvalues: [1] 98846701 97347317 90531035 87171144 85362951 83711789 83536715 81162234 [9] 80409767 77991534 Smallest eigenvalues: [1] 0.30325982 0.29479733 0.28082512 0.26871949 0.19170329 0.10872022 [7] 0.04443420 -0.07489060 -0.08698856 -0.31101186 Largest eigenvalues: [1] 99040845 95757641 89389395 86158691 84625161 82792021 81911989 79490340 [9] 79163782 76211277 Smallest eigenvalues: [1] 0.46666791 0.46358262 0.43353654 0.38437966 0.31903084 0.31256042 [7] 0.20298092 0.01698847 0.01189491 -0.12225563 Largest eigenvalues: [1] 99189783 95551189 89327909 86041551 83511165 82568855 82074468 79868670 [9] 79231508 76633605 Smallest eigenvalues: [1] 0.39020227 0.34092285 0.33598386 0.31321449 0.29964486 0.25196604 [7] 0.10743470 -0.09202008 -0.23172585 -0.28804027 Largest eigenvalues: [1] 99830095 96586112 90626323 85991053 85643736 83472272 83231004 80910369 [9] 80175591 77889234 Smallest eigenvalues: [1] 0.28320454 0.25958116 0.24378756 0.21870046 0.18277943 0.15390318 [7] 0.04188932 -0.24710383 -0.28858293 -0.36889302 Largest eigenvalues: [1] 101899157 98574697 92137381 87769714 86597328 84622061 84026574 [8] 82082088 81075974 78993620 Smallest eigenvalues: [1] 0.26631089 0.26286016 0.25898521 0.17578746 0.11403746 0.10354723 [7] 0.09354100 0.04253485 0.02346783 -0.17119786 Largest eigenvalues: [1] 98973759 97381954 90351276 86779232 85723563 84366020 83195249 81591094 [9] 80064656 78448919 Smallest eigenvalues: [1] 0.40071810 0.35422130 0.30762008 0.26855154 0.26194039 0.21403270 [7] 0.20320264 0.19192062 0.16898296 -0.03978557 Largest eigenvalues: [1] 99487606 97172688 90350023 86958578 85541470 84051364 83278495 81328406 [9] 80445128 78359890 Smallest eigenvalues: [1] 0.37763075 0.34001618 0.28316890 0.23632699 0.19810442 0.19480682 [7] 0.10493518 0.04993961 0.04031737 -0.38129538 Largest eigenvalues: [1] 100290854 96205546 89940106 86521334 85425125 83376536 82163317 [8] 80568292 79277241 77426745 Smallest eigenvalues: [1] 0.21571452 0.20970990 0.20097836 0.11149273 0.10433972 0.10234894 [7] 0.06543447 -0.06218629 -0.23637317 -0.37511666 Largest eigenvalues: [1] 100576103 97580992 90701826 86826562 85550576 83903146 82531801 [8] 80895510 79608835 78168928 Smallest eigenvalues: [1] 0.35107306 0.34475681 0.27594283 0.21324193 0.17394462 -0.01265951 [7] -0.05325034 -0.49364756 -0.59916208 -1.23622475 Largest eigenvalues: [1] 100736836 96096396 90067013 86516393 86276193 83922357 83471951 [8] 81481829 80119847 78470199 Smallest eigenvalues: [1] 0.31895155 0.30904963 0.29664551 0.25066719 0.23202901 0.21034124 [7] 0.19445494 0.03857835 -0.37225559 -0.38495409 Largest eigenvalues: [1] 99761822 96610921 90319999 85840125 85708797 83609452 83235783 81095857 [9] 80061666 78087957 Smallest eigenvalues: [1] 0.18897963 0.18286349 0.17811690 0.16424739 0.10453966 0.05541427 [7] 0.03618658 -0.18426589 -0.32394880 -0.32896853 Largest eigenvalues: [1] 99150309 96482620 90156508 85906934 84737615 83667286 82719843 80988628 [9] 79849181 77611173 Smallest eigenvalues: [1] 0.4650368 0.4189460 0.4117889 0.3849716 0.2966940 0.2152522 [7] 0.2110367 0.1690589 0.1104567 -0.6699063 Largest eigenvalues: [1] 98453176 97063541 90347654 87207103 85115244 83877910 83511672 81377239 [9] 80131819 77766178 Smallest eigenvalues: [1] 0.390759166 0.375720334 0.296813812 0.255742485 0.251404776 [6] 0.219734925 0.208227600 -0.006735731 -0.047181825 -0.267267814 Largest eigenvalues: [1] 100769543 97989060 91102873 87505758 86260085 85101359 83957227 [8] 82365189 81240584 79497117 Smallest eigenvalues: [1] 0.258215394 0.210897573 0.170801222 0.159052154 0.119704950 [6] 0.088160921 0.008721204 -0.079877502 -0.158543241 -0.381340640 Largest eigenvalues: [1] 100449376 96841399 90697012 86941380 85326661 85039637 83246693 [8] 81970080 80678840 79232128 Smallest eigenvalues: [1] 0.1884011 0.1700106 0.1484323 0.1279615 0.1265200 0.1106676 [7] -0.1065177 -0.1340896 -0.3502637 -0.3932765 Largest eigenvalues: [1] 98254099 96307564 90137516 85943560 84685490 83692881 83318673 81019168 [9] 80059348 77656369 Smallest eigenvalues: [1] 0.41833972 0.40632956 0.39214475 0.32056459 0.26185378 0.10531804 [7] -0.07650263 -0.11396690 -0.39511743 -0.62749559 Largest eigenvalues: [1] 100195719 96648284 90503245 86685696 86243520 84319094 83364073 [8] 81433612 80262396 78094466 Smallest eigenvalues: [1] 0.28162721 0.26686780 0.20659324 0.16136058 0.08912136 0.07378089 [7] 0.01215832 -0.19537132 -0.38042876 -0.75577945 Largest eigenvalues: [1] 101016364 96971299 90202489 86785003 86781813 83554222 83023950 [8] 80834995 80104615 77517945 Smallest eigenvalues: [1] 0.3686360 0.3676027 0.3422527 0.3045278 0.2608960 0.1700752 [7] 0.1384833 0.0324884 -0.1374538 -0.3630848 Largest eigenvalues: [1] 99539531 96670101 90344339 86589730 85151165 84254208 83245116 81567788 [9] 80319398 77993292 Smallest eigenvalues: [1] 0.32741697 0.32279430 0.22375320 0.22352534 0.04608776 0.04078883 [7] 0.01247902 -0.01979584 -0.06089093 -0.10959968 Largest eigenvalues: [1] 97974152 97394416 90690320 87393482 83851608 83818091 83303394 80740865 [9] 80168394 77393837 Smallest eigenvalues: [1] 0.46678422 0.42066312 0.41700106 0.37687560 0.30033924 0.17604920 [7] 0.16054940 0.08964765 0.04675098 -0.08867313 Largest eigenvalues: [1] 99913878 95913751 89858761 86041960 85328677 83478911 82944365 80811351 [9] 79891956 77815040 Smallest eigenvalues: [1] 0.15966331 0.12270555 0.11976892 0.11798695 0.05763677 0.02585065 [7] 0.01901152 -0.06469881 -0.11457037 -0.48985042 Largest eigenvalues: [1] 97427824 96519589 90454526 86039843 84167560 83325984 82574734 80526596 [9] 79872892 77558667 Smallest eigenvalues: [1] 0.3281647 0.2880198 0.2522436 0.2284610 0.2008078 0.1638020 [7] 0.1162220 0.1088844 -0.4722262 -0.7772378 Largest eigenvalues: [1] 98586712 96546355 90657682 86786894 84507911 83611350 83282389 81143462 [9] 80248744 78076916 Smallest eigenvalues: [1] 0.46583470 0.44468708 0.41853264 0.41170238 0.36337790 0.27495904 [7] 0.25240456 -0.00750709 -0.05576002 -0.09204529 Largest eigenvalues: [1] 100858934 96215397 90181030 86492275 85695305 83519666 83219920 [8] 81162417 79966928 77640696 Smallest eigenvalues: [1] 0.40871638 0.40178277 0.30449931 0.28230541 0.27699379 0.27692281 [7] 0.23814933 0.18395907 0.04911989 -0.01962100 Largest eigenvalues: [1] 98732994 96563135 89042577 85932266 85227431 83009885 81967803 79860631 [9] 79094495 76713285 Smallest eigenvalues: [1] 0.27829057 0.22412160 0.20581549 0.18830344 0.18050499 0.14787885 [7] 0.02589929 -0.08581674 -0.25400724 -0.34305644 Largest eigenvalues: [1] 99569912 96217685 90299475 85671414 84571169 83276896 82205908 80335955 [9] 79805224 76999603 Smallest eigenvalues: [1] 0.44707692 0.43711738 0.41458408 0.39973400 0.39854641 0.23795090 [7] 0.16222320 0.11418480 0.08753536 -0.21234781 Largest eigenvalues: [1] 99801853 95739061 89995376 85330387 84684245 82900277 82288655 80495238 [9] 79524284 77430307 Smallest eigenvalues: [1] 0.413811209 0.394259562 0.333798583 0.307790140 0.277660551 [6] 0.251070096 0.201726082 0.056909372 0.002845021 -0.169623783 Largest eigenvalues: [1] 99793791 96027886 89825430 85730029 85360926 83621402 82485074 81069036 [9] 79295451 77638993 Smallest eigenvalues: [1] 0.11995874 0.03919464 -0.07243507 -0.08412915 -0.11057988 -0.32456428 [7] -0.36273331 -0.55924449 -0.80779483 -1.61712177 Largest eigenvalues: [1] 101652519 96009699 89751050 87301471 85990450 84835964 82802743 [8] 82470617 79598948 78771856 Smallest eigenvalues: [1] 0.44998631 0.38067714 0.38036905 0.35732227 0.30758059 0.19522543 [7] 0.14394653 0.04264131 -0.16017647 -0.33033004 Largest eigenvalues: [1] 100969084 95716841 90146154 85691965 85244704 83599701 82634517 [8] 81105501 79871539 78310264 Smallest eigenvalues: [1] 0.469243955 0.428198488 0.422090069 0.421018415 0.408523360 [6] 0.357623788 0.322640652 0.192963784 0.169908836 -0.002812238 Largest eigenvalues: [1] 98556672 96118360 89565355 85664886 85257483 83062379 82770246 80565719 [9] 79479977 77604551 Smallest eigenvalues: [1] 0.41860136 0.37029896 0.31801096 0.24897891 0.20796656 0.18052219 [7] 0.08919671 0.07344524 -0.04600283 -0.69180783 Largest eigenvalues: [1] 99457607 97448552 90480151 87226710 86155651 84073151 83899395 81516304 [9] 80673796 78294809 Smallest eigenvalues: [1] 0.28362831 0.27983886 0.22630221 0.21591160 0.20072536 0.17158643 [7] 0.08049235 -0.04447852 -0.18347106 -0.29191282 Largest eigenvalues: [1] 99271150 97124508 90285176 86778725 85488007 84243654 83539255 81711264 [9] 80343914 78407622 Smallest eigenvalues: [1] 0.40221550 0.36517080 0.33047893 0.29337977 0.27269660 0.23886325 [7] 0.22303246 0.12265450 -0.02931478 -0.11411915 Largest eigenvalues: [1] 98308881 97373500 91212837 87680922 84549016 84320257 84011142 81749694 [9] 80588719 78313682 Smallest eigenvalues: [1] 0.39895763 0.37175341 0.30362410 0.26865365 0.25120102 0.23109612 [7] 0.20973494 0.14286938 0.05734573 -0.05568522 Largest eigenvalues: [1] 100556966 96505408 90521617 86599748 85025891 83399858 82985071 [8] 80741879 80084031 77628075 Smallest eigenvalues: [1] 0.24787018 0.22293180 0.17273842 0.16346320 0.15246370 0.13319736 [7] 0.04228685 -0.01485719 -0.07777430 -0.53297647 Largest eigenvalues: [1] 96334844 96082126 89863532 86355295 83260722 83255156 82283971 80008003 [9] 79548141 76773201 Smallest eigenvalues: [1] 0.3618484 0.2915707 0.2651846 0.2441289 0.2237961 0.2214666 [7] 0.1345436 0.1077194 -0.2025304 -0.3289915 Largest eigenvalues: [1] 100797820 97332170 90719504 86642098 86471455 84710706 82580986 [8] 81678026 79981180 78732765 Smallest eigenvalues: [1] 0.3503480 0.3260445 0.3035851 0.3026767 0.2936594 0.1982876 [7] 0.1776095 0.1578595 0.1473551 -0.3187226 Largest eigenvalues: [1] 97951103 97775431 90789912 87454569 84764436 84427198 83901762 81338180 [9] 80618620 77820694 Smallest eigenvalues: [1] 0.328628473 0.326765207 0.248949641 0.245435263 0.148692339 [6] 0.057359369 0.056986789 0.003396798 -0.013635293 -0.215169570 Largest eigenvalues: [1] 99183861 97128128 91012404 86338119 85465276 83605826 83168600 80959356 [9] 80466445 77890839 Smallest eigenvalues: [1] 0.47939074 0.45914412 0.42490396 0.36786352 0.30914964 0.26874575 [7] 0.26685334 0.21623590 0.09964064 -0.09219625 Largest eigenvalues: [1] 99653232 96524501 90777916 86282607 85117981 83589651 83106185 81027820 [9] 80050314 78171692 Smallest eigenvalues: [1] 0.4098949 0.3896041 0.3015959 0.2935863 0.2894355 0.2777673 [7] 0.2637986 0.1581019 0.1345543 -0.3122339 Largest eigenvalues: [1] 99873829 98023905 91067532 87884588 86044064 84914448 83469801 82017838 [9] 80333634 78940175 Smallest eigenvalues: [1] 0.44653273 0.43131648 0.39904705 0.39088873 0.38143333 0.31887100 [7] 0.21951130 0.20311545 0.04105688 -0.02464155 Largest eigenvalues: [1] 99519101 95716967 89880498 85804448 84183529 82952541 82590511 80681774 [9] 79697880 77546489 Smallest eigenvalues: [1] 0.38409100 0.35642755 0.35481662 0.34147760 0.34130559 0.31010757 [7] 0.26311322 -0.07400601 -0.08813636 -0.62520030 Largest eigenvalues: [1] 99111387 96020971 89638692 85729068 84520098 82873395 82765339 80617042 [9] 79486791 77420003 Smallest eigenvalues: [1] 0.18644207 0.16785706 0.12970683 0.05168045 0.01943262 0.00919379 [7] -0.03104875 -0.31121409 -0.38931875 -0.42857215 Largest eigenvalues: [1] 99671953 97942890 90966245 87209799 86137985 84985181 83949626 82553353 [9] 81031691 79671049 Smallest eigenvalues: [1] 0.41273150 0.40773405 0.37294028 0.36140985 0.34767676 0.29962898 [7] 0.28639645 0.27853129 0.27105357 -0.02228512 Largest eigenvalues: [1] 98952140 96972201 90423726 86533980 85035379 83903218 83578216 81212177 [9] 80520281 78010510 Smallest eigenvalues: [1] 0.41297424 0.41061207 0.39001577 0.35779259 0.35570481 0.27470053 [7] 0.22408587 0.14111807 0.01769003 -0.59496670 Largest eigenvalues: [1] 100058669 96235937 90011682 85883275 85414252 83740733 82740005 [8] 80908048 79853121 77825327 Smallest eigenvalues: [1] 0.4351055222 0.3926015555 0.3497409722 0.3335023264 0.2936171643 [6] 0.2104956290 0.1769735200 0.1634078285 0.0006303139 -0.3215011954 Largest eigenvalues: [1] 100745479 96884741 90078457 86466393 86296507 84674447 82430804 [8] 81675155 79621302 78491697 Smallest eigenvalues: [1] 0.41200828 0.39806753 0.36857776 0.33593407 0.27815240 0.26919631 [7] 0.20373225 0.02794539 -0.13077873 -0.44102054 Largest eigenvalues: [1] 99988073 96219352 90182236 86099725 85193816 83465233 82878315 81066049 [9] 79713255 77835209 Smallest eigenvalues: [1] 0.40071427 0.38451405 0.32828446 0.31009699 0.28877841 0.24107593 [7] 0.14281846 0.12196693 -0.04961201 -0.10280425 Largest eigenvalues: [1] 99305319 96357607 90087146 86082944 84742490 83115165 82999260 80706502 [9] 79756895 77392064 Smallest eigenvalues: [1] 0.32157280 0.28438689 0.26418235 0.23064139 0.23039579 0.11899563 [7] 0.01544149 -0.05733516 -0.16830966 -0.67765665 Largest eigenvalues: [1] 100357762 96096191 90401907 85961377 84642925 83644533 82543021 [8] 80948917 79815592 77679269 Smallest eigenvalues: [1] 0.4371261 0.3120702 0.2750353 0.2590111 0.2381815 0.1240182 [7] 0.1238669 0.1161227 -0.1186057 -0.3717290 Largest eigenvalues: [1] 100184234 97829350 91264660 87447525 86100902 84929635 83934665 [8] 82054740 80888801 78984779 Smallest eigenvalues: [1] 0.34794391 0.34330033 0.31268796 0.22063082 0.21116366 0.12587686 [7] 0.07884995 0.06437375 -0.02300992 -0.22594675 Largest eigenvalues: [1] 99606735 97598903 90585185 86966271 85429962 83217316 83104608 80412144 [9] 79887589 77060904 Smallest eigenvalues: [1] 0.4157508 0.3932418 0.3588528 0.3462015 0.3135687 0.2287778 [7] 0.1920207 0.1831763 0.0811108 -0.2172652 Largest eigenvalues: [1] 99549113 95426060 89884784 85003268 84960071 82663530 82247757 80477534 [9] 79335161 77402876 Smallest eigenvalues: [1] 0.37946752 0.37172274 0.31859915 0.27792094 0.27648965 0.26314745 [7] 0.22205832 0.20741180 -0.02925941 -0.40423012 Largest eigenvalues: [1] 100137334 97114814 90566136 86209824 86206208 84474293 83032546 [8] 81685085 80145636 78575101 Smallest eigenvalues: [1] 0.214524849 0.209667174 0.154280963 0.137810455 0.126889796 [6] 0.107633910 0.073928279 0.008884107 -0.154450990 -0.349349998 Largest eigenvalues: [1] 99982408 95964374 89634490 85792525 85505828 83198698 82695617 80759804 [9] 79581141 77699081 Smallest eigenvalues: [1] 0.29444729 0.26323111 0.23640645 0.22904055 0.18474092 0.15958907 [7] 0.12228186 0.08612822 -0.23710986 -1.27384046 Largest eigenvalues: [1] 98574313 97959636 91766096 88034147 84859206 84820948 84115404 81701433 [9] 81218354 78487362 Smallest eigenvalues: [1] 0.4599506 0.4514126 0.4463866 0.4001985 0.3389677 0.3248367 [7] 0.2274095 0.2262217 0.1965150 -0.1191005 Largest eigenvalues: [1] 99334340 96629775 90242238 86515861 84830660 84056419 82641022 81329606 [9] 79727904 77942348 Smallest eigenvalues: [1] 0.335924592 0.335065124 0.331494287 0.300316411 0.286209628 [6] 0.276442072 0.006766482 -0.113275006 -0.152435429 -0.286789171 Largest eigenvalues: [1] 101934834 96627139 90833858 86591782 85598163 83655458 82586700 [8] 81064613 79870608 78119439 Smallest eigenvalues: [1] 0.32574374 0.32171409 0.30992380 0.25755374 0.24781882 0.23511191 [7] 0.16005718 0.10275583 -0.03278057 -0.46249065 Largest eigenvalues: [1] 101253008 96048572 90207021 86047744 85693611 84012591 82760519 [8] 81690900 80169985 78984582 Smallest eigenvalues: [1] 0.4857009 0.4110675 0.3825500 0.3383431 0.2787793 0.2636261 [7] 0.2452745 0.2054012 -0.1736380 -0.2938922 Largest eigenvalues: [1] 99952339 97156374 90424184 87169041 85341461 84011819 83531924 81440231 [9] 80210364 78227056 Smallest eigenvalues: [1] 0.42333337 0.29813212 0.29264586 0.27994932 0.21052209 0.18326102 [7] 0.07881272 0.06673573 -0.07370267 -0.56037379 Largest eigenvalues: [1] 99683874 96794020 90449190 86826819 85128844 83493661 83138906 80801915 [9] 80047548 77440253 Smallest eigenvalues: [1] 0.47905799 0.46046822 0.42756646 0.32161236 0.26047172 0.15406170 [7] 0.10397924 0.06858076 -0.10662799 -0.22108296 Largest eigenvalues: [1] 98685068 96318846 89678597 86211585 85078920 83609171 82250553 80791929 [9] 79238734 77639610 Smallest eigenvalues: [1] -0.03590173 -0.11457988 -0.23278926 -0.24937634 -0.26483858 -0.27397646 [7] -0.33962305 -0.38154724 -0.51329823 -0.76300245 Largest eigenvalues: [1] 97631881 96622744 89425155 85612966 85486524 83806217 83126574 81357396 [9] 79405689 77832771 Smallest eigenvalues: [1] 0.4533305 0.4297536 0.4201626 0.3814635 0.2831721 0.2826120 [7] 0.2443980 0.1396527 -0.1626018 -0.4293091 Largest eigenvalues: [1] 100237093 96056232 90073703 86067952 85752373 83646035 82658894 [8] 81178187 79490601 77890454 Smallest eigenvalues: [1] 0.28916751 0.27512700 0.26575476 0.23124121 -0.02715027 -0.08137438 [7] -0.08515129 -0.12878559 -0.26455862 -0.61549841 Largest eigenvalues: [1] 100382808 97518847 90838070 87012495 86697504 85272715 83522276 [8] 82385801 80255137 79051281 Smallest eigenvalues: [1] 0.33100635 0.29530680 0.29513579 0.26185482 0.25711152 0.19401975 [7] 0.12769166 0.11880813 0.02088322 -0.32586642 Largest eigenvalues: [1] 100040960 96583417 90487916 86355342 85186330 84961869 82826427 [8] 81949653 80508212 79029515 Smallest eigenvalues: [1] 0.30526755 0.28313257 0.24632652 0.20657573 0.18327488 0.15211597 [7] 0.06874121 -0.05516681 -0.14165578 -0.42727101 Largest eigenvalues: [1] 98830094 96119589 89581998 86717612 83978205 83321860 82855384 80422625 [9] 79891379 76917442 Smallest eigenvalues: [1] 0.26525632 0.22470979 0.19688889 0.17806636 0.10733989 0.08158045 [7] 0.05977386 -0.02077177 -0.34689190 -0.39992598 Largest eigenvalues: [1] 100048790 97349755 91100888 86769919 85708245 83976975 83652349 [8] 81225002 80664457 77856030 Smallest eigenvalues: [1] 0.36910747 0.36412448 0.31408484 0.27878684 0.21115075 0.13463200 [7] 0.12378193 0.07704030 0.01208162 -0.53785989 Largest eigenvalues: [1] 99430598 96340614 90137236 86626746 84356942 82944329 82812844 80061215 [9] 79597498 76825666 Smallest eigenvalues: [1] 0.37050021 0.34258409 0.33784094 0.32122007 0.25750004 0.23923273 [7] 0.23502325 0.17198663 -0.05557334 -0.06063662 Largest eigenvalues: [1] 98513256 96600482 89694569 86386383 84998999 84155038 82577246 81532620 [9] 79800589 78546112 Smallest eigenvalues: [1] 0.45282561 0.41421463 0.30710189 0.30136572 0.29551314 0.18750389 [7] 0.16591856 0.10110126 0.03084501 -0.25978644 Largest eigenvalues: [1] 98925115 97032644 90724672 87328993 84756524 84604864 83602966 82223380 [9] 80881434 79027953 Smallest eigenvalues: [1] 0.44385771 0.41353578 0.35820682 0.35222261 0.32569639 0.30147233 [7] 0.26474657 0.26010906 0.09172766 -0.15328164 Largest eigenvalues: [1] 99137807 97045167 90100732 86971108 84859528 83998254 82629475 81163659 [9] 79948977 78216298 Smallest eigenvalues: [1] 0.308794766 0.307812530 0.256323747 0.219629923 0.214666521 [6] 0.195143492 0.048318529 0.001454203 -0.002153526 -0.027453624 Largest eigenvalues: [1] 99448259 97144021 90523897 86416046 85507958 84812399 83284488 81958704 [9] 80365638 78563121 Smallest eigenvalues: [1] 0.3535440 0.3452995 0.3429877 0.3392241 0.3378901 0.2754374 [7] 0.2489767 0.2108280 0.1211729 -0.1334780 Largest eigenvalues: [1] 100588000 96598302 90336237 85818727 85654072 84222431 82500906 [8] 81417949 79816854 78343092 Smallest eigenvalues: [1] 0.33931675 0.33519505 0.28395574 0.27051586 0.18284945 0.08224592 [7] 0.06686479 -0.03790621 -0.26468082 -0.29959123 Largest eigenvalues: [1] 99339225 95241356 89687057 85114818 85015087 83009507 82335006 80692608 [9] 79247637 77683059 Smallest eigenvalues: [1] 0.37020018 0.33712496 0.32751211 0.24210929 0.21230647 0.09959205 [7] 0.05482187 -0.26992859 -0.50441247 -0.71550576 Largest eigenvalues: [1] 102154921 96191347 90776653 87214824 85402737 84168524 82539854 [8] 81248851 80008383 78552512 Smallest eigenvalues: [1] 0.44297332 0.39596349 0.38209998 0.34205767 0.32397433 0.22301753 [7] 0.01304074 -0.01600393 -0.01612155 -0.04727207 Largest eigenvalues: [1] 101904204 96239462 90106460 86658129 86620686 84256124 82737000 [8] 81563019 80119000 78517832 Smallest eigenvalues: [1] 0.4074380 0.3984621 0.2965099 0.2587612 0.2450089 0.1818042 [7] 0.1623147 0.1331376 -0.1806240 -0.2465380 Largest eigenvalues: [1] 101471223 96946978 90962823 86335969 86304951 83915367 83464833 [8] 81789074 80429631 78632441 Smallest eigenvalues: [1] 0.41594618 0.40292830 0.39912891 0.35642104 0.34214715 0.27730808 [7] 0.25263374 0.16892183 0.10103507 -0.02928523 Largest eigenvalues: [1] 100132834 96970782 90193581 86602022 86025884 84607407 82566458 [8] 81527585 79938777 78308097 Smallest eigenvalues: [1] 0.45741268 0.42523873 0.41780677 0.37227785 0.29100024 0.25260691 [7] 0.19008345 0.14551790 0.04884313 -0.25648368 Largest eigenvalues: [1] 101665818 96741537 91246745 86441670 86292573 84964711 83248846 [8] 82298896 80739273 79161245 Smallest eigenvalues: [1] 0.378598402 0.361240460 0.300501811 0.290002184 0.270561871 [6] 0.234869258 0.106716611 -0.008069957 -0.256619834 -0.468712989 Largest eigenvalues: [1] 99525641 96799276 91042909 86543519 84891544 83613183 83113246 81069936 [9] 80032432 78016522 Smallest eigenvalues: [1] 0.41169138 0.33717606 0.30021891 0.28790297 0.28380580 0.28221251 [7] 0.21823274 0.15755762 -0.01927377 -0.04683377 Largest eigenvalues: [1] 99167728 95996643 89655738 85828946 84356177 84115270 82108036 81428352 [9] 79336643 78213326 Smallest eigenvalues: [1] 0.4087712 0.3682560 0.3178610 0.2716648 0.1769101 0.1692591 [7] -0.1062793 -0.1347701 -0.3127829 -0.3326485 Largest eigenvalues: [1] 100302481 95818034 90270789 86059077 84819437 83034242 82792789 [8] 80565589 79768763 77293530 Smallest eigenvalues: [1] 0.32943264 0.30553848 0.29684109 0.25534367 0.22507157 0.13589005 [7] -0.01301935 -0.08712144 -0.20448882 -0.24821395 Largest eigenvalues: [1] 100534488 95979779 89829568 85838925 85631711 83842355 83079140 [8] 81561566 79712801 78424088 Smallest eigenvalues: [1] 0.3530961 0.3253809 0.2736174 0.2409434 0.2360708 0.1660788 [7] 0.1338282 -0.0333838 -0.1430207 -0.5858916 Largest eigenvalues: [1] 100512593 95892927 89919173 86179336 85747566 83637314 82509235 [8] 81253531 79476638 78034720 Smallest eigenvalues: [1] 0.3864776 0.3706377 0.3139742 0.3008183 0.2355772 0.2217630 [7] 0.1893592 0.1630022 0.1159066 -0.2718316 Largest eigenvalues: [1] 99693227 97502175 91801509 86956927 85445489 84933143 83436753 82311668 [9] 80316033 79340757 Smallest eigenvalues: [1] 0.38374686 0.33831406 0.32297664 0.30275801 0.27410673 0.26178423 [7] 0.18602216 0.01032676 -0.04964811 -0.16237160 Largest eigenvalues: [1] 99323475 97425391 90989949 86871741 85423995 85222654 83314660 82294763 [9] 80552144 79447805 Smallest eigenvalues: [1] 0.41387061 0.39088158 0.38532791 0.34992032 0.34016442 0.30571860 [7] 0.28110070 0.22171181 -0.03541281 -0.86860895 Largest eigenvalues: [1] 101301235 95923502 89978253 85524046 85449237 83678039 82683271 [8] 81384965 79755647 78212598 Smallest eigenvalues: [1] 0.39241626 0.38615728 0.29179294 0.28278681 0.26761982 0.24147663 [7] 0.14352167 -0.06275526 -0.11670627 -0.27009033 Largest eigenvalues: [1] 99919744 97568305 90528271 87518107 86104294 84404360 83460198 81392131 [9] 80773193 78470696 Smallest eigenvalues: [1] 0.38719490 0.38128697 0.37137300 0.29253625 0.23260258 0.19386983 [7] 0.09723603 0.09028213 -0.20608594 -0.38754870 Largest eigenvalues: [1] 101573675 97265975 91094229 86727869 86505302 84110706 83176442 [8] 81433427 80312861 78373686 Smallest eigenvalues: [1] 0.36979053 0.36037104 0.35282089 0.30986048 0.29735694 0.18659920 [7] 0.13799608 0.07989385 -0.21270289 -0.25359430 Largest eigenvalues: [1] 99099338 96400206 90615684 86235203 85138808 84257163 83801906 81801626 [9] 80550008 78467057 Smallest eigenvalues: [1] 0.36067447 0.33037590 0.32519103 0.28914632 0.27926988 0.25833699 [7] 0.20620909 0.17348839 0.04308379 -0.08857343 Largest eigenvalues: [1] 100109333 95779059 89793253 85959638 84429492 82324295 82113748 [8] 79702619 79228068 76713738 Smallest eigenvalues: [1] 0.42304311 0.36042991 0.31271548 0.28791304 0.27684811 0.23723371 [7] 0.21796849 0.07120660 -0.02237187 -0.63493388 Largest eigenvalues: [1] 101722966 95994150 90287994 85947993 85251462 82820882 82309043 [8] 80531250 79701594 77492205 Smallest eigenvalues: [1] 0.35159164 0.27469262 0.26731641 0.22975085 0.20200425 0.14574051 [7] 0.10283339 0.03553057 -0.24223512 -0.29002538 Largest eigenvalues: [1] 100104393 96679358 91377399 86677848 84295123 83974915 83402248 [8] 81853921 80533243 78568519 Smallest eigenvalues: [1] 0.24541885 0.22921133 0.20942235 0.17306889 0.14471083 0.13181056 [7] 0.12840794 0.06594180 -0.05268891 -0.13857291 Largest eigenvalues: [1] 98347628 97715285 91119325 86792860 84982724 84058554 83806782 81522682 [9] 80656158 78422707 Smallest eigenvalues: [1] 0.45043161 0.42815873 0.41127570 0.40312496 0.29111002 0.28456549 [7] 0.16291775 0.12988396 0.07920708 -0.11304293 Largest eigenvalues: [1] 98659812 97220020 90334387 87374829 84993913 84300274 83322906 81471387 [9] 80318216 78307722 Smallest eigenvalues: [1] 0.414645561 0.405161356 0.391337232 0.309882720 0.281418801 [6] 0.257629127 0.212674421 -0.009580257 -0.256228673 -0.269336426 Largest eigenvalues: [1] 100545573 95690410 89410685 85947519 85509873 83344931 82584344 [8] 80697921 79513686 77545403 Smallest eigenvalues: [1] 0.23581934 0.22796968 0.18294131 0.15828560 0.10241977 0.09736069 [7] 0.04861629 -0.09036118 -0.10028776 -0.27017882 Largest eigenvalues: [1] 97964961 97854617 91594218 86985569 84233435 84017202 83848501 81545500 [9] 80785376 78225536 Smallest eigenvalues: [1] 0.40792442 0.40063651 0.34636946 0.30914291 0.26640944 0.26014813 [7] 0.23482755 0.12047004 -0.04598855 -0.63290009 Largest eigenvalues: [1] 100284057 97428356 91057740 86985165 86358178 84598565 83457028 [8] 82094778 80498048 78984909 Smallest eigenvalues: [1] 0.360022975 0.350879660 0.331159082 0.306940003 0.167590046 [6] 0.085092829 0.079089555 0.001253826 -0.138100988 -0.561401944 Largest eigenvalues: [1] 99609677 97043304 90422612 87030629 85620908 83565551 83379717 80870558 [9] 80119930 77504901 Smallest eigenvalues: [1] 0.3415913 0.3309569 0.3149134 0.2865829 0.2631073 0.2591825 [7] 0.2083322 -0.1622128 -0.3029000 -0.5120033 Largest eigenvalues: [1] 101076244 95846751 90372576 85468963 84829325 82587223 82310554 [8] 80219609 79759623 77312261 Smallest eigenvalues: [1] 0.38710124 0.37010100 0.34765493 0.34716105 0.30501143 0.30040755 [7] 0.17430119 0.07250678 0.02114434 -0.09409915 Largest eigenvalues: [1] 101359247 96037799 90037897 85930293 85687172 83360660 82131275 [8] 80823348 79752626 77730805 Smallest eigenvalues: [1] 0.36442324 0.26062399 0.24861432 0.24711362 0.21461070 0.18237713 [7] 0.05285535 -0.38625953 -0.41595973 -0.49799320 Largest eigenvalues: [1] 101146649 96782490 90859991 86105633 85955891 83720021 83004798 [8] 81245029 80077986 78112681 Smallest eigenvalues: [1] 0.34406127 0.30603621 0.26345613 0.19493754 0.14651040 0.13084890 [7] -0.03040242 -0.19287732 -0.40788037 -1.27105975 Largest eigenvalues: [1] 99697647 97567490 91272965 86752775 86499952 84078647 83478288 81520268 [9] 80449796 78311124 Smallest eigenvalues: [1] 0.28593112 0.26158130 0.25038029 0.23835768 0.21921678 0.17174015 [7] 0.12009712 0.03804566 -0.31729980 -0.45209937 Largest eigenvalues: [1] 99766203 96952479 90618998 86609463 85153245 83474773 83258585 81043328 [9] 79926760 77841713 Smallest eigenvalues: [1] 0.31854883 0.31559296 0.29078055 0.25868532 0.22862717 0.15863644 [7] 0.06076703 -0.12953862 -0.30356301 -0.33887356 Largest eigenvalues: [1] 100667652 96504714 90790332 86454895 85798432 84038749 83748470 [8] 81969629 80169274 78579118 Smallest eigenvalues: [1] 0.329206836 0.295314581 0.285474527 0.219552353 0.192551997 [6] 0.164640646 0.155556805 -0.003948534 -0.029137318 -0.625787271 Largest eigenvalues: [1] 98208591 96365324 90324737 85859108 84797160 84098703 82625706 81459100 [9] 79575894 78379991 Smallest eigenvalues: [1] 0.35921361 0.33405873 0.32220054 0.31447523 0.30925022 0.26963646 [7] 0.26081412 -0.04587507 -0.07890507 -0.36534894 Largest eigenvalues: [1] 99920911 97105968 90748278 86550439 86221569 84040569 83631416 81672739 [9] 80131570 78224111 Smallest eigenvalues: [1] 0.44059449 0.40085540 0.36749858 0.36224092 0.33859151 0.23099110 [7] 0.10010755 -0.09364577 -0.41785746 -0.55836732 Largest eigenvalues: [1] 101858683 96287530 90733113 87195431 86281906 84163096 83209403 [8] 81761802 80287065 78603641 Smallest eigenvalues: [1] 0.387240987 0.385768354 0.262362390 0.262190307 0.218876142 [6] 0.121571188 0.094767420 0.008501898 -0.104583847 -0.285813405 Largest eigenvalues: [1] 100712525 95132380 88761982 85378495 85370680 82960006 82109194 [8] 80440187 78998839 77268080 Smallest eigenvalues: [1] 0.26912992 0.26069417 0.25444648 0.23181594 0.05138118 0.03159496 [7] 0.00938838 -0.29604102 -0.30825268 -0.36712438 Largest eigenvalues: [1] 100658703 96273749 90304140 86404238 85518271 83998323 83044597 [8] 81457908 79972726 78372514 Smallest eigenvalues: [1] 0.32407416 0.32114539 0.27748895 0.20810011 0.20258967 0.15805709 [7] 0.06696131 -0.29603293 -0.39726876 -0.40579943 Largest eigenvalues: [1] 102414373 96866761 91030424 86737956 86241733 83311155 83111241 [8] 81099157 80055928 78039565 Smallest eigenvalues: [1] 0.3333415 0.3307614 0.2679452 0.2353896 0.2278405 0.1887978 [7] 0.1863526 0.1000907 -0.1084047 -0.3222269 Largest eigenvalues: [1] 98916897 98272143 91085356 87671540 85458981 84930253 84063181 82249181 [9] 80542929 78842452 Smallest eigenvalues: [1] 0.3252432 0.3236702 0.2587936 0.2570901 0.2138200 0.1898233 [7] 0.1823028 -0.1941736 -0.5080307 -0.5878257 Largest eigenvalues: [1] 100534729 96270286 90312455 86447931 85916946 83876272 82927739 [8] 81415808 79810049 78194514 Smallest eigenvalues: [1] 0.33978195 0.32450688 0.32304182 0.30291759 0.26746959 0.22356956 [7] 0.19171474 0.06420481 -0.09361734 -0.40027207 Largest eigenvalues: [1] 98945519 96535586 90251214 86846749 83963327 83509976 82363560 79988630 [9] 79744645 76677797 Smallest eigenvalues: [1] 0.45524621 0.37080956 0.34075105 0.30435148 0.30271412 0.23148284 [7] 0.20631440 0.10943952 -0.06066836 -0.33361190 Largest eigenvalues: [1] 100989164 97190809 91151960 86878468 86686303 85313047 83146892 [8] 82387827 80567068 79197596 Smallest eigenvalues: [1] 0.3892958 0.3470475 0.3399532 0.3319880 0.2516991 0.2427675 [7] 0.2335483 0.1406213 -0.1165941 -0.4440134 Largest eigenvalues: [1] 100304475 96621454 90436083 86267121 84252811 83359025 82988258 [8] 80567454 80171649 77548091 Smallest eigenvalues: [1] 0.269288253 0.250293868 0.220366559 0.196425584 0.178630889 [6] 0.062653629 -0.005917483 -0.203564171 -0.355100577 -0.646384177 Largest eigenvalues: [1] 99015534 96684774 90474022 86083428 85458611 83101851 82657322 80460969 [9] 79591096 77254873 Smallest eigenvalues: [1] 0.36290943 0.34703396 0.33644038 0.33398851 0.29401877 0.27648343 [7] 0.17385559 0.10716651 0.04718870 -0.04219012 Largest eigenvalues: [1] 100962054 96221876 90325982 85848614 85510701 83740432 82137177 [8] 80795176 79751739 77817228 Smallest eigenvalues: [1] 0.37829220 0.35311905 0.33909192 0.31716540 0.30581494 0.25547262 [7] 0.15061953 -0.01193091 -0.09586587 -0.29030324 Largest eigenvalues: [1] 100002542 95813457 89908710 85616428 84842557 82955173 82268649 [8] 80359788 79633119 77446573 Smallest eigenvalues: [1] 0.47754787 0.43981971 0.37899259 0.33518024 0.31973254 0.31118224 [7] 0.21432213 0.19998290 0.08201302 -0.03258115 Largest eigenvalues: [1] 99440940 97895066 91436862 87745685 85154047 84298587 83359671 81226742 [9] 80817557 78268165 Smallest eigenvalues: [1] 0.27101616 0.25588935 0.19517155 0.15755007 0.14420408 0.11234196 [7] 0.09332968 -0.05251366 -0.22909777 -0.41137410 Largest eigenvalues: [1] 98308238 97132015 90012293 86531408 85850984 84161356 83048449 81068236 [9] 79892954 77995240 Smallest eigenvalues: [1] 0.25891842 0.20286471 0.17648655 0.08692107 0.07540490 0.07400722 [7] 0.04513013 0.03796385 -0.19277212 -0.82219494 Largest eigenvalues: [1] 98395293 95491996 89541130 85747771 83885151 82472547 81754538 79630633 [9] 78855486 76777922 Smallest eigenvalues: [1] 0.265034117 0.263216770 0.200060769 0.144824518 0.135951402 [6] 0.094062813 0.002719668 -0.089333358 -0.128194444 -0.378709045 Largest eigenvalues: [1] 100802974 96898953 89779128 86965323 86297769 83536123 83378850 [8] 80990625 80249987 77933634 Smallest eigenvalues: [1] 0.44423223 0.43057468 0.41141786 0.32293411 0.32022882 0.30047708 [7] 0.07015480 -0.02047790 -0.07635961 -0.11637907 Largest eigenvalues: [1] 99719997 96606527 90319375 86291306 85699906 83641316 83518529 81218185 [9] 80007646 78114742 Smallest eigenvalues: [1] 0.30648148 0.30177833 0.28353165 0.26055169 0.19746398 0.12267941 [7] 0.09542178 0.08065466 0.05374874 -0.06527863 Largest eigenvalues: [1] 98588148 96346058 90370063 85724436 84300938 83214285 82635419 80551794 [9] 79680096 77495749 Smallest eigenvalues: [1] 0.46611392 0.42809735 0.38164417 0.37014454 0.32838964 0.28033429 [7] 0.17073663 0.07292024 -0.09220727 -0.23463554 Largest eigenvalues: [1] 101294813 96030655 90574643 86036519 84917832 83871287 82887272 [8] 81548618 80122583 78511230 Smallest eigenvalues: [1] 0.14164692 0.13048144 0.12009368 0.11884011 0.05088143 -0.03386325 [7] -0.06549473 -0.49987929 -0.58595928 -0.98003778 Largest eigenvalues: [1] 99174427 96849984 90964309 87009184 85277483 84101003 83063713 80734758 [9] 80186701 77339438 Smallest eigenvalues: [1] 0.35522881 0.33391898 0.29018010 0.22665490 0.22489750 0.19816241 [7] 0.15149107 0.06507401 0.01013361 -0.10566087 Largest eigenvalues: [1] 97200604 95901273 89607947 85539639 83936670 83484729 82416416 80698852 [9] 79293464 77501731 Smallest eigenvalues: [1] 0.51736894 0.43903965 0.37079657 0.36382610 0.36316506 0.33474014 [7] 0.19095110 0.09643754 0.06758517 -0.18097689 Largest eigenvalues: [1] 100936465 97124387 90753727 86737058 86442390 84014544 83472842 [8] 81521887 80311551 78597793 Smallest eigenvalues: [1] 0.318307310 0.301670750 0.278214607 0.269367713 0.174941153 [6] 0.169132420 0.033620267 0.006543355 -0.006508230 -0.055428566 Largest eigenvalues: [1] 100244369 97214126 90199603 87074347 85975058 83849172 83054874 [8] 80901051 80337398 78221677 Smallest eigenvalues: [1] 0.32679061 0.30489287 0.30441204 0.24104726 0.22965224 0.18448882 [7] 0.18358250 0.16968781 -0.06203376 -0.82547669 Largest eigenvalues: [1] 103665366 97141944 91610786 87576172 86630814 84820978 83185698 [8] 82510992 80823785 79767710 Smallest eigenvalues: [1] 0.38101368 0.36948409 0.28139799 0.27135121 0.24256993 0.14743772 [7] 0.10809945 -0.01741811 -0.50122570 -0.61658680 Largest eigenvalues: [1] 100888608 96120543 90450930 86333026 85707894 83322707 82858889 [8] 80856460 79919502 77616693 Smallest eigenvalues: [1] 0.21387365 0.18062358 0.17254018 0.15777111 0.12167394 -0.09450063 [7] -0.17962922 -0.22851672 -0.27521279 -0.55376973 Largest eigenvalues: [1] 100763222 96275385 90546819 86250284 84847821 83707330 83397208 [8] 81611896 80042645 78293932 Smallest eigenvalues: [1] 0.2769779693 0.2749239376 0.2419440858 0.2331986929 0.2137693792 [6] 0.1503627679 0.0621359785 -0.0002230965 -0.0205912358 -0.1211693698 Largest eigenvalues: [1] 98918204 96958873 90387079 87079185 84074003 83653882 83320904 80522168 [9] 80219359 77195632 Smallest eigenvalues: [1] 0.15289437 0.14447446 0.10667951 0.09756873 0.06910796 0.02391637 [7] -0.08199393 -0.13848079 -0.97552196 -1.16078334 Largest eigenvalues: [1] 100946034 98203215 91632302 87502976 86311216 84351735 83885678 [8] 82017208 81008746 78868439 Smallest eigenvalues: [1] 0.42175493 0.41310529 0.35287356 0.33863731 0.27437949 0.21571342 [7] 0.18168980 0.16464877 0.02214248 -0.31607842 Largest eigenvalues: [1] 97726547 95821281 89436304 85873586 84010214 82824036 82060915 80087201 [9] 79240600 77205563 Smallest eigenvalues: [1] 0.45530619 0.40657997 0.40343068 0.35507777 0.27414260 0.26171305 [7] 0.23582644 0.12773550 0.07895893 -0.02662757 Largest eigenvalues: [1] 99501572 96108529 89886463 86232160 84735244 83089361 82524225 80357233 [9] 79486635 77412799 Smallest eigenvalues: [1] 0.37546576 0.36217346 0.33612685 0.27188506 0.25536395 0.22506505 [7] 0.07722396 0.06542981 -0.03454740 -0.38038333 Largest eigenvalues: [1] 101888207 96687900 90557291 86534274 86087605 84249645 82657748 [8] 81489801 80241120 78657434 Smallest eigenvalues: [1] 0.3829663 0.3576730 0.3179348 0.2904865 0.2726574 0.1814798 [7] 0.1340488 0.1246567 0.1002205 -0.7081133 Largest eigenvalues: [1] 100781688 96162057 90305828 86307933 85730517 84313254 82584914 [8] 81579365 80155495 78392114 Smallest eigenvalues: [1] 0.25720185 0.18441927 0.18036709 0.16851042 0.16516973 0.10176839 [7] -0.01023039 -0.03232582 -0.21278562 -0.70305152 Largest eigenvalues: [1] 99682244 97225307 90212783 87040243 86139362 84252145 83938661 81806961 [9] 80311342 78343625 Smallest eigenvalues: [1] 0.4427047 0.4049815 0.3925852 0.3780030 0.3215626 0.3124073 [7] 0.2027723 0.1571198 0.1049125 -0.3180428 Largest eigenvalues: [1] 100183480 96962421 90331201 86332950 86245620 84384667 82499721 [8] 81396873 79970492 78628466 Smallest eigenvalues: [1] 0.3428997 0.3125843 0.2793097 0.1889007 0.1762229 0.1567958 [7] 0.1406190 -0.1067381 -0.5360240 -1.2386752 Largest eigenvalues: [1] 101439994 99196613 92461994 88214410 87205290 85133520 84912125 [8] 82482582 81685771 79730755 Smallest eigenvalues: [1] 0.22330734 0.15532996 0.12645531 0.11513909 0.11454979 0.09818996 [7] 0.07608425 -0.24173806 -0.29513137 -0.39955572 Largest eigenvalues: [1] 100981529 97675053 90907080 86988525 86401914 84981329 83076282 [8] 82100043 80425333 79342156 Smallest eigenvalues: [1] 0.375467012 0.314186094 0.298370076 0.243743570 0.227951687 [6] 0.221269875 0.152860590 0.001978762 -0.087691693 -0.205439193 Largest eigenvalues: [1] 98822775 96789331 90454575 86732671 84462378 84026242 83007030 80811443 [9] 80352580 77642301 Smallest eigenvalues: [1] 0.34395981 0.32282129 0.31898461 0.30593223 0.19170489 0.15521998 [7] 0.15206199 0.07796181 0.02909169 -0.09118520 Largest eigenvalues: [1] 100431246 96485226 90277635 86816354 84523858 83869449 83298993 [8] 80820301 80313929 77669780 Smallest eigenvalues: [1] 0.31570595 0.31261599 0.27705103 0.24795505 0.24509980 0.21083553 [7] 0.09374186 0.08078667 -0.03057652 -0.37628683 Largest eigenvalues: [1] 98315310 96914895 90686815 86727557 83795096 83667986 83330736 81420720 [9] 80220792 78280765 Smallest eigenvalues: [1] 0.42315833 0.41228060 0.33859392 0.32698765 0.31095940 0.21625435 [7] 0.18027965 0.07734574 0.07627199 -0.27090047 Largest eigenvalues: [1] 98310324 96337950 89568266 85889820 84968454 82737517 82137430 79741747 [9] 79385288 76757215 Smallest eigenvalues: [1] 0.32874101 0.32329138 0.28301205 0.25990655 0.20710777 0.07916048 [7] 0.05360883 0.03074685 -0.12304220 -0.39724004 Largest eigenvalues: [1] 101742329 96161868 90214280 86082323 85946858 84139315 82504125 [8] 81524842 79737845 78334147 Smallest eigenvalues: [1] 0.33902812 0.25588174 0.17073009 0.09768705 0.08358784 0.07925768 [7] 0.04610301 -0.02036309 -0.06923355 -0.52023621 Largest eigenvalues: [1] 99377946 96227507 89932661 85832248 85750447 83340534 82723554 80388273 [9] 79592430 77126032 Smallest eigenvalues: [1] 0.37370135 0.35292936 0.34376954 0.32726138 0.32332720 0.20673636 [7] 0.15508779 -0.01555319 -0.08432910 -0.24511262 Largest eigenvalues: [1] 101660122 96579303 90659656 86381006 85903692 83663435 82505088 [8] 80963760 79759318 78122160 Smallest eigenvalues: [1] 0.40698124 0.39746455 0.39392774 0.38482903 0.34322729 0.30728987 [7] 0.23443709 0.17958136 0.12850855 -0.02104188 Largest eigenvalues: [1] 100893912 95701430 89691623 85403276 84983109 83930661 81967629 [8] 81253545 79286682 78109945 Smallest eigenvalues: [1] 0.28058589 0.27557005 0.26785546 0.16717104 0.14404553 0.13562624 [7] 0.04387775 -0.16510617 -0.22027758 -0.23868236 Largest eigenvalues: [1] 100833855 95686900 89407919 85637824 85183376 83578922 81894249 [8] 80601992 79355152 77321316 Smallest eigenvalues: [1] 0.30856184 0.29498890 0.24870723 0.22521840 0.17845647 0.13930659 [7] 0.13073043 0.11074970 0.04135221 -0.58631023 Largest eigenvalues: [1] 98925226 97225131 90958200 86527590 85330656 83819258 83430344 81500425 [9] 80064969 78455089 Smallest eigenvalues: [1] 0.435408496 0.426051207 0.370830420 0.365491524 0.363332338 [6] 0.325505455 0.289726870 0.120512469 0.009152599 -0.016328755 Largest eigenvalues: [1] 101491481 97786222 91109919 87077604 86258623 84899958 83224649 [8] 81984571 80559872 79213474 Smallest eigenvalues: [1] 0.26949642 0.25064022 0.23805653 0.22387735 0.17247543 0.11357622 [7] 0.06407078 0.03800658 -0.14528434 -0.50267908 Largest eigenvalues: [1] 98579488 97288599 90601787 86566712 85395685 84207791 83360711 81621257 [9] 79990749 78148388 Smallest eigenvalues: [1] 0.24630152 0.21286801 0.19139528 0.12797883 0.10520245 0.07003822 [7] 0.06932143 0.05127862 -0.20322455 -0.45219757 Largest eigenvalues: [1] 99788504 96781095 90323029 86288802 85447151 83499151 83054511 80790721 [9] 79825934 77999628 Smallest eigenvalues: [1] 0.28233847 0.27332421 0.24255549 0.19223129 0.17509779 0.16892407 [7] 0.13634097 -0.04575108 -0.07619969 -0.62832893 Largest eigenvalues: [1] 102070975 96958974 91032466 86551815 85698721 84401152 82687724 [8] 81811097 80251122 78846673 Smallest eigenvalues: [1] 0.367992592 0.354952071 0.277123911 0.264630827 0.248221722 [6] 0.216616993 0.004580147 -0.026011828 -0.032745576 -0.335493320 Largest eigenvalues: [1] 99692373 95593283 89967695 85487108 85040278 83482774 82833556 81205149 [9] 79490604 77931499 Smallest eigenvalues: [1] 0.4373976 0.3934819 0.3720379 0.3267914 0.2967690 0.2916497 [7] 0.2151919 0.1217187 -0.1927631 -0.5144548 Largest eigenvalues: [1] 100185529 96235469 90477765 85865236 85778839 83593597 82983255 [8] 81200962 79617963 77829308 Smallest eigenvalues: [1] 0.193964713 0.173858068 0.145228973 0.108851648 -0.001530533 [6] -0.021580024 -0.043332081 -0.116365992 -0.153404170 -0.835777802 Largest eigenvalues: [1] 100802551 95578919 90012157 86001004 85697013 84074191 83009300 [8] 82009325 79261955 78352545 Smallest eigenvalues: [1] 0.25350959 0.23266529 0.22954026 0.19772753 0.18457490 0.14639718 [7] 0.13458830 0.06311683 0.05870040 -1.03453013 Largest eigenvalues: [1] 97361770 96457179 89753151 86851004 84125034 83674723 82366893 79922875 [9] 79691922 76462850 Smallest eigenvalues: [1] 0.49098702 0.47429287 0.41323306 0.40573073 0.26364523 0.21980028 [7] 0.17063921 0.02151618 -0.01661733 -0.02147081 Largest eigenvalues: [1] 100022185 97312183 90266161 86879663 85779451 83981762 82966927 [8] 80922784 79861088 77645428 Smallest eigenvalues: [1] 0.393929726 0.379628970 0.348769947 0.298077084 0.294498408 [6] 0.171287650 0.067825543 -0.006327819 -0.497079525 -0.977199512 Largest eigenvalues: [1] 101372680 96965911 90831603 86849883 86441207 84213463 84106152 [8] 81777948 80744674 78691573 Smallest eigenvalues: [1] 0.23379998 0.22478629 0.21326304 0.16991607 0.10952807 0.09163568 [7] -0.04791301 -0.05687094 -0.08480244 -0.71676801 Largest eigenvalues: [1] 99470854 96600709 91073089 86419683 84576439 83599188 83325904 81356330 [9] 80266527 78037531 Smallest eigenvalues: [1] 0.35868647 0.30046439 0.28978962 0.24332217 0.23071174 0.22867006 [7] 0.22038347 0.09394980 0.08676295 -0.35854221 Largest eigenvalues: [1] 100447321 96125988 90691290 86066397 85655981 84163810 82437309 [8] 81510642 79615706 78343649 Smallest eigenvalues: [1] 0.4989216 0.4526539 0.4414517 0.3820443 0.3325915 0.2464236 [7] 0.1788345 0.1579513 -0.2706808 -0.3568685 Largest eigenvalues: [1] 100442674 95887200 90404768 85704093 85393585 83179683 82575634 [8] 80765677 79827911 77887586 Smallest eigenvalues: [1] 0.49987368 0.48355347 0.38170439 0.28558072 0.28056123 0.24441594 [7] 0.23474553 0.08672474 0.02762622 -0.09416828 Largest eigenvalues: [1] 100044102 96904455 90751792 86012106 85719400 84449730 83177800 [8] 81680852 80226444 78923793 Smallest eigenvalues: [1] 0.26570293 0.21788362 0.19856372 0.19441752 0.18930588 0.16594464 [7] -0.06969678 -0.16173829 -0.37795123 -0.38770709 Largest eigenvalues: [1] 99540389 96801706 90545219 87039358 84644766 84020759 83837644 81644190 [9] 80743756 78095750 Smallest eigenvalues: [1] 0.28533745 0.27285097 0.26439308 0.17680395 0.14750726 0.12236675 [7] 0.12025387 0.01609772 -0.31863381 -0.46615717 Largest eigenvalues: [1] 98756030 96260343 89626714 85869366 84112312 83533849 81823022 80673171 [9] 79167506 77430289 Smallest eigenvalues: [1] 0.497556737 0.495172261 0.454786979 0.407647662 0.404733371 [6] 0.351111730 0.303168744 0.295739882 -0.004874979 -0.081850305 Largest eigenvalues: [1] 100001593 96811445 90443219 86781841 84871065 83371787 83088770 [8] 80697214 80193685 77717951 Smallest eigenvalues: [1] 0.27024888 0.25228953 0.24906585 0.20699573 0.09297569 0.04605862 [7] 0.02870689 -0.12258123 -0.12616889 -1.75371013 Largest eigenvalues: [1] 101681597 96852039 90262326 86596967 86592030 85585003 81924257 [8] 81640207 79715809 79079677 Smallest eigenvalues: [1] 0.42669423 0.37619827 0.36227879 0.35485227 0.33659022 0.31194881 [7] 0.24630984 0.21527855 0.04338562 -0.13760546 Largest eigenvalues: [1] 100209101 95784757 90113499 85595258 84192749 83019598 82347334 [8] 80583952 79906829 77679194 Smallest eigenvalues: [1] 0.21364505 0.19610150 0.18307508 0.16729730 0.12284053 0.11405841 [7] 0.05020886 0.02771747 -0.15077623 -0.40034629 Largest eigenvalues: [1] 97885161 96990916 90435021 86145726 84984294 83532149 83221923 80997211 [9] 80090705 77825558 Smallest eigenvalues: [1] 0.3736230 0.3374071 0.3067095 0.2522343 0.2263458 0.2020081 [7] 0.1282889 0.1108718 -0.1697477 -0.3468982 Largest eigenvalues: [1] 99792901 97049188 90499093 86578980 85587743 85201281 83368518 82706389 [9] 80240701 79320293 Smallest eigenvalues: [1] 0.23983745 0.16937519 0.14493286 0.12064042 0.03046395 -0.12404895 [7] -0.22804957 -0.26109377 -0.40687424 -0.43243059 Largest eigenvalues: [1] 98663221 96184836 90206755 86439200 84275766 82709888 82577236 80233181 [9] 79406053 76959661 Smallest eigenvalues: [1] 0.4451699 0.4431561 0.3947587 0.3713716 0.3136438 0.2597714 [7] 0.2557163 0.1972763 0.1755912 -0.3928913 Largest eigenvalues: [1] 100227114 96001951 90487612 85755312 84843863 83588693 82290334 [8] 80968861 79644563 78360316 Smallest eigenvalues: [1] 0.410919202 0.307611160 0.299616485 0.234345693 0.189199443 [6] 0.176813484 0.066231980 -0.006448311 -0.118182795 -0.602259108 Largest eigenvalues: [1] 102053617 95728577 90355837 86643866 85137664 83299393 82201737 [8] 81101762 79636955 78313268 Smallest eigenvalues: [1] 0.486125659 0.462965181 0.459883153 0.434099116 0.384306000 [6] 0.271925116 0.214930852 0.208859088 -0.003055272 -0.078360690 Largest eigenvalues: [1] 99359780 95574364 89192463 85598319 85008420 82913472 81878901 80293010 [9] 79259568 77481033 Smallest eigenvalues: [1] 0.36708383 0.34148077 0.30836965 0.29042021 0.28701400 0.26216188 [7] 0.20728511 0.15805510 -0.03650854 -0.04990305 Largest eigenvalues: [1] 100905529 96010188 90135306 86022233 85319383 83609551 82578319 [8] 81422949 79897572 78583589 Smallest eigenvalues: [1] 0.2676233 0.2613640 0.2535789 0.2405641 0.1499121 0.1167343 [7] -0.1251079 -0.1319817 -0.5378806 -1.2653246 Largest eigenvalues: [1] 102480994 96922635 90456361 87227572 85749218 83918850 82009016 [8] 80981080 79575975 78067282 Smallest eigenvalues: [1] 0.37307124 0.36002937 0.26492682 0.25421795 0.19016202 0.17794390 [7] 0.12851989 0.08671662 -0.12206186 -0.33635941 Largest eigenvalues: [1] 101253708 96630967 90319504 86442156 86119368 84615128 82805730 [8] 81754687 80189235 78845408 Smallest eigenvalues: [1] 0.19353523 0.18695231 0.18301145 0.12087163 0.05417411 0.04874524 [7] -0.07298045 -0.22430083 -1.00062071 -1.07746785 Largest eigenvalues: [1] 99220169 96459103 90764410 86440524 85109591 84000907 83141039 81651755 [9] 80264644 78165685 Smallest eigenvalues: [1] 0.34473549 0.33805133 0.31608425 0.30257462 0.27864723 0.27376822 [7] 0.26083911 0.21872766 0.15576333 -0.02846172 Largest eigenvalues: [1] 99215541 96925455 90335002 86217316 85649208 83289874 83072192 80935185 [9] 79716165 77669572 Smallest eigenvalues: [1] 0.422062726 0.365105044 0.361541424 0.303638691 0.259016320 [6] 0.214095283 0.192809534 0.118222199 0.009957487 -0.163335701 Largest eigenvalues: [1] 99177312 96264953 89897189 85962893 85213247 83119823 82925459 80590512 [9] 79726333 77359286 Smallest eigenvalues: [1] 0.31748023 0.28010689 0.24958676 0.21534981 0.19876165 0.09469529 [7] 0.03420157 -0.03116153 -0.15281649 -0.62831360 Largest eigenvalues: [1] 101330400 96871011 90645525 86900087 86836824 84445946 83190552 [8] 81956624 80114943 78717887 Smallest eigenvalues: [1] 0.42182003 0.37321893 0.36559867 0.33599278 0.33403131 0.27628590 [7] 0.20453144 0.07251892 0.01448049 -0.08169950 Largest eigenvalues: [1] 101234354 96465352 90016593 86792321 86096229 83612975 82844564 [8] 80836623 80094273 77879991 Smallest eigenvalues: [1] 0.28502165 0.28159563 0.22076535 0.19000304 0.09163479 0.04482758 [7] 0.02011410 -0.21463395 -0.36370739 -0.86907074 Largest eigenvalues: [1] 98163290 96429949 90566274 85523478 84916286 83346669 82556011 80477976 [9] 79921517 77690084 Smallest eigenvalues: [1] 0.413034634 0.357226641 0.333035459 0.313837245 0.257118456 [6] 0.253594618 0.130557493 0.009496544 -0.138486543 -0.198375630 Largest eigenvalues: [1] 101215833 96028439 89631163 86527916 85422348 83023537 82324586 [8] 80534470 79481975 77594865 Smallest eigenvalues: [1] 0.36057929 0.32146896 0.29908777 0.26386354 0.23132451 0.19775808 [7] 0.17241370 0.13260063 0.07459158 -0.10803125 Largest eigenvalues: [1] 99376317 97184722 90442253 86784157 84800762 83849830 83444424 81289139 [9] 80409697 78260669 Smallest eigenvalues: [1] 0.45093523 0.38375617 0.35825271 0.35012618 0.33568940 0.31060216 [7] 0.29666262 0.14716025 0.12556358 -0.09481176 Largest eigenvalues: [1] 101980191 96206299 90831338 85940800 85783007 85085476 82397328 [8] 82011499 80149349 79132190 Smallest eigenvalues: [1] 0.3740530 0.3039464 0.2805691 0.2709624 0.2694180 0.2439939 [7] 0.2059426 0.1340264 -0.1184669 -0.2225059 Largest eigenvalues: [1] 98648677 97075359 90251792 87204225 84167032 83955898 82377871 80322949 [9] 79992359 76953498 Smallest eigenvalues: [1] 0.3117263 0.3092279 0.3082531 0.2673207 0.2572633 0.2421880 [7] 0.2332364 0.1088713 -0.2652469 -0.7921246 Largest eigenvalues: [1] 100637291 97663155 91600432 87250839 84906391 84033935 83790281 [8] 81630410 80520051 78204892 Smallest eigenvalues: [1] 0.3157915 0.3105208 0.3082454 0.2919145 0.2196778 0.2187327 [7] 0.2039208 0.2018314 -0.3792878 -0.5097217 Largest eigenvalues: [1] 101033333 96817430 90996261 86819957 86157753 83907712 83380270 [8] 81360411 80435152 78555220 Smallest eigenvalues: [1] 0.33536689 0.31122465 0.26599466 0.26344337 0.13415317 0.07480666 [7] 0.02879741 -0.06689987 -0.29059358 -1.27806633 Largest eigenvalues: [1] 100439353 96335858 91029684 85996570 85515142 83614326 82638087 [8] 80738874 80168594 77694829 Smallest eigenvalues: [1] 0.3701886 0.3474071 0.3370041 0.3316635 0.3249870 0.2999766 [7] 0.2607384 0.1335747 0.1105421 -0.0654896 Largest eigenvalues: [1] 99504253 98056766 90921346 87582338 85392336 84069003 83785429 81299277 [9] 80504347 78085088 Smallest eigenvalues: [1] 0.4252150 0.3165391 0.2465866 0.2359261 0.2105595 0.1898413 [7] 0.1357968 0.1347607 -0.1606183 -0.9055855 Largest eigenvalues: [1] 98257049 96441349 90446250 86421283 84383851 83330517 83129535 80835803 [9] 79838166 77554343 Smallest eigenvalues: [1] 0.367314405 0.352603458 0.308061400 0.297493166 0.163974263 [6] 0.141354236 -0.002717346 -0.004521682 -0.248289443 -0.595272185 Largest eigenvalues: [1] 100906724 95213698 89765312 85708252 85344429 82988737 82547424 [8] 80739200 79522527 77559180 Smallest eigenvalues: [1] 0.393009763 0.378530213 0.324461601 0.302548215 0.241551709 [6] 0.234259919 0.168916531 0.004956604 -0.115822843 -0.489686327 Largest eigenvalues: [1] 101709030 96455109 90694697 86307157 85146624 83591293 82835652 [8] 81225314 80108428 78107648 Smallest eigenvalues: [1] 0.35924798 0.32192219 0.27615622 0.24254617 0.20674056 0.20018933 [7] 0.14136990 0.12057195 -0.07844178 -0.36648820 Largest eigenvalues: [1] 101047268 97146837 91464966 86183610 85932396 83866939 83325563 [8] 81746621 80473233 78979450 Smallest eigenvalues: [1] 0.41432250 0.41208545 0.38470291 0.36856348 0.28672240 0.25119610 [7] 0.24546984 0.13816861 0.08463546 -0.06641738 Largest eigenvalues: [1] 98339014 97060796 90331726 86398801 85231788 83542340 83318184 80935956 [9] 80130436 78173536 Smallest eigenvalues: [1] 0.22786452 0.17739314 0.17048518 0.12784292 0.07301168 -0.01564448 [7] -0.06232523 -0.12448032 -0.14011643 -0.52728264 Largest eigenvalues: [1] 99407923 97677023 91448515 87075277 84967459 84014943 83426744 81236343 [9] 80535389 77794700 Smallest eigenvalues: [1] 0.2820138228 0.2780053945 0.2638150379 0.2284649713 0.1867169368 [6] 0.1042612267 0.0003991635 -0.0143361306 -0.1345914961 -0.6845269066 Largest eigenvalues: [1] 102642127 96328627 91046735 87054249 85290591 84378978 82529313 [8] 81812072 80362220 79259705 Smallest eigenvalues: [1] 0.26857557 0.25274310 0.24237258 0.19933513 0.11992270 0.08692335 [7] -0.09039050 -0.18979159 -0.46425347 -0.53226819 Largest eigenvalues: [1] 100536333 95697564 90566787 85582419 84716885 84104030 82268116 [8] 81585512 79762008 78785993 Smallest eigenvalues: [1] 0.3016737 0.2956429 0.2274541 0.2234153 0.2223100 0.2106710 [7] 0.1682070 0.1412075 -0.2994679 -0.3766576 Largest eigenvalues: [1] 100094327 96835449 90255828 87078302 85315128 84641113 82775165 [8] 81751115 80472503 79091788 Smallest eigenvalues: [1] 0.09782941 0.09120725 0.07632415 0.04633846 -0.01714826 -0.04149802 [7] -0.09844518 -0.10613495 -0.26293153 -0.59201036 Largest eigenvalues: [1] 98674990 96711708 90168630 85702560 85294522 84019255 82902394 81174221 [9] 79888084 77820834 Smallest eigenvalues: [1] 0.25390550 0.18468622 0.15901635 0.07189273 0.03538747 0.01936834 [7] -0.04194306 -0.08051520 -0.49222738 -0.53984591 Largest eigenvalues: [1] 99175993 96649196 89925313 86253973 86101869 84000552 83755032 81721742 [9] 79862414 78194303 Smallest eigenvalues: [1] 0.24267871 0.24088851 0.17119081 0.16683323 0.10931059 0.10693634 [7] 0.04144335 0.01269298 -0.04081666 -0.38048138 Largest eigenvalues: [1] 98934673 97181600 90305099 86085000 85741660 83165856 83032314 80392633 [9] 79906505 77289383 Smallest eigenvalues: [1] 0.3781959 0.3543007 0.3539110 0.3079073 0.2268129 0.1736289 [7] 0.1718044 0.1321291 -0.1225458 -0.1894113 Largest eigenvalues: [1] 98684280 96221883 89833537 85734345 85170175 82998426 82903153 80813628 [9] 79377888 77464617 Smallest eigenvalues: [1] 0.31729163 0.28393247 0.27828721 0.26678566 0.21702361 0.17935646 [7] 0.11290860 0.08813261 0.06397922 -0.10362615 Largest eigenvalues: [1] 101164957 97533564 91142876 86842767 86022148 85339588 83056556 [8] 81873315 80903182 79243170 Smallest eigenvalues: [1] 0.24847780 0.24646271 0.24385713 0.21807976 0.21541971 0.19307716 [7] 0.18976281 0.05842689 -0.14285929 -0.16916444 Largest eigenvalues: [1] 97610850 96159742 90082255 85717357 84648842 83825354 83080373 81225083 [9] 79932941 77848776 Smallest eigenvalues: [1] 0.18130475 0.15441579 0.13750425 0.06814803 0.06230960 0.03145429 [7] -0.02237198 -0.13409704 -0.14146857 -0.61639628 Largest eigenvalues: [1] 99991771 96470641 90822747 85909133 85508230 84417820 82826756 81562519 [9] 79987602 78454738 Smallest eigenvalues: [1] 0.39190286 0.36999360 0.36725042 0.33784954 0.31260116 0.28227761 [7] 0.19034259 0.02615499 -0.08496859 -0.66139602 Largest eigenvalues: [1] 101170933 95860523 90164961 86120116 85242302 83528208 82850945 [8] 81229091 79872702 77867409 Smallest eigenvalues: [1] 0.3018918 0.2916068 0.2690303 0.2573570 0.2059022 0.1788958 [7] 0.1604716 0.1112276 -0.1276134 -0.3260372 Largest eigenvalues: [1] 100348802 95383948 89115177 85543579 84787836 83865916 82284820 [8] 81144793 79522613 77939634 Smallest eigenvalues: [1] 0.21806243 0.20097464 0.17019440 0.09983011 0.07671475 0.04034179 [7] -0.13874662 -0.14632229 -0.42843390 -1.12865011 Largest eigenvalues: [1] 100446891 96752064 90624076 86526833 85815778 84110916 83093020 [8] 81450180 80031898 78344085 Smallest eigenvalues: [1] 0.34347912 0.33771385 0.30388027 0.26068041 0.22429142 0.12533827 [7] 0.05406321 -0.16790513 -0.34473263 -0.67226335 Largest eigenvalues: [1] 100954020 96530919 90644338 86510091 86166157 84572986 82896129 [8] 81887376 80043080 78783008 Smallest eigenvalues: [1] 0.32976304 0.32817440 0.29558574 0.19935133 0.06820648 0.03141085 [7] 0.01616753 -0.16307514 -0.37224911 -0.91049903 Largest eigenvalues: [1] 100073644 96974452 91277944 86140647 86019630 83777852 83449228 [8] 81577300 80206511 78471908 Smallest eigenvalues: [1] 0.4859582 0.4778705 0.3907490 0.3769227 0.3325242 0.2431768 [7] 0.1475656 0.1063857 -0.1099742 -0.2387493 Largest eigenvalues: [1] 100843574 97657236 91224040 86872348 86578842 84189771 83887339 [8] 81908675 80531393 78774095 Smallest eigenvalues: [1] 0.41091831 0.37959180 0.36609571 0.30828534 0.30820319 0.29566864 [7] 0.23653728 0.23617240 -0.03778251 -0.07781687 Largest eigenvalues: [1] 98849756 95883902 89641143 85977425 84329514 83834821 82138007 80976035 [9] 79453437 77901773 Smallest eigenvalues: [1] 0.3597069 0.3426749 0.3176368 0.3066898 0.3008171 0.2362749 [7] 0.2255470 0.1266001 0.0215460 -0.3858261 Largest eigenvalues: [1] 99685992 96083623 89974822 85781833 85086431 83154277 82496939 80687315 [9] 79559764 77496596 Smallest eigenvalues: [1] 0.34401435 0.32443904 0.31272906 0.30271971 0.25868588 0.19641356 [7] 0.19347415 0.04161880 0.01143266 -0.01861231 Largest eigenvalues: [1] 99526737 97599324 90739713 86851354 84768870 83933782 83288217 81059766 [9] 80239519 77968785 Smallest eigenvalues: [1] 0.31958511 0.24201136 0.24045561 0.20323544 0.19925910 0.16504003 [7] 0.06541139 0.01959612 -0.22043898 -0.49159819 Largest eigenvalues: [1] 99389963 97077459 90241400 86256408 85395784 83688590 83460306 81001723 [9] 79921756 77555647 Smallest eigenvalues: [1] 0.4019783 0.3851504 0.3728061 0.3665693 0.2722349 0.2492861 [7] 0.2387072 0.1566864 0.1494581 -0.2031747 Largest eigenvalues: [1] 100250819 97554856 91451339 86923529 86370624 85303230 83389507 [8] 82392815 80458509 79204142 Smallest eigenvalues: [1] 0.4174715 0.3964313 0.3753994 0.3532460 0.3337285 0.3157935 [7] 0.2328301 0.0538846 -0.1664282 -0.6054575 Largest eigenvalues: [1] 101218859 95451407 89119243 85773390 85330127 83351268 82143931 [8] 80631644 79413157 77627363 Smallest eigenvalues: [1] 0.247810414 0.203461416 0.172893552 0.131337930 0.099074611 [6] 0.041276482 0.033758348 0.002250354 -0.099130422 -0.579543265 Largest eigenvalues: [1] 100127740 97125677 90568981 87083268 86531624 84981164 83416024 [8] 82330022 80437442 78884262 Smallest eigenvalues: [1] 0.3261207 0.3131559 0.2912936 0.2673997 0.2652748 0.1410470 [7] 0.1131774 -0.1064315 -0.1227680 -0.4471696 Largest eigenvalues: [1] 99803615 95916262 89859432 85844871 83964593 83282382 82882476 80819039 [9] 79869351 77600178 Smallest eigenvalues: [1] 0.22086688 0.20527194 0.20484562 0.19209282 0.14680942 0.12868537 [7] 0.05852761 -0.17623479 -0.30502828 -0.35009102 Largest eigenvalues: [1] 100773414 97440254 90462421 87053710 86544023 84653914 83347248 [8] 81711713 80404946 78731973 Smallest eigenvalues: [1] 0.43178468 0.40362088 0.34779946 0.27933677 0.24824041 0.19570727 [7] 0.18820812 0.15917898 -0.01524716 -0.05846435 Largest eigenvalues: [1] 98705859 95258465 88951857 85295467 84632320 82496491 82014205 80147669 [9] 79011301 76861834 Smallest eigenvalues: [1] 0.4298952 0.3298005 0.3181860 0.3139809 0.2805922 0.2355021 [7] 0.2087183 0.1169353 -0.3322489 -0.5148637 Largest eigenvalues: [1] 99740042 97098475 90821440 86668124 85420287 83640597 83520211 80888302 [9] 80460971 77860036 Smallest eigenvalues: [1] 0.4133652 0.3894668 0.3580659 0.3536213 0.3262899 0.2934145 [7] 0.2265833 0.1346292 0.1014016 -0.1088358 Largest eigenvalues: [1] 101042206 95733767 89403257 86406096 85510865 84336353 82026821 [8] 81374630 79411243 78341398 Smallest eigenvalues: [1] 0.38987647 0.30183137 0.29022469 0.28771409 0.27436498 0.26862774 [7] 0.20945322 0.08533152 -0.14396644 -0.54787710 Largest eigenvalues: [1] 100181949 97346029 91153469 86891362 85474813 84293709 83082966 [8] 81494852 79792988 78460229 Smallest eigenvalues: [1] 0.35898569 0.26377683 0.22188948 0.21136922 0.08472485 -0.01356438 [7] -0.03667985 -0.07921603 -0.16598165 -0.81080051 Largest eigenvalues: [1] 100807757 96517035 91007425 86558814 86001376 84142841 82944098 [8] 82040829 80131488 79099517 Smallest eigenvalues: [1] 0.46184799 0.41285785 0.37399167 0.30409468 0.28056764 0.26628987 [7] 0.25465284 0.23195175 0.14651147 -0.03860563 Largest eigenvalues: [1] 99857962 96986364 90463621 86629042 85754393 83527884 83332071 81022403 [9] 79974752 77694400 Smallest eigenvalues: [1] 0.36466491 0.33555811 0.31252402 0.30098028 0.29458908 0.21853265 [7] 0.15170526 0.11998501 0.09915988 -0.07292839 Largest eigenvalues: [1] 100811004 96670618 90920318 86678218 85721395 84719400 83242146 [8] 81851574 80753979 78987519 Smallest eigenvalues: [1] 0.44598612 0.44013086 0.41854185 0.31997958 0.30250959 0.29829036 [7] 0.24781988 0.20233861 -0.04654796 -0.39349475 Largest eigenvalues: [1] 98313810 95636098 89221450 85726450 84483585 83137141 82759818 80821819 [9] 79294555 77421350 Smallest eigenvalues: [1] 0.23989531 0.22090523 0.21455050 0.16486679 0.15884446 0.15840597 [7] 0.05598711 -0.04339037 -0.38878132 -0.49868785 Largest eigenvalues: [1] 98789330 96737489 90634120 86462586 84912757 83648484 83415411 81118730 [9] 80207245 77965196 Smallest eigenvalues: [1] 0.31168222 0.25353680 0.24949300 0.24021093 0.10174613 0.09481438 [7] 0.04240132 0.02840958 -0.22619922 -0.51343839 Largest eigenvalues: [1] 98571227 95006935 89206289 85122555 84330635 83028969 82022366 80452708 [9] 79145343 77415463 Smallest eigenvalues: [1] 0.4356259 0.2943868 0.2841524 0.2626148 0.2459918 0.2028113 [7] 0.2014719 0.1960665 0.1558654 -0.3909477 Largest eigenvalues: [1] 98645618 96999844 89988999 86642169 85932831 83894257 83644449 81331765 [9] 80073997 78042546 Smallest eigenvalues: [1] 0.29604328 0.29275349 0.25501350 0.22155154 0.12901531 0.12792562 [7] -0.01038097 -0.14064843 -0.19711501 -0.27851100 Largest eigenvalues: [1] 99826191 96638642 90782386 86355378 85632277 83680330 82911629 81234733 [9] 79988670 78337364 Smallest eigenvalues: [1] 0.3905256 0.3512474 0.3503530 0.3019063 0.2872718 0.2746599 [7] 0.1325682 -0.1414563 -0.3217902 -0.5096902 Largest eigenvalues: [1] 99439559 96099265 89657085 85914612 85023736 83216149 82045496 80202562 [9] 79314430 77136311 Smallest eigenvalues: [1] 0.35512886 0.33572438 0.27205764 0.26343692 0.24087203 0.19521688 [7] 0.14989329 0.11865864 0.09634692 -0.20818026 Largest eigenvalues: [1] 99313115 98943551 91672512 87995046 86206852 84658099 84550148 81772491 [9] 81090329 78590846 Smallest eigenvalues: [1] 0.4176510 0.4123693 0.3740232 0.3533558 0.3501120 0.2910960 [7] 0.2196074 0.1644901 -0.2416777 -0.4304060 Largest eigenvalues: [1] 99300748 97008419 91005478 86882992 85305778 83810269 83641137 81392641 [9] 80519647 78570503 Smallest eigenvalues: [1] 0.42783581 0.33525190 0.32505385 0.31782397 0.25703251 0.05261268 [7] 0.03851447 -0.12354776 -0.12645968 -0.14051009 Largest eigenvalues: [1] 100872972 96462069 90884476 86305128 85628522 83283524 82956559 [8] 80836011 80182261 77942612 Smallest eigenvalues: [1] 0.3654109 0.3503852 0.2750677 0.2730756 0.2332120 0.1445943 [7] 0.1171699 0.1128073 -0.5573580 -0.5791528 Largest eigenvalues: [1] 102041803 96745366 91211167 87049489 86529897 85507986 83164655 [8] 82638721 80661069 79663244 Smallest eigenvalues: [1] 0.15036286 0.11633921 0.11612360 0.07169196 0.06805087 0.01348978 [7] -0.07297831 -0.15168004 -0.45481533 -1.08288060 Largest eigenvalues: [1] 100481178 95598998 90225580 86193010 85105276 84420073 82055738 [8] 81742213 79332865 78432874 Smallest eigenvalues: [1] 0.413418226 0.410581623 0.375521935 0.350286370 0.295574365 [6] 0.257760878 0.196999313 0.195384777 -0.005708832 -0.146178692 Largest eigenvalues: [1] 98659506 97336137 90470268 87226046 85277366 84101153 83722740 81443367 [9] 80460739 78368846 Smallest eigenvalues: [1] 0.3493328 0.3210295 0.2938926 0.2633207 0.2515230 0.2184117 [7] 0.1234785 -0.3392918 -0.4321458 -0.7186832 Largest eigenvalues: [1] 103000364 96991662 91290069 87558242 86065316 84245699 82719487 [8] 81803102 80020080 78775299 Smallest eigenvalues: [1] 0.38873555 0.38228775 0.35190385 0.30146636 0.22268057 0.19337000 [7] 0.15367902 0.03586512 -0.28537440 -0.36822807 Largest eigenvalues: [1] 99807124 97462112 90549676 87122542 86024576 84727028 83737617 81978660 [9] 80667245 78896223 Smallest eigenvalues: [1] 0.45802985 0.40430872 0.37328945 0.30458125 0.27351608 0.17827483 [7] 0.15988937 0.07150365 -0.13564795 -0.98566650 Largest eigenvalues: [1] 98565510 96356127 89377955 86021926 85209589 83355612 82422409 80715630 [9] 79285456 77553673 Smallest eigenvalues: [1] 0.36198986 0.29722165 0.27378697 0.24281578 0.20708917 0.20637064 [7] -0.05774765 -0.28746609 -0.35010056 -0.41462727 Largest eigenvalues: [1] 100443291 97370005 91576859 86871494 85576274 84474251 83476583 [8] 81881762 80614884 78902166 Smallest eigenvalues: [1] 0.412420724 0.397234631 0.372601233 0.343982289 0.276425600 [6] 0.073605785 0.066395119 0.006211796 -0.092384215 -0.412626624 Largest eigenvalues: [1] 101592904 96468565 90930067 86662332 85826233 84073104 83167226 [8] 81931662 80245909 78873855 Smallest eigenvalues: [1] 0.31766340 0.28555370 0.26657389 0.25207415 0.12964632 0.05470906 [7] 0.05138081 0.01219506 -0.11888441 -0.24786382 Largest eigenvalues: [1] 97513489 97459606 89847751 87170016 85034123 83898672 83241974 80669351 [9] 79915457 77321076 Smallest eigenvalues: [1] 0.36259016 0.32510649 0.31104789 0.31054227 0.22494381 0.12830367 [7] 0.10534501 -0.01811261 -0.11267499 -0.19945695 Largest eigenvalues: [1] 101581557 97371933 90752795 86642617 86593811 84478237 82929531 [8] 81555534 80134920 78638303 Smallest eigenvalues: [1] 0.34852809 0.30154705 0.28182805 0.27422679 0.21324471 0.20509612 [7] 0.11915295 0.05850887 -0.15246653 -0.17324254 Largest eigenvalues: [1] 100959225 96947317 90632515 86595530 86200845 84030255 82914741 [8] 81191769 80237991 78319704 Smallest eigenvalues: [1] 0.3306743 0.3267151 0.3260201 0.2644086 0.2437870 0.2324932 [7] 0.2275857 0.1547772 0.1322022 -0.2226303 Largest eigenvalues: [1] 99427851 96842193 90335725 86651494 85398602 84666975 82748954 81481666 [9] 80312199 78823051 Smallest eigenvalues: [1] 0.28036522 0.20974969 0.19924252 0.19535833 0.07686242 -0.06838964 [7] -0.09790813 -0.20138624 -0.27076025 -0.59267703 Largest eigenvalues: [1] 100186486 95192459 89605903 85899692 84925204 82748408 81483289 [8] 80133167 78641730 76729541 Smallest eigenvalues: [1] 0.39567951 0.37255765 0.33091148 0.32920575 0.24986001 0.22078849 [7] 0.10474609 0.09977335 -0.01451989 -0.07664195 Largest eigenvalues: [1] 97576027 96634922 90277359 86515204 84403290 84059790 83063013 81005403 [9] 80241211 77894234 Smallest eigenvalues: [1] 0.46196283 0.44702071 0.42106215 0.38881487 0.34270979 0.28966687 [7] 0.12610041 0.08757987 0.07175879 -0.17344314 Largest eigenvalues: [1] 99446021 97876793 91056313 87805679 85616386 84230947 83275239 80918587 [9] 80630147 77457093 Smallest eigenvalues: [1] 0.38013011 0.32168334 0.28323011 0.26469973 0.16896389 0.14120495 [7] 0.04221954 -0.02844278 -0.09389949 -0.69687334 Largest eigenvalues: [1] 100938869 97327282 90984649 87075130 86867850 84631827 83084530 [8] 81742345 80281937 78608471 Smallest eigenvalues: [1] 0.32451366 0.29226107 0.26930681 0.21650710 0.15242247 0.14996509 [7] 0.03492967 -0.08650536 -0.14121931 -0.52673655 Largest eigenvalues: [1] 98207381 96015909 90220533 86779395 84299597 83799183 82474227 81130599 [9] 79560418 78160258 Smallest eigenvalues: [1] 0.38247182 0.33960666 0.33632712 0.33614558 0.33448039 0.31918940 [7] 0.06603729 -0.21687199 -0.48108407 -0.53153690 Largest eigenvalues: [1] 100506121 97324269 91087321 86971520 86522545 84543591 83887817 [8] 81907949 80645708 78448382 Smallest eigenvalues: [1] 0.40966937 0.40552871 0.40461496 0.31634271 0.28671932 0.25735547 [7] 0.24254003 0.21292655 0.19136091 -0.03800068 Largest eigenvalues: [1] 100366602 96299516 90081679 86061161 85693226 85215718 82329827 [8] 82039059 79801765 78833439 Smallest eigenvalues: [1] 0.367481885 0.325608474 0.312482113 0.301844344 0.286118792 [6] 0.178648339 0.140210187 0.105325389 0.006689325 -0.140624904 Largest eigenvalues: [1] 101152795 96340251 89994067 86137877 86072559 84462059 82157791 [8] 81366706 79756736 78634466 Smallest eigenvalues: [1] 0.26433533 0.24645939 0.22258122 0.20439770 0.19219744 0.17692440 [7] 0.01654297 -0.03861417 -0.16754769 -0.53568710 Largest eigenvalues: [1] 100385612 97370908 90605723 86866913 85775265 84338632 83168766 [8] 81816590 79804868 78564805 Smallest eigenvalues: [1] 0.31470725 0.29454019 0.26824987 0.25385231 0.25300604 0.21998877 [7] 0.20568504 0.11972803 -0.08919151 -0.55488497 Largest eigenvalues: [1] 99531000 96757245 90677520 85743029 84545139 83436285 82677411 80579039 [9] 80017944 77596081 Smallest eigenvalues: [1] 0.33153485 0.31889949 0.29358724 0.27698368 0.27496241 0.21402571 [7] 0.18882513 0.07641162 -0.01237906 -0.20276627 Largest eigenvalues: [1] 98358100 97587822 91101491 87478398 84519448 84278432 83985561 81668966 [9] 80899400 78731260 Smallest eigenvalues: [1] 0.47636692 0.46264344 0.40341899 0.39259755 0.28619891 0.27660441 [7] 0.26615804 0.25970389 0.24814522 -0.03421058 Largest eigenvalues: [1] 99516066 97817099 91433870 87241328 85441102 84250136 83740582 81595518 [9] 80499757 78705907 Smallest eigenvalues: [1] 0.3130544 0.2721272 0.2647464 0.1678493 0.1634615 0.1501569 [7] 0.1170997 -0.1026341 -0.3805293 -0.5620523 Largest eigenvalues: [1] 101038478 95999075 90631344 85919896 84544183 83873621 82729992 [8] 81517372 80007967 78202866 Smallest eigenvalues: [1] 0.4930289 0.4266294 0.3881942 0.3764321 0.3678763 0.3052265 [7] 0.2951427 0.1868237 0.1046018 -0.1401305 Largest eigenvalues: [1] 100142376 96471243 90057896 86034674 85826868 83496529 82257378 [8] 81035687 79433736 78069602 Smallest eigenvalues: [1] 0.4417768 0.3938884 0.3816582 0.3635002 0.3356939 0.2253713 [7] 0.1907556 0.1902335 0.1620243 -0.3335311 Largest eigenvalues: [1] 100510442 96648144 90819797 86268962 85648605 84744178 83043526 [8] 82259391 79972448 78940390 Smallest eigenvalues: [1] 0.49576138 0.48729719 0.43282818 0.41013811 0.32650665 0.29477459 [7] 0.15968936 0.05172536 -0.01414389 -0.07858247 Largest eigenvalues: [1] 99399366 96981827 90457232 87214965 85410754 83983908 83807348 81353989 [9] 80540737 78239019 Smallest eigenvalues: [1] 0.30888447 0.30242531 0.28613162 0.21658071 0.21546123 0.21271676 [7] 0.15560434 0.12327398 -0.05126137 -0.06203630 Largest eigenvalues: [1] 97769589 96085284 89105479 86175243 84071642 83671538 82392293 80606501 [9] 79304595 77622715 Smallest eigenvalues: [1] 0.29759824 0.29147718 0.28363514 0.20669748 0.12468125 0.09164781 [7] 0.07364580 -0.09970118 -0.29555256 -1.07550728 Largest eigenvalues: [1] 100963119 96944552 91797519 86566994 85065406 84129288 83301730 [8] 81853250 80259993 78550399 Smallest eigenvalues: [1] 0.3872525 0.3368564 0.3157052 0.2706642 0.2641446 0.2269352 [7] 0.1953448 0.1298331 -0.1255989 -0.3009752 Largest eigenvalues: [1] 100710071 96900710 90770975 86403134 86384578 85041336 82780290 [8] 82264861 80028037 79038059 Smallest eigenvalues: [1] 0.27527613 0.27137581 0.25914801 0.25656747 0.18461267 -0.07290681 [7] -0.22345898 -0.30605851 -0.37479661 -0.66340140 Largest eigenvalues: [1] 102341349 97296731 91632741 87176338 86239546 84193230 83462415 [8] 81879646 80564525 78812216 Smallest eigenvalues: [1] 0.18093415 0.16889585 0.16401746 0.12027430 0.11921471 0.02689398 [7] -0.05238253 -0.08571017 -0.21302257 -0.78366284 Largest eigenvalues: [1] 99273908 96703045 90691733 85924890 85183323 83474669 83282159 81211530 [9] 79906412 78023656 Smallest eigenvalues: [1] 0.40504477 0.38761633 0.36105110 0.31586540 0.27253369 0.27170056 [7] 0.17905399 0.16897847 0.04275914 -0.31065256 Largest eigenvalues: [1] 99181698 96337933 90693090 85942945 85549255 84301171 82891302 81839458 [9] 79912227 78530318 Smallest eigenvalues: [1] 0.32497730 0.31502244 0.31166086 0.24544025 0.15936889 0.01772494 [7] -0.18640595 -0.25401010 -0.75985697 -1.06714046 Largest eigenvalues: [1] 100692647 96124679 90141395 86941286 84984543 83897592 83584307 [8] 81554695 80684697 78010335 Smallest eigenvalues: [1] 0.42801832 0.42539177 0.38526550 0.37777895 0.32664254 0.19038603 [7] 0.13137168 -0.06903234 -0.12470086 -0.19110222 Largest eigenvalues: [1] 100802700 95469561 89269078 86234024 85305939 83013523 82030838 [8] 80378974 79238458 77538546 Smallest eigenvalues: [1] 0.389360340 0.307090100 0.275553361 0.190172059 0.167413842 [6] 0.142664031 0.034919390 0.002410147 -0.187142511 -0.524603582 Largest eigenvalues: [1] 99882346 96742565 90319643 86810194 85668244 84921044 83670895 82163323 [9] 80655221 79207638 Smallest eigenvalues: [1] 0.4444926 0.3876377 0.3421871 0.2715840 0.2691509 0.2576597 [7] 0.2287924 0.1353497 0.1300004 -0.4540134 Largest eigenvalues: [1] 99247085 97300266 90772171 86359388 86203535 84036542 83389326 81440103 [9] 80121510 78255658 Smallest eigenvalues: [1] 0.3367188 0.3363577 0.3163925 0.3077456 0.2520839 0.1984519 [7] 0.1654329 0.1511559 0.1218176 -0.6849484 Largest eigenvalues: [1] 98103629 96808812 89824855 87433487 84193380 83302332 82831640 80372829 [9] 79986354 77263103 Smallest eigenvalues: [1] 0.35844824 0.32557692 0.32028014 0.27086770 0.24328510 0.23321196 [7] 0.16191931 0.08792023 0.08357682 -0.41716542 Largest eigenvalues: [1] 100064707 97117938 91043256 86667965 85307498 84400614 83384408 [8] 81951674 80233113 78321996 Smallest eigenvalues: [1] 0.31235982 0.28653734 0.26557183 0.21289238 0.18735190 0.13647567 [7] -0.02043652 -0.08609886 -0.39657922 -0.42953845 Largest eigenvalues: [1] 101497705 96558429 90989372 86085057 85672474 84128802 82489598 [8] 81342491 79805539 78182649 Smallest eigenvalues: [1] 0.4434507 0.4402761 0.4272075 0.4084900 0.3901887 0.2774006 [7] 0.2319455 0.1820148 -0.1699446 -0.2283848 Largest eigenvalues: [1] 101230361 97505289 91292684 86916883 86370348 84471908 83559688 [8] 81883329 80778357 78737330 Smallest eigenvalues: [1] 0.47443623 0.33366809 0.32528364 0.30299483 0.28556437 0.23937332 [7] 0.15941807 0.15485803 0.03977466 -0.76673232 Largest eigenvalues: [1] 101064732 95934326 90388999 86225516 86127291 84366754 82548097 [8] 81989279 79670604 78618232 Smallest eigenvalues: [1] 0.3763945 0.3703879 0.2971830 0.2949618 0.2809408 0.1497314 [7] 0.1345459 0.1339935 0.1173175 -0.1741223 Largest eigenvalues: [1] 99324338 95980869 89475536 85664404 84681862 82978472 82534680 80315564 [9] 79327386 77113054 Smallest eigenvalues: [1] 0.32014156 0.27355147 0.26006149 0.23813363 0.16395446 0.14456900 [7] 0.12797590 0.10187202 0.02259674 -0.18304101 Largest eigenvalues: [1] 98239583 96522651 89671222 86831295 84096990 83702641 83327060 80711535 [9] 80091839 77628541 Smallest eigenvalues: [1] 0.51832589 0.50853354 0.46171003 0.36713185 0.35744094 0.31503639 [7] 0.23356697 0.14202624 -0.02140405 -0.47520121 Largest eigenvalues: [1] 100826841 97186879 90642394 86932673 86306226 84271884 83405009 [8] 81716878 80259589 78492801 Smallest eigenvalues: [1] 0.33055003 0.26887783 0.23941970 0.22154527 0.21153702 0.16444013 [7] 0.05541203 0.02172149 -0.07982424 -0.59516971 Largest eigenvalues: [1] 99860388 96375843 90051865 86101020 85026663 82761676 82531838 80174690 [9] 79740935 77199788 Smallest eigenvalues: [1] 0.40094796 0.39698628 0.36372813 0.30916698 0.26878533 0.23061996 [7] 0.15816240 0.08863852 -0.16325574 -0.41367608 Largest eigenvalues: [1] 99339572 96177885 89119526 86128071 85178866 83250724 82181430 80228139 [9] 79206758 77206148 Smallest eigenvalues: [1] 0.27022034 0.25738389 0.24325426 0.18231782 0.16899300 0.15882719 [7] 0.05213702 0.00232125 -0.08915689 -0.55623809 Largest eigenvalues: [1] 101154560 97359458 90439775 86940477 86327440 85379846 83484008 [8] 82588059 80668174 79556214 Smallest eigenvalues: [1] 0.26476612 0.25453524 0.24074930 0.19302081 0.15186811 0.09148297 [7] 0.02960722 -0.05878278 -0.22715014 -0.47184486 Largest eigenvalues: [1] 99374674 96143651 90020105 86004860 84711374 83310391 83169945 80608895 [9] 79894433 77226321 Smallest eigenvalues: [1] 0.2555768 0.2437922 0.1855864 0.1835593 0.1677392 0.1359722 [7] -0.1626289 -0.3879118 -0.4752315 -0.5627773 Largest eigenvalues: [1] 99603949 97714900 90945085 87474762 85535671 85097065 84118697 82102221 [9] 81212835 79386653 Smallest eigenvalues: [1] 0.42103244 0.36843288 0.35070493 0.30339784 0.26206657 0.24816267 [7] 0.11020235 -0.03674066 -0.08479632 -0.11568730 Largest eigenvalues: [1] 99966369 97238194 90968452 87089423 86045335 85159104 83716747 82058895 [9] 80886408 79007651 Smallest eigenvalues: [1] 0.41964079 0.39708324 0.36798591 0.32837872 0.28816739 0.24332365 [7] 0.20902962 0.07001906 -0.28917419 -0.34205088 Largest eigenvalues: [1] 100274123 95590151 89807011 85429433 85277995 83539786 82549506 [8] 81004468 79672496 78180012 Smallest eigenvalues: [1] 0.238578507 0.204091551 0.163361071 0.097138253 -0.003480877 [6] -0.011437154 -0.084189455 -0.222451568 -0.450870889 -0.459885916 Largest eigenvalues: [1] 98631208 98502639 91682619 87527928 85997843 84834210 84658397 82144352 [9] 81322062 79615434 Smallest eigenvalues: [1] 0.31775003 0.31259503 0.29501773 0.28488925 0.25772885 0.22963215 [7] 0.15138230 0.06356559 -0.35227936 -0.37865105 Largest eigenvalues: [1] 100835779 96614215 91052843 86178704 85978099 83477858 82950042 [8] 81197642 79849336 78130332 Smallest eigenvalues: [1] 0.30700013 0.30382554 0.22228123 0.22120591 0.20781446 0.16799861 [7] 0.09631524 0.04219502 -0.38080375 -1.01285960 Largest eigenvalues: [1] 99852021 97804180 91033134 87381280 85618725 84090058 83788899 81601724 [9] 80423487 78332127 Smallest eigenvalues: [1] 0.3556360 0.3469958 0.3372829 0.3291750 0.2365599 0.2196748 [7] 0.1652917 -0.1564478 -0.2888138 -1.0287194 Largest eigenvalues: [1] 100934143 96516788 90460779 86612506 86080385 83588681 82883591 [8] 80999062 80124093 78214540 Smallest eigenvalues: [1] 0.41521572 0.39352013 0.28040467 0.27938557 0.27487905 0.19901880 [7] 0.16677045 0.10998470 -0.07011668 -0.24481959 Largest eigenvalues: [1] 100232367 96664166 90607881 86391789 85775096 85234793 82572038 [8] 81961799 79907160 78883343 Smallest eigenvalues: [1] 0.456757452 0.409897708 0.364451849 0.341830965 0.298728278 [6] 0.264774395 0.179002052 0.002590262 -0.014032614 -0.097905251 Largest eigenvalues: [1] 100398340 96152118 89812650 86022307 85404940 83667160 82603318 [8] 80968069 79875938 77775304 Smallest eigenvalues: [1] 0.22910671 0.18627107 0.12889673 0.11385283 0.09121772 0.04640370 [7] -0.03224603 -0.05696002 -0.13875573 -0.45451063 Largest eigenvalues: [1] 98401990 96132936 90046505 85392589 85258346 83158323 82688916 80911795 [9] 79371969 77908138 Smallest eigenvalues: [1] 0.200857702 0.171291083 0.150766148 0.133182230 0.073107500 [6] 0.022559550 0.019792492 -0.009079662 -0.096222206 -0.517303959 Largest eigenvalues: [1] 100496639 97913830 90973567 87288930 85943361 83984851 83318784 [8] 81539834 80135231 78334055 Smallest eigenvalues: [1] 0.325403210 0.322213689 0.239763807 0.158657945 0.142719925 [6] 0.120036090 0.098669925 0.085226741 0.002312567 -0.129679458 Largest eigenvalues: [1] 98468892 97023170 90062160 86234456 85318479 84454984 83049998 81659863 [9] 80166136 79058901 Smallest eigenvalues: [1] 0.47093306 0.46537889 0.42278739 0.40808225 0.34524350 0.23265912 [7] 0.18663709 0.15769439 -0.03348797 -0.09378785 Largest eigenvalues: [1] 101412363 96733528 90795682 86751817 86161238 85037972 83173419 [8] 82310430 80517471 79197617 Smallest eigenvalues: [1] 0.37746889 0.36906160 0.35372689 0.33227728 0.27779715 0.22030154 [7] 0.11112100 0.09159873 -0.01520428 -0.15226064 Largest eigenvalues: [1] 98507840 96049962 89685590 86030609 84114950 83071707 82351260 80424932 [9] 79398183 77186555 Smallest eigenvalues: [1] 0.4510728 0.4166553 0.3955503 0.3911207 0.3901021 0.3390220 [7] 0.2454311 0.2192114 0.1066379 -0.1003724 Largest eigenvalues: [1] 99385739 95877045 89926437 85626417 84428922 83769044 82406760 80842115 [9] 79892017 78052860 Smallest eigenvalues: [1] 0.45917983 0.43705319 0.39917284 0.32644766 0.32244990 0.25560739 [7] 0.20754910 0.17152837 0.02960772 -0.30649185 Largest eigenvalues: [1] 97593758 96797793 90412581 86843835 83763077 83657085 83503416 81252114 [9] 80393664 78365015 Smallest eigenvalues: [1] 0.5577591 0.5422413 0.4550689 0.3970801 0.3969024 0.2743381 [7] 0.2419286 0.1838882 0.1512396 -0.2603315 Largest eigenvalues: [1] 99749981 95985642 90152596 85829393 84716477 83634117 82692199 81117954 [9] 79968939 78322475 Smallest eigenvalues: [1] 0.225602554 0.214581145 0.145728807 0.137412819 0.009044246 [6] -0.025110306 -0.071930109 -0.078152355 -0.818993267 -1.079613921 Largest eigenvalues: [1] 99145018 98039822 92026200 87580033 84741617 84724122 83885947 81650270 [9] 81202669 78199522 Smallest eigenvalues: [1] 0.27295827 0.27126668 0.25338751 0.20571338 0.19921919 0.14020680 [7] 0.07485622 -0.00696153 -0.08793807 -0.30348721 Largest eigenvalues: [1] 98714579 95510878 89163120 85375294 85003878 82879972 82100894 79885885 [9] 79218544 76802091 Smallest eigenvalues: [1] 0.39016713 0.34351609 0.31708102 0.28833646 0.19754479 0.16785071 [7] 0.15538290 -0.01928409 -0.21052918 -0.63022140 Largest eigenvalues: [1] 98952563 96259597 90249322 86635513 84666844 83189106 82699595 80565157 [9] 79948541 77542668 Smallest eigenvalues: [1] 0.3110508 0.3071504 0.2833117 0.2313054 0.2177674 0.1944799 [7] 0.1605563 -0.1197110 -0.5500344 -0.5923815 Largest eigenvalues: [1] 99952098 97206664 91280644 86848216 85243148 84561371 83422386 81941578 [9] 80416363 78916156 Smallest eigenvalues: [1] 0.3058200 0.2953359 0.2774179 0.2463047 0.2106506 0.1819372 [7] 0.1802838 -0.2475356 -0.4367461 -1.1228400 Largest eigenvalues: [1] 99782269 98246863 92254381 87741042 85344211 84510955 84218629 81875595 [9] 80746008 78916457 Smallest eigenvalues: [1] 0.35097233 0.33685414 0.27344704 0.23838261 0.22604015 0.20232826 [7] 0.16410251 0.13838710 -0.01559964 -0.08264279 Largest eigenvalues: [1] 98494382 96327689 89393280 85694590 85087190 83780496 82577073 80876820 [9] 79653915 77757428 Smallest eigenvalues: [1] 0.37937807 0.36589304 0.35130278 0.32011392 0.28659130 0.24159562 [7] 0.12639446 0.12224412 0.10368273 -0.07252465 Largest eigenvalues: [1] 99531731 96082083 90444344 85923944 84600149 83404067 82337174 80584053 [9] 79712198 77530214 Smallest eigenvalues: [1] 0.238748482 0.202007249 0.164039169 0.070645165 0.030505432 [6] -0.003217926 -0.039184376 -0.183825122 -0.305765444 -0.468407192 Largest eigenvalues: [1] 99803943 95824833 89523787 86292236 84991522 83002839 82704141 81046391 [9] 79261750 77864668 Smallest eigenvalues: [1] 0.076232917 0.064960254 0.042619159 -0.002496888 -0.009726674 [6] -0.056054187 -0.057546895 -0.126693962 -0.560913727 -0.631223870 Largest eigenvalues: [1] 100906869 96438701 89636458 86996065 85945626 83634729 82832010 [8] 80971638 79665932 77660396 Smallest eigenvalues: [1] 0.23007883 0.18217963 0.14480795 0.12472199 0.09424502 0.04590686 [7] 0.01098493 -0.04388355 -0.32845037 -0.34599752 Largest eigenvalues: [1] 99644240 97125114 90488781 86214707 85921969 83448268 83191621 81032966 [9] 79975993 78067678 Smallest eigenvalues: [1] 0.36686289 0.35672981 0.35636914 0.32576554 0.31711246 0.27608313 [7] 0.21698663 0.15408451 -0.01159193 -0.09183335 Largest eigenvalues: [1] 100676934 98294168 91737070 88109327 85598193 84297736 84139066 [8] 81350700 80891018 78184995 Smallest eigenvalues: [1] 0.297019246 0.234955405 0.223689486 0.197098203 0.159538660 [6] 0.107199518 0.031883553 -0.005987563 -0.185209530 -0.464716667 Largest eigenvalues: [1] 99403028 96995729 91271197 86334470 84845225 83720711 83141619 81051248 [9] 80386006 78016618 Smallest eigenvalues: [1] 0.30125163 0.29857364 0.27697696 0.23653599 0.22493355 0.15931825 [7] 0.15719980 0.09585035 -0.07523587 -0.24563079 Largest eigenvalues: [1] 99255187 97601232 91540697 86557384 85320456 84259688 83430092 81740052 [9] 80300100 78699978 Smallest eigenvalues: [1] 0.14770509 0.14703493 0.12877017 0.11995217 0.03044798 0.02842931 [7] -0.02385802 -0.22328690 -0.41613392 -1.18032548 Largest eigenvalues: [1] 98523226 96848887 90449028 87557021 84132674 83955483 82982210 81412613 [9] 79877588 78084687 Smallest eigenvalues: [1] 0.51960806 0.45499548 0.39923555 0.36355990 0.34626187 0.30379534 [7] 0.15830414 0.13624363 0.02287153 -0.01837780 Largest eigenvalues: [1] 98580204 97143162 90240635 87044613 84973194 83060980 82671844 80219489 [9] 79639565 77305825 Smallest eigenvalues: [1] 0.3735375 0.3124046 0.2955252 0.2661430 0.2339361 0.2322620 [7] 0.2296551 0.2208476 0.1665363 -0.2014518 Largest eigenvalues: [1] 100069852 97987902 90857389 87173121 86355576 85114828 82925917 [8] 81785590 80064235 78549562 Smallest eigenvalues: [1] 0.18897226 0.13418871 0.13403572 0.11794544 0.08530734 0.03570521 [7] 0.02717942 -0.02845286 -0.09525021 -1.09938105 Largest eigenvalues: [1] 101445426 97239157 91464509 86942210 86539359 84450507 83229824 [8] 82084077 80216620 78918983 Smallest eigenvalues: [1] 0.32187388 0.30941506 0.28040408 0.27005253 0.07063967 0.01791296 [7] -0.04974077 -0.05007339 -0.07754903 -0.61300587 Largest eigenvalues: [1] 99279205 96481973 90430966 86730510 84266721 83878917 83135030 81054785 [9] 80265359 77496367 Smallest eigenvalues: [1] 0.266249936 0.183439818 0.183122112 0.165237483 0.133126026 [6] 0.086028761 0.080281040 0.002261466 -0.065886258 -0.682818857 Largest eigenvalues: [1] 98104025 96020905 90039357 85819099 84552218 84009847 83176366 81622894 [9] 79703024 78143730 Smallest eigenvalues: [1] 0.4731831 0.4379850 0.3678234 0.3396353 0.3154924 0.1786980 [7] 0.1424094 -0.0735300 -0.2596949 -0.3355862 Largest eigenvalues: [1] 101695333 97016709 90753799 87111137 86413236 84559990 83148366 [8] 81478659 80491103 78825166 Smallest eigenvalues: [1] 0.370881259 0.308468843 0.306375518 0.253293109 0.151681071 [6] 0.064906167 0.034308609 -0.007546741 -0.103995517 -0.303814423 Largest eigenvalues: [1] 100407792 97222775 90887078 86377793 86157911 84855368 83127518 [8] 82177321 80286075 78988394 Smallest eigenvalues: [1] 0.36215672 0.32055746 0.29270195 0.22599062 0.20541405 0.07966848 [7] -0.07010469 -0.08651217 -0.14687652 -0.17682493 Largest eigenvalues: [1] 99742306 96457600 89932801 86458562 85660891 83215673 82796997 80335254 [9] 79862019 77302228 Smallest eigenvalues: [1] 0.4069725 0.3789921 0.3720539 0.3493058 0.2786115 0.2763314 [7] 0.1597281 0.1374649 -0.1555157 -0.3548150 Largest eigenvalues: [1] 99430282 97382075 90744799 86780563 85729494 84453522 83125864 81558582 [9] 80266725 78751869 Smallest eigenvalues: [1] 0.34660680 0.33242825 0.33024667 0.26505687 0.25308096 0.19190169 [7] 0.18440978 -0.02657977 -0.07899601 -0.35406515 Largest eigenvalues: [1] 100092330 97109606 90659208 87013364 85163538 83748493 83105247 [8] 80868731 80483208 77660021 Smallest eigenvalues: [1] 0.315380299 0.300790229 0.298210052 0.240074360 0.216812909 [6] 0.211242548 0.142964705 0.127009591 -0.006673591 -0.619316170 Largest eigenvalues: [1] 98786252 96176105 89886380 85575809 84606864 83246926 82868686 81027626 [9] 79678226 77911568 Smallest eigenvalues: [1] 0.3555102 0.3216519 0.2202893 0.1849291 0.1818633 0.1749043 [7] 0.1500867 -0.1619119 -0.1768534 -0.3630047 Largest eigenvalues: [1] 100026770 96430653 90588311 86126141 85693465 83939133 83177361 [8] 81440171 80301745 78474493 Smallest eigenvalues: [1] 0.42323015 0.38460351 0.38354034 0.33435045 0.29748921 0.28011144 [7] 0.19644361 0.05767292 0.03809383 -0.30141804 Largest eigenvalues: [1] 99632097 96498508 90114598 86605080 84677056 83388952 83273005 80930241 [9] 79913067 77464610 Smallest eigenvalues: [1] 0.34880830 0.32753423 0.31371720 0.31293268 0.29225905 0.24612374 [7] 0.19394336 0.08634842 -0.14975843 -0.45819139 Largest eigenvalues: [1] 100969016 97162852 90589520 86474617 86435663 84540020 83035146 [8] 81850919 79764231 78534592 Smallest eigenvalues: [1] 0.121584650 0.099073605 0.083206678 0.030346252 -0.005349244 [6] -0.030517717 -0.258229769 -0.315619402 -0.662853289 -0.976832846 Largest eigenvalues: [1] 97769125 97727404 90306862 86323686 85593366 84314941 83002220 81440773 [9] 79593279 78106522 Smallest eigenvalues: [1] 0.41539659 0.34861896 0.34535995 0.30761337 0.26335302 0.24672555 [7] 0.19167796 0.07149844 -0.30944370 -0.35463270 Largest eigenvalues: [1] 100925112 95104191 89451130 85567798 85047948 82231602 82103613 [8] 79772505 79301558 76766044 Smallest eigenvalues: [1] 0.42645093 0.38110620 0.34579000 0.26418143 0.23611077 0.22212262 [7] 0.18020006 0.14611503 0.04597814 -0.04967715 Largest eigenvalues: [1] 98230818 96771523 89915329 86314222 84417574 83164438 82590980 80513474 [9] 79235205 77431813 Smallest eigenvalues: [1] 0.33928706 0.30253223 0.29286834 0.27012046 0.24627677 0.20236523 [7] 0.14500627 0.07341435 -0.04890873 -0.46030103 Largest eigenvalues: [1] 99970209 95627966 89812444 85079576 85072865 82827664 82680085 80482524 [9] 79731110 77673679 Smallest eigenvalues: [1] 0.4073399 0.3380502 0.3310765 0.2541292 0.2529722 0.2344397 [7] 0.1328268 0.1247015 0.0222587 -0.1692082 Largest eigenvalues: [1] 99808506 97446505 90799481 86933910 85895421 84754937 83017950 81574556 [9] 80420369 78939377 Smallest eigenvalues: [1] 0.3792166 0.3641544 0.3128769 0.3043855 0.2261739 0.1949854 [7] 0.1394099 0.1139854 -0.0909399 -0.3048475 Largest eigenvalues: [1] 99353343 97031118 90188031 86791455 85242182 83316632 83166375 80456864 [9] 79826073 77194419 Smallest eigenvalues: [1] 0.3207312 0.3084391 0.2566871 0.1728499 0.1347761 0.1288469 [7] 0.1277789 -0.2828261 -0.3376426 -0.5095712 Largest eigenvalues: [1] 101002692 98022261 91173223 87293577 87066456 85253229 83781613 [8] 82125988 81099365 79246043 Smallest eigenvalues: [1] 0.25273977 0.23785645 0.23491200 0.17636359 0.14387486 0.10261795 [7] 0.02288784 -0.04382888 -0.07816426 -0.36475216 Largest eigenvalues: [1] 99865756 97139252 90869065 86204257 85755360 83635046 83462409 81354082 [9] 80279024 78279106 Smallest eigenvalues: [1] 0.4629906 0.4420775 0.4155700 0.3524799 0.2971138 0.2928448 [7] 0.2769946 0.1430292 0.1401606 -0.1545259 Largest eigenvalues: [1] 99735377 96289980 89786104 86217632 84844589 83795729 82774334 81161230 [9] 79908452 78089620 Smallest eigenvalues: [1] 0.40751238 0.34767727 0.33619892 0.31519661 0.27251762 0.26250855 [7] 0.19233978 0.13649158 -0.01791136 -0.19899712 Largest eigenvalues: [1] 99710815 96169856 89743849 85912101 85762431 83777472 82373537 81120251 [9] 79769936 78348070 Smallest eigenvalues: [1] 0.298771596 0.277230016 0.139848803 0.139039924 -0.005230866 [6] -0.036355574 -0.109102942 -0.116315323 -0.397277362 -0.540578190 Largest eigenvalues: [1] 101025774 96513528 90371682 86102986 85864377 83321749 82947449 [8] 80868528 79715410 77632146 Smallest eigenvalues: [1] 0.5131164 0.4907560 0.4739998 0.4694242 0.3360640 0.2722105 [7] 0.2369400 0.2194937 0.1483563 -0.2358872 Largest eigenvalues: [1] 100365683 96070086 89558984 86068350 85825333 82846514 82488891 [8] 80314590 79431942 77418722 Smallest eigenvalues: [1] 0.30105502 0.26894437 0.23960410 0.23295230 0.19304696 0.18578099 [7] 0.13973900 0.09517504 0.04515997 -0.35253910 Largest eigenvalues: [1] 99319558 96716112 89687031 86609810 85574482 84140793 82580873 81109268 [9] 80006296 77732149 Smallest eigenvalues: [1] 0.36358367 0.28819267 0.27403224 0.24161817 0.15204419 0.09333758 [7] 0.07896315 -0.06422971 -0.30831007 -0.64741605 Largest eigenvalues: [1] 101349599 97477660 90545677 87334685 86906170 84328733 83640155 [8] 81839669 80264345 78561610 Smallest eigenvalues: [1] 0.459466185 0.407495612 0.377703889 0.328678514 0.325866528 [6] 0.288111009 0.284745483 0.262835847 0.004364766 -0.082383562 Largest eigenvalues: [1] 99435937 96649412 90044309 86108726 84943872 83928831 82553003 81169786 [9] 79794549 78488240 Smallest eigenvalues: [1] 0.41537497 0.40535374 0.34421274 0.32700339 0.27610709 0.22002078 [7] 0.19710006 0.09897471 -0.00771023 -0.28407823 Largest eigenvalues: [1] 99653965 97224762 91543366 86435375 85683668 84547294 83766634 82106276 [9] 80641352 78901691 Smallest eigenvalues: [1] 0.34030310 0.32689111 0.30790816 0.28885470 0.28430259 0.26379195 [7] 0.22430123 0.08202055 -0.10218147 -0.31692941 Largest eigenvalues: [1] 101903233 96420607 90562588 86831735 85989481 85315131 82582775 [8] 82333614 80284166 79175720 Smallest eigenvalues: [1] 0.29037359 0.25700743 0.25349925 0.22795981 0.15675371 0.08572705 [7] 0.07557650 -0.08264840 -0.15083149 -0.32028752 Largest eigenvalues: [1] 99568059 96461940 89980655 86374277 83802878 83260333 82337601 80554634 [9] 79295001 77231216 Smallest eigenvalues: [1] 0.37759119 0.29231589 0.28884124 0.19587054 0.17960990 0.11485089 [7] 0.10701840 0.09736901 0.06116874 -0.34647536 Largest eigenvalues: [1] 97588541 96680633 90064099 86955767 84209163 83152051 82868282 80732594 [9] 80061395 77592326 Smallest eigenvalues: [1] 0.34686258 0.34583415 0.31361906 0.29654174 0.28332705 0.24200484 [7] 0.21040720 0.04473258 -0.28758198 -0.53082289 Largest eigenvalues: [1] 99641944 95702811 89590167 85920692 85298072 83165041 82682277 80940473 [9] 79586337 77643459 Smallest eigenvalues: [1] 0.29271046 0.29118264 0.26699837 0.25924126 0.19462124 0.13784858 [7] 0.12139078 0.00745901 -0.05622134 -0.13179928 Largest eigenvalues: [1] 100375036 97811815 91231699 87669828 85935423 85551910 83474230 [8] 82490834 81079099 79688696 Smallest eigenvalues: [1] 0.339738667 0.315040093 0.270685844 0.243474820 0.166553139 [6] -0.001948778 -0.059927188 -0.092267569 -0.176340377 -0.529420838 Largest eigenvalues: [1] 101381500 95939084 90410328 85657643 85431468 82834413 82475109 [8] 80436580 79640427 77462497 Smallest eigenvalues: [1] -0.003938976 -0.035704192 -0.047703562 -0.075615587 -0.091875849 [6] -0.106104269 -0.290740082 -0.337407321 -0.454290643 -0.820779699 Largest eigenvalues: [1] 98779695 97112493 91222797 85940889 85936712 84428306 83450079 81575926 [9] 80509973 78521844 Smallest eigenvalues: [1] 0.3762816 0.3382842 0.3103464 0.3021440 0.2777414 0.2718768 [7] 0.2010620 0.1509750 -0.1365034 -0.2849609 Largest eigenvalues: [1] 100009912 95622139 89383683 85082553 85034675 82877415 81973931 [8] 80378962 79035693 77379378 Smallest eigenvalues: [1] 0.390401162 0.372220910 0.367856530 0.342678217 0.337739898 [6] 0.258057348 0.227085397 0.207053595 0.185383695 -0.004998382 Largest eigenvalues: [1] 99742136 95835713 89814745 85492454 85487902 83886129 82161729 80801793 [9] 79627024 77744500 Smallest eigenvalues: [1] 0.42295849 0.38414668 0.32862636 0.30663701 0.28572025 0.23655167 [7] 0.21902998 0.12850101 0.03747723 -0.04931241 Largest eigenvalues: [1] 99163163 95983154 89742544 86374615 84960457 84210958 82121386 81243802 [9] 79487460 78106613 Smallest eigenvalues: [1] 0.45928749 0.43885756 0.34611468 0.31469607 0.29921342 0.25451120 [7] 0.21915914 0.12635405 0.11375772 -0.03626665 Largest eigenvalues: [1] 98549912 97040216 90470396 86830900 84733535 84561694 83279185 81817033 [9] 80136486 78590071 Smallest eigenvalues: [1] 0.21306716 0.20009471 0.18682018 0.14647698 0.11787026 0.05000114 [7] -0.14125761 -0.21322068 -0.46372173 -0.86120880 Largest eigenvalues: [1] 100269835 98786005 92116482 87573609 86744010 85041439 84023523 [8] 82318287 80705836 79046902 Smallest eigenvalues: [1] 0.385178112 0.348892800 0.282647040 0.241740663 0.164744225 [6] 0.088619098 0.061885102 0.026970585 0.002819512 -0.167604845 Largest eigenvalues: [1] 100055869 97106544 90609896 87086111 84957765 84813716 82736560 [8] 81692216 80467524 78745724 Smallest eigenvalues: [1] 0.33164411 0.32916894 0.30685450 0.30008293 0.26250964 0.21092857 [7] 0.18231502 0.06657026 -0.03114995 -0.16383813 Largest eigenvalues: [1] 98384155 95271270 89092485 85945027 83897194 83140667 81942109 80531137 [9] 79245055 77600122 Smallest eigenvalues: [1] 0.265079219 0.257228032 0.229848256 0.210170685 0.204741606 [6] 0.154336346 0.046422343 0.045166559 0.006347771 -0.141326789 Largest eigenvalues: [1] 98578147 96161275 90399797 86264384 84010640 83466480 82965174 80852491 [9] 80078958 77874336 Smallest eigenvalues: [1] 0.34606804 0.32028727 0.29796067 0.27689720 0.17631718 0.15690097 [7] 0.14462176 -0.06529434 -0.10882231 -0.36449220 Largest eigenvalues: [1] 100864270 95669008 89881292 85293074 85068746 83946463 82376830 [8] 81515995 79530016 78273042 Smallest eigenvalues: [1] 0.3883854 0.3671962 0.3368524 0.3034305 0.3008313 0.1890998 [7] 0.1775069 0.1176321 -0.1193875 -0.3366247 Largest eigenvalues: [1] 98352225 96069038 90389142 85424350 84577911 83499850 82951243 80899027 [9] 80133044 77925286 Smallest eigenvalues: [1] 0.36106262 0.35470095 0.30521951 0.28049301 0.09795188 -0.14067826 [7] -0.21879958 -0.32645230 -0.50601919 -0.74705232 Largest eigenvalues: [1] 101063573 95919795 89751196 86673460 85400345 83315771 83215808 [8] 80776479 79901572 78102403 Smallest eigenvalues: [1] 0.39516504 0.38110504 0.37303341 0.35395212 0.30084641 0.20025858 [7] 0.19057465 0.05271087 -0.23323571 -0.45740242 Largest eigenvalues: [1] 99885413 96307683 89771770 86676171 85076885 83019073 82614375 80303697 [9] 79603642 77103908 Smallest eigenvalues: [1] 0.39424520 0.37538102 0.33402201 0.30799472 0.12998411 0.06237170 [7] -0.01022610 -0.02110173 -0.14673734 -0.98352635 Largest eigenvalues: [1] 102415030 97022571 91070926 86939887 86838670 84548558 83326046 [8] 82110262 80543798 78863805 Smallest eigenvalues: [1] 0.4361062 0.4008087 0.3928731 0.3721579 0.3497402 0.2675264 [7] 0.2571315 0.2123516 0.0872545 -0.9087254 Largest eigenvalues: [1] 100686623 96204911 90236622 86349195 85933155 84024063 82640005 [8] 81536864 79876689 78492902 Smallest eigenvalues: [1] 0.25709191 0.20773856 0.18816360 0.13586418 0.10798095 0.03852193 [7] 0.02163756 -0.10657031 -0.38902877 -0.39113221 Largest eigenvalues: [1] 97962786 97177852 91204554 87453856 83910332 83684816 83071436 80588029 [9] 79982093 77176841 Smallest eigenvalues: [1] 0.23437427 0.19959354 0.18937345 0.17051300 0.13882608 -0.01396215 [7] -0.10656787 -0.23977589 -0.66053207 -0.74633591 Largest eigenvalues: [1] 100688951 96970550 91036072 86620464 86402665 84094754 83237912 [8] 81260138 80233082 77971581 Smallest eigenvalues: [1] 0.39539115 0.38491948 0.38317677 0.37115952 0.34755926 0.13455985 [7] 0.11818590 0.02859528 -0.15486518 -0.16713950 Largest eigenvalues: [1] 101464903 96415609 90436351 86115547 85857649 83436349 83034241 [8] 81383073 79680016 78176041 Smallest eigenvalues: [1] 0.32181052 0.29800425 0.26860658 0.26126694 0.13959271 0.13234684 [7] 0.11989553 0.09441495 -0.30411768 -0.37197913 Largest eigenvalues: [1] 99272913 96154529 90791400 85592533 84541947 84031460 83034794 81909517 [9] 80051732 78834820 Smallest eigenvalues: [1] 0.23763741 0.22498885 0.19990755 0.19477061 0.06445346 -0.01800488 [7] -0.07818053 -0.17959615 -0.39533810 -0.51219625 Largest eigenvalues: [1] 102580603 96734068 90517082 86660704 86622258 84227843 83180815 [8] 81476213 80613448 78581549 Smallest eigenvalues: [1] 0.38655803 0.38053033 0.37836786 0.37447160 0.34251566 0.31336099 [7] 0.20662509 0.20312479 0.02490699 -0.76132098 Largest eigenvalues: [1] 100975974 96884353 90200365 87078794 85737971 83582689 83080706 [8] 81070705 80166208 77944224 Smallest eigenvalues: [1] 0.30452042 0.26076954 0.24591417 0.20933430 0.20879046 0.12006577 [7] 0.11093002 0.10421077 -0.05258623 -0.11677477 Largest eigenvalues: [1] 98046924 97357580 90236940 86830032 85125294 84518639 82982591 81414080 [9] 80253451 78326304 Smallest eigenvalues: [1] 0.35453342 0.34721438 0.31396398 0.25436984 0.21222583 0.18570879 [7] 0.17974770 0.16935032 -0.06403733 -0.28670201 Largest eigenvalues: [1] 100901761 98439209 92117787 87513390 86591803 85248430 84064220 [8] 82635464 81333228 79881182 Smallest eigenvalues: [1] 0.30291194 0.29352072 0.27807454 0.24642630 0.16721350 0.13223166 [7] 0.05848940 0.03110647 -0.17415915 -0.31237370 Largest eigenvalues: [1] 99206653 96532968 90979201 86700362 83896114 83713637 83044172 81394988 [9] 80109099 78018445 Smallest eigenvalues: [1] 0.30311467 0.28662159 0.20514807 0.20416644 0.17766178 0.14241885 [7] 0.04313569 -0.04811775 -0.14723551 -0.43805896 Largest eigenvalues: [1] 101484624 98259658 91842667 87784268 87095653 86361392 83678055 [8] 82959433 81170121 80067975 Smallest eigenvalues: [1] 0.352469191 0.334595004 0.333016035 0.282206209 0.273129999 [6] 0.249874447 0.242715658 0.178530461 -0.009845095 -0.035212668 Largest eigenvalues: [1] 101179314 96377482 90500487 86121077 85594758 85129933 81983840 [8] 81675278 79628776 78589350 Smallest eigenvalues: [1] 0.32187477 0.31711150 0.30079343 0.25019736 0.17840017 0.15371245 [7] 0.15218466 0.04991640 0.04053776 -1.15377864 Largest eigenvalues: [1] 98835537 96683404 90110651 86705912 84262716 83317116 82873178 80753057 [9] 79684625 77432756 Smallest eigenvalues: [1] 0.46869881 0.41533301 0.30146510 0.29761191 0.25292186 0.24845649 [7] 0.14603040 0.14203689 0.14073645 -0.06066743 Largest eigenvalues: [1] 98312487 96530996 90043271 86662956 84414400 84151387 82658150 81286553 [9] 79751922 78191785 Smallest eigenvalues: [1] 0.40722325 0.40587020 0.38908461 0.37695216 0.34354839 0.34192766 [7] 0.28157473 0.12306142 0.05431251 -0.28492565 Largest eigenvalues: [1] 99812417 97067209 90592236 86589785 85930944 84385994 83242951 81615158 [9] 80037985 78537490 Smallest eigenvalues: [1] 0.3455527 0.3314203 0.3292558 0.3154814 0.2234377 0.2186212 [7] 0.1724869 0.1548024 -0.1262626 -0.3177654 Largest eigenvalues: [1] 98191025 97154803 90670897 86748933 84345006 83554780 82864815 80413533 [9] 79946137 77448059 Smallest eigenvalues: [1] 0.332306158 0.327118441 0.257679499 0.214663146 0.205322934 [6] 0.192454275 0.120975561 -0.002827462 -0.071015934 -0.225763956 Largest eigenvalues: [1] 97852890 95569590 89472069 85485983 83942979 82683604 82166481 80129898 [9] 79189124 77036463 Smallest eigenvalues: [1] 0.363993904 0.352198396 0.305208094 0.293656653 0.267788939 [6] 0.092145809 0.072045715 -0.004516703 -0.200909374 -0.377911498 Largest eigenvalues: [1] 102528153 96726632 90440910 86998267 86570636 84307025 82448692 [8] 81482137 80157562 78901669 Smallest eigenvalues: [1] 0.28573037 0.25465013 0.24082600 0.20581372 0.13296159 0.11483030 [7] 0.08728299 0.05801403 -0.27326674 -0.54683875 Largest eigenvalues: [1] 100112079 95974471 90312484 85902115 84181482 83855105 82638373 [8] 81437835 79843812 78124692 Smallest eigenvalues: [1] 0.41726805 0.37539765 0.34134341 0.33469012 0.27707074 0.24836518 [7] 0.14073899 -0.03430227 -0.06985549 -0.09744168 Largest eigenvalues: [1] 100125149 96940776 90427045 86810444 85601223 83919196 82892737 [8] 80597307 80217406 77315787 Smallest eigenvalues: [1] 0.35943067 0.34771732 0.26697026 0.23575106 0.20975682 0.07241858 [7] 0.07031827 0.03255753 -0.03004021 -0.63683594 Largest eigenvalues: [1] 98176951 95855694 89868366 85716521 84250493 83576207 82547511 80650145 [9] 79581857 77844258 Smallest eigenvalues: [1] 0.28557159 0.26551614 0.20700079 0.18209746 0.05065113 0.03942093 [7] -0.12434641 -0.46087171 -0.46235863 -1.76492957 Largest eigenvalues: [1] 100077096 96111195 90628436 85909160 85141567 83546863 82692603 [8] 81186269 79790888 78086842 Smallest eigenvalues: [1] 0.4111483 0.3976203 0.3899111 0.3152590 0.2844035 0.2505617 [7] 0.1305652 0.1212050 0.1033168 -0.1378011 Largest eigenvalues: [1] 99797864 97089080 91148147 87114642 84556452 84300647 83274177 81589625 [9] 80372537 78264324 Smallest eigenvalues: [1] 0.3981962 0.3915100 0.3087360 0.2800696 0.2657695 0.2197048 [7] 0.1137246 0.0323599 -0.1035421 -0.3925046 Largest eigenvalues: [1] 101217866 97054376 90976383 86474888 86319244 84343222 82996786 [8] 81892272 79865724 78828586 Smallest eigenvalues: [1] 0.31907584 0.26461081 0.24424412 0.24124268 0.21878337 0.20317477 [7] 0.05882125 -0.03371717 -0.16080534 -0.16909196 Largest eigenvalues: [1] 100270889 96298468 90314915 86036619 85473291 83386635 82768166 [8] 81110721 79674394 78109758 Smallest eigenvalues: [1] 0.322974616 0.289057372 0.256144347 0.221112409 0.201365784 [6] 0.173328484 0.098822350 -0.001235241 -0.205880836 -0.348424094 Largest eigenvalues: [1] 99247846 96545923 90800445 86694861 84103963 83458457 83221519 80904766 [9] 80428559 77697529 Smallest eigenvalues: [1] 0.38964795 0.35431367 0.30614879 0.25479043 0.24739120 0.21091183 [7] 0.03720553 -0.03017836 -0.23143603 -0.63521456 Largest eigenvalues: [1] 99866998 95853008 89510093 86144748 85440584 83236861 82697758 80812974 [9] 79563176 77652981 Smallest eigenvalues: [1] 0.4278225 0.3554092 0.2744333 0.2549966 0.2080785 0.1796390 [7] 0.1720114 0.1236441 -0.3006015 -2.0346026 Largest eigenvalues: [1] 100389684 97867325 91779092 87859077 85728815 84436443 84167199 [8] 81944053 81203542 78948695 Smallest eigenvalues: [1] 0.27628790 0.24825376 0.22973939 0.19013909 0.14944336 0.11101696 [7] 0.09605119 0.04553071 -0.02954497 -0.47174144 Largest eigenvalues: [1] 99959915 97684741 91285233 86727062 85985063 84822032 83185092 82132222 [9] 80007817 79048233 Smallest eigenvalues: [1] 0.4586213 0.4356107 0.4296516 0.3595828 0.3392151 0.2593681 [7] 0.2081121 0.1499460 0.1321672 -0.3467527 Largest eigenvalues: [1] 100032668 96454073 89929788 86566201 85320109 83907484 82520880 [8] 81016567 80053027 78109317 Smallest eigenvalues: [1] 0.37401660 0.35299192 0.34660273 0.29139335 0.22928724 0.13283081 [7] -0.03687561 -0.04373013 -0.10884025 -0.50693959 Largest eigenvalues: [1] 101887158 96571551 90922154 87080143 86129900 84148089 82902701 [8] 81719015 79920624 78478089 Smallest eigenvalues: [1] 0.25324256 0.24390059 0.24042318 0.21037344 0.10444766 0.09657504 [7] 0.04774657 0.03866988 -0.02305990 -0.73335066 Largest eigenvalues: [1] 99845827 96274593 89768098 86279661 86097051 84122010 82756492 81642906 [9] 79551262 78363816 Smallest eigenvalues: [1] 0.25952697 0.25625951 0.24901677 0.22166837 0.14047541 0.09366133 [7] 0.07579929 0.05913745 0.03263012 -0.03930151 Largest eigenvalues: [1] 97230190 96859213 90344167 85788116 84310713 83410107 82365750 80199578 [9] 79511159 76872913 Smallest eigenvalues: [1] 0.377682389 0.366795098 0.350204259 0.343668011 0.335416053 [6] 0.140514283 0.104878472 0.046744973 -0.009289209 -0.183817665 Largest eigenvalues: [1] 98036865 96519470 90046574 86770513 83818676 83678270 82880236 80883901 [9] 80087804 77755691 Smallest eigenvalues: [1] 0.41340924 0.40592664 0.30104953 0.27654574 0.23550943 0.22383489 [7] 0.21516928 0.05563605 -0.02222065 -0.02515350 Largest eigenvalues: [1] 100624671 94961268 89339064 85383654 85150616 83403713 82044135 [8] 81143069 79009458 77557667 Smallest eigenvalues: [1] 0.37696956 0.36206458 0.32771699 0.27784576 0.25140943 0.25009239 [7] 0.24515108 0.10919220 0.06015397 -0.35363277 Largest eigenvalues: [1] 99255327 96565905 89928233 86414858 84848455 83100742 82959381 80752947 [9] 79571499 77578520 Smallest eigenvalues: [1] 0.453172460 0.434767575 0.423925150 0.406591966 0.355176310 [6] 0.214539184 0.119763047 0.057494059 0.007929484 -0.687733849 Largest eigenvalues: [1] 101723310 94876693 89674652 85797391 85251146 83131892 81970469 [8] 80840817 79254368 77759348 Smallest eigenvalues: [1] 0.4507790 0.4130169 0.4026377 0.3753365 0.3571728 0.3431534 [7] 0.3215998 0.2063801 0.2005658 -0.1656048 Largest eigenvalues: [1] 99636062 96502443 90329448 86418834 84993051 84153691 82325849 81193672 [9] 79786634 78187575 Smallest eigenvalues: [1] 4.080344e-01 3.899102e-01 3.327223e-01 3.099713e-01 2.427371e-01 [6] 2.077694e-01 8.397607e-02 -4.113711e-05 -1.303795e-01 -2.282265e-01 Largest eigenvalues: [1] 98693314 96591399 90050668 86410156 84300321 83036811 82594412 80252963 [9] 79530475 77187704 Smallest eigenvalues: [1] 0.40816555 0.35098239 0.34943131 0.32001736 0.31357211 0.22871340 [7] 0.16702336 0.09668769 -0.03566591 -0.15008584 Largest eigenvalues: [1] 99746709 96096946 90357804 86594905 83839828 83503557 82914367 80875502 [9] 79930388 77757554 Smallest eigenvalues: [1] 0.3067219 0.2878642 0.2868506 0.2729622 0.2635577 0.2501202 [7] 0.1673381 0.1150373 -0.2070402 -0.2782853 Largest eigenvalues: [1] 99896314 96541382 90053396 85970943 85826905 83394993 83119396 81285311 [9] 79766616 78115813 Smallest eigenvalues: [1] 0.38952895 0.36599233 0.34030136 0.33864092 0.33726291 0.19689170 [7] 0.16024410 0.09690631 0.09479776 -0.39220075 Largest eigenvalues: [1] 100525698 96856986 90599566 86247700 85826123 84671025 83285939 [8] 82110976 80398812 79134449 Smallest eigenvalues: [1] 0.449143928 0.409087978 0.408891749 0.361338504 0.313418767 [6] 0.300932960 0.239251863 0.202284191 -0.008825494 -0.210481690 Largest eigenvalues: [1] 100321684 96704281 90973381 86275423 85897483 83889489 83012778 [8] 81378730 80093860 78347516 Smallest eigenvalues: [1] 0.2429087 0.2244373 0.2165091 0.1677806 0.1397006 0.1358201 [7] 0.1124126 -0.0612381 -0.3202735 -0.3852067 Largest eigenvalues: [1] 97274296 96796149 90165002 86842332 83744848 83545985 83391879 81355951 [9] 80225509 77808512 Smallest eigenvalues: [1] 0.201515259 0.195937288 0.195769677 0.183496349 0.129163885 [6] 0.093918476 0.068148830 -0.004682843 -0.260849965 -0.337359682 Largest eigenvalues: [1] 99622690 96624333 90442226 86066789 85607733 83690048 83201759 80988805 [9] 80056874 77868438 Smallest eigenvalues: [1] 0.24347053 0.19422175 0.18395027 0.16461483 0.15193739 0.13253342 [7] 0.03672774 -0.09542403 -0.51484701 -2.88459197 Largest eigenvalues: [1] 97671113 97282730 91210145 87175062 84602155 84460492 83336507 81263097 [9] 80789266 78110652 Smallest eigenvalues: [1] 0.41563772 0.40135371 0.29373362 0.29113674 0.27563045 0.25013847 [7] 0.13573349 0.13448045 0.06479809 -0.59213994 Largest eigenvalues: [1] 100227496 96669698 90856256 86988401 85438243 84250775 82837042 [8] 81462806 80185962 78639655 Smallest eigenvalues: [1] 0.37484661 0.37183664 0.32188823 0.24255355 0.21513574 0.16728868 [7] 0.16181601 0.03835117 -0.04485363 -0.15669548 Largest eigenvalues: [1] 100778812 96008010 89872430 86631543 85433844 84247367 82381155 [8] 81540812 80020443 78538087 Smallest eigenvalues: [1] 0.38932276 0.34027222 0.30917936 0.26240392 0.23472337 0.20252948 [7] 0.12977078 0.02302160 -0.08631194 -0.49892837 Largest eigenvalues: [1] 99978302 96629214 89795661 86344218 86126199 83510648 82862504 80808469 [9] 79902198 77928080 Smallest eigenvalues: [1] 0.38492639 0.32656522 0.30842612 0.30271984 0.23018713 0.09248447 [7] 0.03068857 -0.16836597 -0.44606726 -0.81716592 Largest eigenvalues: [1] 101692337 96174710 89914808 86371200 86053193 83331892 82964517 [8] 80873759 80032349 77936425 Smallest eigenvalues: [1] 0.2302873 0.1470418 0.1312704 0.0271602 -0.0881455 -0.1027795 [7] -0.1041649 -0.2075604 -0.3119751 -0.5068960 Largest eigenvalues: [1] 99993529 96325023 90699705 85527482 85280096 83169131 82792332 81096518 [9] 80078573 78226817 Smallest eigenvalues: [1] 0.18744523 0.13058936 0.10235315 0.06900952 -0.08161360 -0.20671691 [7] -0.25101490 -0.53325805 -0.68114330 -0.86612294 Largest eigenvalues: [1] 100653213 96148766 90531749 86402377 85492501 84226407 83277362 [8] 81914492 80121459 78571749 Smallest eigenvalues: [1] 0.29407698 0.24180231 0.22236276 0.21254689 0.17567041 0.17284547 [7] 0.08120150 -0.08693302 -0.18317307 -0.52064802 Largest eigenvalues: [1] 100832092 96650495 90325466 86749979 85335025 84122265 82917483 [8] 81421457 80345933 79003888 Smallest eigenvalues: [1] 0.264724915 0.258843811 0.195494610 0.184610529 0.088515470 [6] 0.074309565 0.070999392 0.005328188 -0.124732863 -0.510606863 Largest eigenvalues: [1] 99090567 98245541 91264745 87472478 85207490 83901145 83506328 80881842 [9] 80319738 77599107 Smallest eigenvalues: [1] 0.277200359 0.268422037 0.265808825 0.250614237 0.222110378 [6] 0.184631817 0.171212229 0.062031430 -0.006115577 -0.242918327 Largest eigenvalues: [1] 98248985 95536017 90099901 85673315 84145439 83097797 82146941 80773034 [9] 79004547 77325644 Smallest eigenvalues: [1] 0.27166956 0.26206803 0.26200433 0.22909717 0.22569074 0.21233238 [7] 0.19328131 0.08194595 0.06850510 -0.44029953 Largest eigenvalues: [1] 99545904 97664383 90991821 86921930 86116022 84113170 83468385 81701287 [9] 80661948 78939909 Smallest eigenvalues: [1] 0.49263370 0.48892537 0.48226160 0.47728157 0.46201899 0.36719750 [7] 0.18364653 -0.03835223 -0.06186405 -0.15636450 Largest eigenvalues: [1] 100086755 97117772 90757907 86590835 85614187 83913922 83643923 [8] 81366824 80476122 78320717 Smallest eigenvalues: [1] 0.39348412 0.36354909 0.33943151 0.31572349 0.28216984 0.12467170 [7] 0.11318620 0.03912772 -0.12735329 -0.22818761 Largest eigenvalues: [1] 101148275 96800842 90432169 86478185 86270065 83767656 83054250 [8] 81361446 79924201 78332179 Smallest eigenvalues: [1] 0.40329922 0.36647583 0.35258265 0.29850903 0.27598431 0.23684841 [7] 0.22174776 0.18389629 -0.04434122 -0.18925915 Largest eigenvalues: [1] 99040882 97495889 90648621 86668296 85824282 84026148 83749449 81514765 [9] 80313497 78251083 Smallest eigenvalues: [1] 0.3813611 0.3757567 0.3700627 0.2527970 0.2178727 0.1551922 [7] 0.1539496 0.1356227 -0.1390212 -0.2505679 Largest eigenvalues: [1] 101417838 97077264 90610871 87001198 86255021 84347372 82569053 [8] 81315004 80022751 78541061 Smallest eigenvalues: [1] 0.3402880 0.3266425 0.3137778 0.3092483 0.2933842 0.1351560 [7] 0.0852462 -0.1097143 -0.1452852 -0.3948485 Largest eigenvalues: [1] 98994240 96068311 90021788 86216177 84135007 83495879 83398553 80988351 [9] 80110106 77586769 Smallest eigenvalues: [1] 0.43791791 0.35005668 0.32257118 0.28767390 0.26560318 0.11048113 [7] 0.10302134 -0.04881567 -0.16451591 -0.61562557 Largest eigenvalues: [1] 100748707 97559421 90773956 86765083 86739104 84069552 83332761 [8] 81216192 80480741 78135229 Smallest eigenvalues: [1] 0.4043422 0.3177594 0.2784231 0.2133265 0.1708052 0.1356024 [7] 0.1063806 -0.1061425 -0.3245745 -0.4479671 Largest eigenvalues: [1] 101088465 98012938 91491760 87103335 86974863 85056779 83794072 [8] 82439630 80868958 79595643 Smallest eigenvalues: [1] 0.38536154 0.37811857 0.34988879 0.33522929 0.24079538 0.21059997 [7] 0.16994271 0.15690070 0.09826273 -0.12992921 Largest eigenvalues: [1] 99865629 96663461 89958666 86757419 85208582 84493959 82829475 81524590 [9] 80246556 78532056 Smallest eigenvalues: [1] 0.49338410 0.46130421 0.29092271 0.28159190 0.26418500 0.16232420 [7] 0.14546499 0.11954391 0.07641062 -0.08335265 Largest eigenvalues: [1] 99095518 97559705 90856172 87389556 84912010 84475239 84178212 81920115 [9] 80750953 78764136 Smallest eigenvalues: [1] 0.43359589 0.39525408 0.37295818 0.36851099 0.36717957 0.25495990 [7] 0.23193364 0.04706044 -0.16496355 -0.23547278 Largest eigenvalues: [1] 100979146 96760934 90216804 86955909 85901711 83736359 83567451 [8] 81242317 80318405 78042261 Smallest eigenvalues: [1] 0.40018801 0.39909966 0.31738285 0.30590433 0.28671083 0.24230635 [7] 0.11973661 0.10973128 -0.08889275 -0.18451396 Largest eigenvalues: [1] 100293113 96752265 90346623 86358908 85730985 83223751 82740899 [8] 80430259 79699411 77470363 Smallest eigenvalues: [1] 0.40202421 0.38881471 0.35932693 0.33676397 0.29138650 0.17240361 [7] 0.14630249 0.06911886 -0.13262315 -0.50811128 Largest eigenvalues: [1] 100832944 96431409 90353577 86205889 85747841 83495848 82696046 [8] 80679546 79947946 77684708 Smallest eigenvalues: [1] 0.26356748 0.22451149 0.21447301 0.14232157 0.13137200 -0.07127335 [7] -0.13443185 -0.33362772 -0.99837504 -1.18086786 Largest eigenvalues: [1] 100390242 98173264 91893760 87500058 86828410 84880436 84328574 [8] 82138988 81172268 78797919 Smallest eigenvalues: [1] 0.4800552 0.4462127 0.4354448 0.3948925 0.2379331 0.2322997 [7] 0.2097992 0.1793300 -0.3530947 -0.5002601 Largest eigenvalues: [1] 100981774 96558546 90758173 86707093 86050339 84256737 83570711 [8] 81815479 80371989 78458984 Smallest eigenvalues: [1] 0.27571578 0.26065675 0.25578484 0.23576732 0.18466510 0.15187383 [7] -0.02681751 -0.06218987 -0.08554207 -1.16660890 Largest eigenvalues: [1] 101581680 97577060 90947364 87531363 86503107 83579168 83332011 [8] 81221729 80484020 78278402 Smallest eigenvalues: [1] 0.3904782 0.3594291 0.3052958 0.2793544 0.2485757 0.2453688 [7] 0.1745193 0.1448788 -0.1491973 -0.1536200 Largest eigenvalues: [1] 99291814 96249964 90451849 86545287 83949247 83493776 82871926 80878488 [9] 80000935 77843866 Smallest eigenvalues: [1] 0.3510358 0.3384971 0.2866311 0.2706063 0.2438889 0.2400042 [7] 0.2266962 0.2144901 -0.2704189 -0.5343419 Largest eigenvalues: [1] 99922899 96592092 90153468 85977694 85844645 84214918 82752700 81633795 [9] 79530021 78308814 Smallest eigenvalues: [1] 0.4733122 0.4319661 0.3873925 0.3771174 0.3625619 0.3438730 [7] 0.2243310 0.1794688 0.1773776 -0.1116724 Largest eigenvalues: [1] 101970919 97791950 91585622 87189810 87172412 85360336 83643751 [8] 82568142 80807703 79398275 Smallest eigenvalues: [1] 0.393039968 0.368643853 0.322298292 0.309749702 0.285880793 [6] 0.282593643 0.268126063 0.194275494 0.164836530 -0.003649929 Largest eigenvalues: [1] 98286634 97646409 90092264 87045466 84526804 83575419 83078846 80482249 [9] 79939778 77654994 Smallest eigenvalues: [1] 0.38365932 0.37383337 0.34581177 0.28814205 0.28425873 0.22996887 [7] 0.21079233 0.14885063 0.07927317 -0.05774738 Largest eigenvalues: [1] 96888799 95893791 89510568 85933737 84050549 83440507 82893314 81102668 [9] 79365895 77689381 Smallest eigenvalues: [1] 0.311420340 0.300188349 0.295505927 0.252008741 0.181267958 [6] 0.108202712 0.029094620 -0.006237588 -0.038084783 -0.045977090 Largest eigenvalues: [1] 98781381 96440684 90263526 86244606 84560070 83286834 82018701 80024254 [9] 79678212 76733335 Smallest eigenvalues: [1] 0.39618532 0.37107574 0.35440561 0.34575269 0.23565279 0.20986112 [7] 0.12936175 0.11495936 0.04073679 -0.42503105 Largest eigenvalues: [1] 98620297 96919526 90063787 86732977 84629115 82889180 82558833 80006530 [9] 79415205 77047451 Smallest eigenvalues: [1] 0.44735863 0.44641456 0.37255313 0.32364501 0.29331807 0.29022188 [7] 0.23849349 0.02658452 -0.20918793 -0.59785198 Largest eigenvalues: [1] 101056305 96996973 91054832 86710358 86100263 84533323 83184887 [8] 82195266 80473665 79260218 Smallest eigenvalues: [1] 0.36241386 0.31138308 0.29292265 0.23617172 0.22013910 0.21675891 [7] 0.15521651 0.10960781 0.03415315 -0.58779559 Largest eigenvalues: [1] 101126333 96863151 90994802 86227800 86093682 84397758 82785691 [8] 81685588 80365588 78695393 Smallest eigenvalues: [1] 0.506219235 0.417583088 0.346790814 0.332654503 0.317417865 [6] 0.266494843 0.129736341 0.090086620 0.016767973 -0.008225712 Largest eigenvalues: [1] 99381178 96437029 89975891 86274652 85570088 83339908 82528139 80251657 [9] 79925509 77270287 Smallest eigenvalues: [1] 0.3439869 0.2665879 0.2534117 0.2417891 0.1754622 0.1615696 [7] 0.1331950 0.0540091 -0.1143302 -0.6108836 Largest eigenvalues: [1] 99073826 96700227 90978605 86337679 85072132 84380848 83281173 81916588 [9] 80447986 78857262 Smallest eigenvalues: [1] 0.293402028 0.278644806 0.276265665 0.240825291 0.191697310 [6] 0.128571887 0.102248489 0.004756226 -0.043267861 -0.527282814 Largest eigenvalues: [1] 99882661 98129168 91292878 87586988 85730423 84926281 83523043 81873661 [9] 80428391 78404257 Smallest eigenvalues: [1] 0.379407283 0.362086914 0.346272677 0.308077854 0.286368418 [6] 0.283776227 0.202448530 0.129322070 0.009221141 -0.039161630 Largest eigenvalues: [1] 98100239 95520350 89375854 85675253 84912679 83311565 82136337 80559403 [9] 79253112 77508797 Smallest eigenvalues: [1] 0.4100102 0.3463401 0.3195339 0.3109376 0.2942632 0.2868886 [7] 0.2791449 0.1249521 -0.0497405 -0.4112079 Largest eigenvalues: [1] 99560966 95801734 90028359 85178451 84934083 83419193 82516631 80993146 [9] 79630875 77892340 Smallest eigenvalues: [1] 0.2547524 0.2527505 0.2282470 0.2022748 0.1964301 0.1761039 [7] -0.1720405 -0.3822107 -0.4299169 -0.6946195 Largest eigenvalues: [1] 100708551 95602974 89658119 85451577 85323963 83347000 81973268 [8] 80597570 79162671 77506090 Smallest eigenvalues: [1] 0.39484395 0.36896472 0.34554784 0.30024134 0.25104791 0.21104823 [7] 0.18564306 0.12105521 -0.06337661 -0.11010582 Largest eigenvalues: [1] 99723297 96361411 89807508 86075249 85378135 83795462 82235628 80751911 [9] 79425592 77665325 Smallest eigenvalues: [1] 0.36284785 0.35740650 0.33983036 0.29340283 0.27773649 0.25658583 [7] 0.22541331 0.14350461 0.01495241 -0.13980115 Largest eigenvalues: [1] 101359059 97865910 91410205 86940631 86659298 84950120 83218493 [8] 82184588 80381962 79064494 Smallest eigenvalues: [1] 0.43793085 0.39760352 0.39074365 0.34187650 0.34000102 0.33852246 [7] 0.24277200 0.21697439 0.09572884 -0.34370367 Largest eigenvalues: [1] 99219476 97108852 90424475 86727963 85708827 83794399 83475852 81306494 [9] 80229615 77998140 Smallest eigenvalues: [1] 0.4972526 0.4639053 0.4385339 0.4284383 0.3638186 0.2602172 [7] 0.2419404 0.1053181 -0.0941487 -0.3227498 Largest eigenvalues: [1] 101822862 96408557 90340843 86922257 86340829 84112911 82873961 [8] 81403520 80162161 78314967 Smallest eigenvalues: [1] 0.331858671 0.320957571 0.247665006 0.238869900 0.220157655 [6] 0.211447520 0.208976691 -0.002574907 -0.166582416 -0.887740275 Largest eigenvalues: [1] 99632081 97388221 91381184 87089156 85244696 84219380 83587030 81557863 [9] 81006529 78211664 Smallest eigenvalues: [1] 0.36788190 0.32001120 0.31545956 0.31376330 0.24545454 0.19928379 [7] 0.18519352 0.02475088 -0.01013018 -0.37512035 Largest eigenvalues: [1] 102647292 96490275 90359486 87643116 86099837 84514729 82453163 [8] 81840563 79922282 78958143 Smallest eigenvalues: [1] 0.3403537 0.3226680 0.2740128 0.2722914 0.2644779 0.2058532 [7] 0.2050473 0.1799879 -0.1157739 -0.4702667 Largest eigenvalues: [1] 99144565 96526106 90596256 86778793 84295126 84111618 83124020 81770148 [9] 80025736 78757240 Smallest eigenvalues: [1] 0.37273813 0.31265552 0.30724930 0.29208617 0.12161757 0.11522665 [7] 0.10921576 0.03942921 -0.11088957 -0.29827369 Largest eigenvalues: [1] 99445561 96840434 90979856 85891147 85624261 83233686 82963795 80850504 [9] 79762985 77757864 Smallest eigenvalues: [1] 0.21507247 0.21298813 0.19395247 0.12737758 0.09687688 0.07474328 [7] 0.01717948 0.01104912 -0.08148290 -0.47219891 Largest eigenvalues: [1] 97888482 97703120 91477933 87356903 84198046 84120936 83988286 81544958 [9] 80593040 77878761 Smallest eigenvalues: [1] 0.37308596 0.35387240 0.29954254 0.27456920 0.23744850 0.20289497 [7] 0.18591032 0.02410526 -0.09735906 -0.56366714 Largest eigenvalues: [1] 99698470 96799376 90359588 86500388 85084278 83818599 83175088 81512281 [9] 80280527 78611201 Smallest eigenvalues: [1] 0.34892941 0.30570820 0.27228825 0.20866940 0.18211246 0.18199969 [7] 0.13957301 0.04012145 -0.16965244 -0.26689151 Largest eigenvalues: [1] 97389063 96265473 89953125 86231064 83986486 83280922 82689191 80534935 [9] 79766553 77147379 Smallest eigenvalues: [1] 0.37680995 0.34035917 0.31604257 0.27570143 0.20309732 0.18452736 [7] 0.16348719 0.10820788 0.02574604 -0.50124354 Largest eigenvalues: [1] 99646367 96788510 90390061 86588350 85510505 83555549 83176716 81156657 [9] 80445605 78266078 Smallest eigenvalues: [1] 0.198487040 0.194549255 0.155245100 0.152756827 0.029231457 [6] -0.006804909 -0.013351996 -0.121656373 -0.232257020 -0.500016815 Largest eigenvalues: [1] 99240414 96292483 90691690 85967065 84001631 83101233 82837370 80658859 [9] 79844506 77389724 Smallest eigenvalues: [1] 0.4267451893 0.4233246475 0.4021618790 0.3852301182 0.3708822417 [6] 0.2731831692 -0.0007449758 -0.0074197543 -0.0529398758 -0.1992280678 Largest eigenvalues: [1] 100570511 95148407 88976913 85919313 85527341 82772333 82523271 [8] 80709668 79169621 77521104 Smallest eigenvalues: [1] 0.29090479 0.28820215 0.26432088 0.24056216 0.21820681 0.15305127 [7] 0.13148121 0.02415131 -0.29209458 -0.39016864 Largest eigenvalues: [1] 99001937 95491620 89269398 85456689 84621355 83065149 82521233 80438351 [9] 79430348 77409064 Smallest eigenvalues: [1] 0.28404874 0.27036254 0.23151940 0.13913560 0.13131545 0.06670308 [7] -0.04230993 -0.12395241 -0.14779080 -0.74805357 Largest eigenvalues: [1] 100884631 97753043 91364766 86991891 86418275 84273222 83607786 [8] 81827050 80474251 78734563 Smallest eigenvalues: [1] 0.4328600 0.4245368 0.4161147 0.4063520 0.3905964 0.3048738 [7] 0.2307820 0.1584419 0.1256102 -0.1080835 Largest eigenvalues: [1] 99831633 95908065 90059593 85734566 85230668 83701243 82267580 81102798 [9] 79342012 78078385 Smallest eigenvalues: [1] 0.44679600 0.42377007 0.42075692 0.34206124 0.33230111 0.31449920 [7] 0.22472654 0.20365782 0.08851559 -0.33627441 Largest eigenvalues: [1] 100393817 97254427 90762479 86450057 86218972 84411331 83198256 [8] 81836676 80040540 78737205 Smallest eigenvalues: [1] 0.190997265 0.186162773 0.182402608 0.160308937 0.083751504 [6] 0.070974593 0.002285711 -0.011662083 -0.376131535 -0.948477094 Largest eigenvalues: [1] 98524063 97254307 90755260 86866121 84913397 83980115 83596797 81657475 [9] 80549619 78339363 Smallest eigenvalues: [1] 0.35947341 0.33645326 0.26217516 0.23367938 0.20683331 0.19621870 [7] 0.16525453 0.11428263 0.05841062 -0.42754018 Largest eigenvalues: [1] 99877032 97627347 90556755 87338228 84997829 84706766 83291459 81609259 [9] 80698739 78454036 Smallest eigenvalues: [1] 0.247307854 0.243469569 0.237687753 0.216629177 0.202754675 [6] 0.092330960 0.004475102 -0.054947023 -0.140016597 -0.232351759 Largest eigenvalues: [1] 100186554 96168805 90329236 85635886 84647593 83768200 82599229 [8] 81253919 79743218 77950176 Smallest eigenvalues: [1] 0.25972182 0.25059425 0.17261335 0.14187451 0.10833977 0.04218391 [7] -0.03277217 -0.16094434 -0.42070023 -1.25671433 Largest eigenvalues: [1] 100001529 97393912 91026739 86624232 86264630 83935050 82844603 [8] 81412331 80074245 78462878 Smallest eigenvalues: [1] 0.35806642 0.35520400 0.23062769 0.22569461 0.20317648 0.15623837 [7] 0.07324149 0.04390717 -0.11820527 -0.17180659 Largest eigenvalues: [1] 99597645 97275510 90177420 86548833 85643354 83616296 83418027 80804323 [9] 80181309 77766173 Smallest eigenvalues: [1] 0.28701483 0.23194268 0.22903914 0.21306152 0.19508947 0.16958079 [7] 0.06159995 -0.32740951 -0.47267045 -0.61831650 Largest eigenvalues: [1] 100976543 96134201 89826239 86429337 85741143 83532179 82981773 [8] 80981013 79783573 77805706 Smallest eigenvalues: [1] 0.24279516 0.23622489 0.23012926 0.22570586 0.18211526 0.11449491 [7] 0.09994666 0.06484078 -0.09762873 -0.43075741 Largest eigenvalues: [1] 99279965 96751850 90718636 86323690 85319956 83611826 83276585 80961642 [9] 80354313 77622645 Smallest eigenvalues: [1] 0.38794686 0.33809405 0.30313295 0.22434297 0.21235466 0.18180557 [7] 0.10457038 0.06234384 -0.09688636 -0.39290492 Largest eigenvalues: [1] 98984532 95681934 89048401 86023564 83950188 83116340 81927294 80310615 [9] 79358089 76989419 Smallest eigenvalues: [1] 0.24836266 0.21266743 0.10305982 0.09731136 0.06365286 0.02732050 [7] 0.02411234 -0.21930789 -0.25479932 -0.29050692 Largest eigenvalues: [1] 99679786 96173093 90449520 85134128 84931584 83717569 82811696 81211423 [9] 79909550 78290420 Smallest eigenvalues: [1] 0.45385413 0.39321620 0.34867710 0.33821243 0.33460574 0.26115108 [7] 0.10940122 0.09625644 -0.01033738 -0.13699444 Largest eigenvalues: [1] 99427503 97358968 90294885 86986612 85684684 83737764 83266973 80811354 [9] 80074421 77467855 Smallest eigenvalues: [1] 0.42410989 0.38361422 0.34560381 0.33895464 0.32301962 0.30356709 [7] 0.29681884 0.26066376 0.02122969 -0.18259312 Largest eigenvalues: [1] 99955807 97428657 90937329 86637689 86248007 84847013 83170518 81997996 [9] 80175256 78871810 Smallest eigenvalues: [1] 0.44245899 0.42751626 0.40490803 0.31406116 0.30340180 0.27662559 [7] 0.24855024 0.19542661 0.11076843 -0.08850199 Largest eigenvalues: [1] 101204554 96257271 90711391 86457056 85501447 84439312 82580171 [8] 81819902 79778863 78464867 Smallest eigenvalues: [1] 0.31588335 0.29136636 0.28642596 0.27020694 0.26662616 0.16006694 [7] 0.14925996 0.14711091 0.04028025 -0.23175618 Largest eigenvalues: [1] 99460005 97456416 90900324 86572903 85421556 84162030 82976620 81375688 [9] 79935294 78040747 Smallest eigenvalues: [1] 0.39565615 0.37680723 0.35811189 0.33834702 0.30986179 0.28168920 [7] 0.23649542 0.11038323 0.07549815 -0.64563451 Largest eigenvalues: [1] 100133693 97300735 90510679 86748829 86605075 85078644 83551626 [8] 82277764 80423095 79057297 Smallest eigenvalues: [1] 0.25586073 0.24256663 0.20329761 0.16748236 0.10756114 0.08208523 [7] -0.14255647 -0.17277764 -0.22898239 -0.38131806 Largest eigenvalues: [1] 98877224 96823835 89754841 86319487 85298803 84210817 82955018 81264358 [9] 80057130 78459494 Smallest eigenvalues: [1] 0.3230090 0.2943943 0.2928252 0.2698441 0.2555536 0.1605081 [7] 0.1258876 -0.2555022 -0.2563254 -0.5642405 Largest eigenvalues: [1] 100029797 96809429 90548057 86409947 85841085 83754786 83625660 [8] 81369979 80406427 78344727 Smallest eigenvalues: [1] 0.46013335 0.45172698 0.37933118 0.35477214 0.33368496 0.33212310 [7] 0.23573405 0.21858632 0.08841917 -0.01647791 Largest eigenvalues: [1] 98741796 96664446 90100381 86584721 84688271 83574991 82908023 80627864 [9] 79901763 77268093 Smallest eigenvalues: [1] 0.3779101 0.3721540 0.3415406 0.3081000 0.2855563 0.2656054 [7] 0.2484234 0.1810401 -0.1259701 -0.5919691 Largest eigenvalues: [1] 99105214 96123828 89948032 86626069 84050761 83186947 82847873 80233426 [9] 79819175 77151568 Smallest eigenvalues: [1] 0.352348739 0.290859846 0.284488355 0.266559664 0.257935947 [6] 0.193266438 0.009113708 -0.012312298 -0.019982819 -0.350382423 Largest eigenvalues: [1] 99275851 98075499 91210454 87748557 85703596 84956508 83390584 81180174 [9] 80873916 78117211 Smallest eigenvalues: [1] 0.40740684 0.34125705 0.28032934 0.27970711 0.26223554 0.17809201 [7] 0.10190274 0.04231496 0.00806742 -0.80720759 Largest eigenvalues: [1] 99715109 95379477 89691581 85853106 84475245 83260431 81933265 80609732 [9] 79169886 77314398 Smallest eigenvalues: [1] 0.377260491 0.326692777 0.321614025 0.307795325 0.286824766 [6] 0.078509067 0.048341098 0.009870761 -0.265951462 -0.543595123 Largest eigenvalues: [1] 100861640 96260824 90046190 85922546 85834778 83940120 82146502 [8] 81012453 79789192 77995383 Smallest eigenvalues: [1] 0.304449301 0.293732995 0.288601735 0.285795259 0.083624387 [6] 0.082763101 0.073632232 -0.009529578 -0.132864793 -0.681461786 Largest eigenvalues: [1] 99671057 95844936 90057854 85481707 84732712 82727493 82174569 80102899 [9] 79318588 77107175 Smallest eigenvalues: [1] 0.46845287 0.43155178 0.42104952 0.39154198 0.38805607 0.32539189 [7] 0.21714954 0.18806339 0.03685169 -0.12523500 Largest eigenvalues: [1] 100123496 96151552 89660750 86352522 84853409 83151390 82439092 [8] 80486149 79406546 77041972 Smallest eigenvalues: [1] 0.234963129 0.215578717 0.159159208 0.094570242 0.073241427 [6] 0.057668746 0.001049839 -0.034124153 -0.046536557 -1.350489856 Largest eigenvalues: [1] 102702822 97185491 91703988 87838422 86480263 85145899 83218522 [8] 82454254 80443827 79106450 Smallest eigenvalues: [1] 0.36345346 0.30941397 0.25829211 0.24709930 0.24199553 0.18688051 [7] 0.11249785 0.05197606 -0.14009560 -0.19988168 Largest eigenvalues: [1] 99638794 96426152 89938378 85762403 85289697 83238317 82326783 80696879 [9] 79436937 77713524 Smallest eigenvalues: [1] 0.2064835 0.2038126 0.1546624 0.1216712 0.0451268 0.0181933 [7] -0.1072878 -0.3903535 -0.4671638 -1.0560489 Largest eigenvalues: [1] 98184452 97553685 91070823 86898805 85213966 84681657 82980625 81204877 [9] 80512739 77854518 Smallest eigenvalues: [1] 0.43006129 0.41948602 0.39302868 0.36717094 0.31140421 0.29346683 [7] 0.25834340 0.17057346 -0.09687251 -0.14070740 Largest eigenvalues: [1] 98950552 96608828 89558237 86644176 84919745 83108440 83022169 80581548 [9] 79640043 77388041 Smallest eigenvalues: [1] 0.44421067 0.41728523 0.40631615 0.38573123 0.31705101 0.27197940 [7] 0.24308161 0.14681293 0.06298365 -0.65569114 Largest eigenvalues: [1] 99088612 96500805 90202450 86408842 84757276 83060922 82809392 80622844 [9] 79834002 77555554 Smallest eigenvalues: [1] 0.3260899 0.2938251 0.2754448 0.2607610 0.2417266 0.2351440 [7] 0.1956722 0.1130951 -0.2668751 -0.4026913 Largest eigenvalues: [1] 101520109 97164022 90960803 86258191 86215708 83986764 82858126 [8] 81446908 80072676 78283860 Smallest eigenvalues: [1] 0.471729760 0.445851319 0.380950250 0.375796247 0.275314041 [6] 0.235208604 0.168679532 0.088743823 -0.006149734 -0.402542540 Largest eigenvalues: [1] 100595255 96332790 90081730 86584230 86063565 84805234 82578697 [8] 81869669 79873112 78807383 Smallest eigenvalues: [1] 0.392574909 0.323227841 0.264275981 0.252799316 0.238876125 [6] 0.227615335 0.200830252 0.041784983 -0.006614034 -0.108080453 Largest eigenvalues: [1] 100762607 96707435 90541590 86584934 85628613 85229283 83068335 [8] 82270394 80231814 78984955 Smallest eigenvalues: [1] 0.40519056 0.37007143 0.32743284 0.31850236 0.31575536 0.28210140 [7] 0.24574488 0.22704934 0.07715977 -0.03278965 Largest eigenvalues: [1] 100240231 96424402 90179426 86214014 85569065 83626347 82334800 [8] 80834413 79544488 77902464 Smallest eigenvalues: [1] 0.41225718 0.38215567 0.36886156 0.26053381 0.22753264 0.16553038 [7] 0.10917071 0.06955956 -0.56813493 -0.59725692 Largest eigenvalues: [1] 99824524 97281407 90775003 86522876 86363463 83719662 83471638 80944465 [9] 80264267 77761691 Smallest eigenvalues: [1] 0.21474917 0.21037460 0.20895953 0.18273155 0.17798000 0.11727051 [7] 0.02795542 0.01352027 -0.30015233 -0.53471066 Largest eigenvalues: [1] 98833116 96859634 90718039 86612346 84966168 83705134 83534268 81244852 [9] 80202804 77814034 Smallest eigenvalues: [1] 0.33054363 0.31714123 0.31127685 0.30968255 0.18828159 0.18696858 [7] 0.07079336 -0.05126187 -0.21514980 -0.69903244 Largest eigenvalues: [1] 100895559 95495595 89628997 85972704 85723392 83801830 81931669 [8] 81130744 79290178 77871736 Smallest eigenvalues: [1] 0.30787214 0.27796940 0.25956291 0.25672811 0.20404935 0.11322161 [7] 0.09856056 -0.11611236 -0.14190489 -0.23225321 Largest eigenvalues: [1] 100951158 96861480 91035093 86119147 85608333 84141413 82542283 [8] 81393987 80074680 78226729 Smallest eigenvalues: [1] 0.44443009 0.43524738 0.36923795 0.31517234 0.29267114 0.24828446 [7] 0.22830373 0.06689916 -0.02593872 -0.24431659 Largest eigenvalues: [1] 101042233 97670728 91169261 87110163 86472134 85295635 83329473 [8] 82462170 80260519 79203703 Smallest eigenvalues: [1] 2.179788e-01 2.100277e-01 2.076166e-01 1.994445e-01 1.231648e-01 [6] 3.651859e-02 4.330197e-05 -3.749344e-01 -4.338104e-01 -8.534398e-01 Largest eigenvalues: [1] 99260075 96329449 90225616 85939512 85284896 84589449 83119924 81703875 [9] 79953740 78409856 Smallest eigenvalues: [1] 0.28824889 0.28033143 0.22677680 0.21238950 0.18512684 0.09991076 [7] 0.09185984 0.07305105 -0.02590437 -0.22247670 Largest eigenvalues: [1] 97111755 97004984 89964628 86612650 83491548 83097118 82525378 80003343 [9] 79570390 76870339 Smallest eigenvalues: [1] 0.418407311 0.415534907 0.386480525 0.379556646 0.280339956 [6] 0.181208609 0.108048974 -0.001095688 -0.153554310 -0.214763853 Largest eigenvalues: [1] 100567332 95263971 89702030 85304646 84703051 83147391 82604433 [8] 80814607 79694823 77716387 Smallest eigenvalues: [1] 0.4956499 0.4760013 0.4670619 0.3805585 0.3481619 0.3148870 [7] 0.2722805 0.2324156 0.2058396 -0.1207783 Largest eigenvalues: [1] 100310975 96384137 90198434 86346192 86112040 83594443 83040168 [8] 81126391 79824167 77749250 Smallest eigenvalues: [1] 0.20448030 0.18144414 0.17740617 0.16937166 0.15550766 0.11872069 [7] 0.09445057 -0.07012099 -0.10272554 -0.13203024 Largest eigenvalues: [1] 99405212 95748036 89940197 85699934 84857378 83998991 82631351 81390858 [9] 79466973 78315757 Smallest eigenvalues: [1] 0.4451035 0.4266185 0.3914764 0.3860346 0.3414694 0.2951384 [7] 0.1540427 0.1252575 0.1008103 -0.5550346 Largest eigenvalues: [1] 99765650 95582564 89332909 85774827 85055904 83098730 82561010 80719186 [9] 79497425 77683525 Smallest eigenvalues: [1] 0.3160270 0.2892428 0.2747357 0.2288929 0.2265579 0.2079793 [7] 0.1217725 0.0316530 -0.1088142 -0.3470824 Largest eigenvalues: [1] 99040206 96422647 90697487 85858616 85469413 84761903 82982737 81800592 [9] 80064562 78784216 Smallest eigenvalues: [1] 0.4651646 0.3107724 0.3101555 0.2824105 0.2178087 0.2160932 [7] 0.1095507 0.0721208 -0.3617690 -0.5908036 Largest eigenvalues: [1] 100362525 96904267 91268895 86132560 86006762 83557376 83390343 [8] 81288675 80243744 78378847 Smallest eigenvalues: [1] 0.38868526 0.34683812 0.32353636 0.32238483 0.24837171 0.18955717 [7] 0.13432165 0.04198960 -0.06460492 -0.23390628 Largest eigenvalues: [1] 99919675 96820131 90125085 86445168 85794325 84237649 82937776 81578278 [9] 79835306 78269959 Smallest eigenvalues: [1] 0.37311825 0.36972448 0.34270298 0.34008906 0.33211904 0.17576808 [7] 0.16723274 0.12966235 0.08624482 -0.02075481 Largest eigenvalues: [1] 100086518 95902673 90119445 85842675 84581413 84272580 82596578 [8] 81703288 80025570 78681901 Smallest eigenvalues: [1] 0.30881388 0.27243168 0.25884345 0.23250052 0.19309561 0.16723259 [7] 0.10246137 0.04040194 -0.14089564 -0.25350740 Largest eigenvalues: [1] 99657533 97532976 90747322 86626788 85641425 84391298 83386709 81503493 [9] 80568493 78390741 Smallest eigenvalues: [1] 0.24463514 0.21844144 0.18165696 0.17303054 0.13643230 0.05197567 [7] -0.04922595 -0.06065563 -0.08286892 -0.63467387 Largest eigenvalues: [1] 98060817 96703834 90558880 86282344 83616317 83094716 82880062 80589608 [9] 79737879 77146465 Smallest eigenvalues: [1] 0.21663736 0.19417719 0.17739353 0.13572463 0.13132323 0.10317923 [7] 0.08028882 -0.07406903 -0.30661969 -0.33970460 Largest eigenvalues: [1] 99896726 96453623 89998986 85923121 85418809 85305090 82235699 82048315 [9] 79589906 78819091 Smallest eigenvalues: [1] 0.51327769 0.47274899 0.36001167 0.33464594 0.30419647 0.27134758 [7] 0.21620494 0.19975064 -0.05327562 -0.21927458 Largest eigenvalues: [1] 99554077 96970869 90513599 86752614 85478780 84137016 83109249 81307119 [9] 80312570 78523084 Smallest eigenvalues: [1] 0.34245120 0.33703236 0.31645378 0.30957622 0.29882817 0.18180118 [7] 0.15382880 0.01757532 -0.20525686 -0.26333565 Largest eigenvalues: [1] 98819968 96536508 90173802 86464275 84920258 84158385 83064242 81550721 [9] 80258485 78500536 Smallest eigenvalues: [1] 0.47149807 0.46933557 0.43265550 0.40862105 0.28662916 0.19070740 [7] 0.18953012 0.15282231 0.03081602 -0.06932745 Largest eigenvalues: [1] 98447453 97895091 91194764 87384178 84858116 84623625 83034910 80906728 [9] 80576462 77632363 Smallest eigenvalues: [1] 0.31309406 0.22926712 0.22379404 0.20734590 0.13822084 0.11147504 [7] 0.01610159 -0.07663903 -0.30658487 -1.14533747 Largest eigenvalues: [1] 100063896 98569363 91840572 87619550 86992570 84620386 84132713 [8] 81683606 80841963 78161452 Smallest eigenvalues: [1] 0.23699729 0.23574788 0.22415042 0.18785558 0.16502717 0.11216462 [7] 0.01113985 -0.07831166 -0.35582282 -0.66083180 Largest eigenvalues: [1] 99855928 97291562 91134981 87408119 85178122 84097459 83378486 81219289 [9] 80756285 77792490 Smallest eigenvalues: [1] 0.40938699 0.40497708 0.38389218 0.32635873 0.28461028 0.19933101 [7] 0.15149618 0.14903744 -0.01757108 -0.22750128 Largest eigenvalues: [1] 98972156 96687780 90331592 85947453 85845368 83787374 82951271 81289427 [9] 79566265 77802825 Smallest eigenvalues: [1] 0.35800394 0.31259346 0.31075941 0.26987087 0.19032206 0.09711144 [7] 0.07420255 -0.00278496 -0.02229466 -0.05083056 Largest eigenvalues: [1] 97654481 96591357 90118915 86282097 84164496 84013902 82634424 81237556 [9] 79460941 77876820 Smallest eigenvalues: [1] 0.09394667 0.03464270 0.01420493 0.01394758 -0.05270145 -0.12205341 [7] -0.15597161 -0.19860629 -0.46390066 -0.73604692 Largest eigenvalues: [1] 98836111 96454337 89991742 85568270 85528688 84383824 82863591 81950467 [9] 79424769 78517130 Smallest eigenvalues: [1] 0.32853099 0.32488451 0.30678680 0.28087943 0.24718031 0.14338928 [7] -0.02343517 -0.03214751 -0.08411257 -0.60704692 Largest eigenvalues: [1] 100384077 96641395 89685871 85842347 85380365 83393178 81681901 [8] 80187571 78934890 76935248 Smallest eigenvalues: [1] 0.4313435 0.4150248 0.4097807 0.2934095 0.2311940 0.2203699 [7] 0.1825480 0.1282958 0.1277575 -0.4107511 Largest eigenvalues: [1] 99352215 96010157 89697132 85921731 84983810 83528410 82300190 80913603 [9] 79534610 77749033 Smallest eigenvalues: [1] 0.4314470 0.4008653 0.3801594 0.3162361 0.2700170 0.2661314 [7] 0.2191119 0.1767977 -0.1669867 -0.3904630 Largest eigenvalues: [1] 101471359 95120397 89769489 85400105 84629324 82888008 81613822 [8] 80521157 79326385 77820404 Smallest eigenvalues: [1] 0.39233761 0.35841107 0.34893938 0.27862364 0.19057811 0.05633138 [7] -0.13416829 -0.17038230 -0.68389569 -1.49265958 Largest eigenvalues: [1] 99861595 97551231 91390210 86941398 86360513 84490578 83845045 81693101 [9] 80854582 78545998 Smallest eigenvalues: [1] 0.27228578 0.26075399 0.23250886 0.22587276 0.22433658 0.21678978 [7] 0.21343736 0.14712862 0.01910522 -0.55556833 Largest eigenvalues: [1] 99863374 96633282 90690760 85670239 85446954 83674163 82627108 81332909 [9] 79701708 78136863 Smallest eigenvalues: [1] 0.41902382 0.31229784 0.29942695 0.28044150 0.27321020 0.23520273 [7] 0.02549636 -0.09897169 -0.14524003 -0.23738846 Largest eigenvalues: [1] 100117057 96078151 89647092 86359739 85386295 82425277 82137457 [8] 79673602 79277254 76578930 Smallest eigenvalues: [1] 0.313430049 0.250841235 0.222226866 0.111620935 0.097479814 [6] 0.062645253 0.062467936 0.007186818 -0.097425043 -0.189550821 Largest eigenvalues: [1] 96454977 96264513 89950923 85510968 84103076 82875140 82773899 80106079 [9] 79241447 77097145 Smallest eigenvalues: [1] 0.43801219 0.43195103 0.33991264 0.32067627 0.24395068 0.23884219 [7] 0.23509164 0.23079284 0.01354983 -0.06906893 Largest eigenvalues: [1] 100268014 95437137 89218950 85432872 84557123 82924115 81825278 [8] 80289200 79118828 77169264 Smallest eigenvalues: [1] 0.35727265 0.34357011 0.33833948 0.33599097 0.21770200 0.20204036 [7] 0.11892617 0.09337013 0.02774419 -0.38989145 Largest eigenvalues: [1] 98678682 96582434 90875657 86157545 84469035 83570950 83294510 81169433 [9] 80248695 77876590 Smallest eigenvalues: [1] 0.34504011 0.33240924 0.29920790 0.25345707 0.11818112 0.08088973 [7] 0.00466336 -0.12445963 -0.39288758 -1.11295579 Largest eigenvalues: [1] 99487526 97497026 91416960 87228282 85494876 83994299 83674735 81552643 [9] 80850089 78674596 Smallest eigenvalues: [1] 0.22451401 0.20716344 0.18076921 0.15532263 0.13958293 0.10940484 [7] -0.03693148 -0.20207682 -0.31562009 -0.71839444 Largest eigenvalues: [1] 99131684 96613556 90677841 86771170 84403972 83827670 83274666 81091855 [9] 80355039 77447836 Smallest eigenvalues: [1] 0.4411756 0.4348785 0.4176587 0.3883593 0.3433553 0.2834340 [7] 0.2757746 0.2216968 0.1718022 -0.2249895 Largest eigenvalues: [1] 100530481 98120690 91249223 87475784 86820402 85058625 83767097 [8] 82076360 80932534 79291314 Smallest eigenvalues: [1] 0.40701262 0.36444763 0.31798034 0.25170800 0.24253319 0.23246722 [7] 0.19037237 0.02353331 -0.01980566 -0.22281943 Largest eigenvalues: [1] 99845822 95658921 89016624 86086192 85597304 83460777 81663203 80292147 [9] 79241119 77504940 Smallest eigenvalues: [1] 0.42938860 0.42232802 0.38569818 0.35964695 0.33818541 0.20711774 [7] 0.19604398 -0.01116782 -0.04836319 -0.53445122 Largest eigenvalues: [1] 101518396 94843250 89187008 85484258 84811305 82791289 81557457 [8] 80374253 79213162 77397827 Smallest eigenvalues: [1] 0.36791286 0.34202708 0.32387201 0.31664417 0.28536432 0.17959381 [7] 0.16217525 0.02244408 -0.22787515 -0.43247088 Largest eigenvalues: [1] 100703462 97275422 91144866 87125103 85610313 83823161 83707504 [8] 81483061 80394763 78061853 Smallest eigenvalues: [1] 0.5107679 0.4504307 0.3862566 0.3419404 0.3312794 0.2159643 [7] 0.1122371 0.1102816 -0.2765152 -0.3566640 Largest eigenvalues: [1] 99078199 96680604 90302250 86910674 84734243 83850855 82994355 80314676 [9] 80063684 76824722 Smallest eigenvalues: [1] 0.33584651 0.33415630 0.32597759 0.30133554 0.22612872 0.22086517 [7] 0.20920614 0.03269466 -0.15333993 -0.38172266 Largest eigenvalues: [1] 99820028 97404656 90906689 87495730 85379794 83847134 83510644 81360701 [9] 80530741 78630872 Smallest eigenvalues: [1] 0.301103904 0.294335396 0.259228732 0.192033088 0.181042400 [6] 0.143889505 0.079508826 0.003081642 -0.144245990 -0.199709327 Largest eigenvalues: [1] 100435240 96489309 90450238 86025577 85977384 83498022 82882485 [8] 81189264 79561519 77670875 Smallest eigenvalues: [1] 0.42058418 0.38554597 0.34851068 0.34202552 0.26997938 0.26894196 [7] 0.25655286 0.19736059 0.17361859 -0.04413678 Largest eigenvalues: [1] 99023161 96328445 89498440 85939871 85019576 83613597 82511049 80909543 [9] 79519530 77831932 Smallest eigenvalues: [1] 0.303192171 0.284061189 0.276148216 0.222682643 0.138140092 [6] 0.075580999 0.030817723 0.002024801 -0.177952722 -0.521314087 Largest eigenvalues: [1] 98725310 97580545 90253903 87267628 84928209 84775015 83481571 81797897 [9] 80483111 78610177 Smallest eigenvalues: [1] 0.428196559 0.415758367 0.365618094 0.295780025 0.123686959 [6] 0.085966011 -0.002675043 -0.005514798 -0.041399761 -0.607787564 Largest eigenvalues: [1] 102246914 97222191 91532156 87259224 86631117 85115018 83364369 [8] 82330333 80937789 79645197 Smallest eigenvalues: [1] 0.36001287 0.34460250 0.33253890 0.31142534 0.27089841 0.14060762 [7] 0.13114054 0.07209750 -0.08634331 -0.10732603 Largest eigenvalues: [1] 98960149 96631249 90166884 86295350 85633049 84523381 83360410 81636240 [9] 80434764 78751342 Smallest eigenvalues: [1] 0.40110068 0.40027748 0.36613797 0.30691530 0.29299316 0.24761910 [7] 0.19348533 0.18056832 -0.06352012 -0.39490320 Largest eigenvalues: [1] 99190839 97048944 90358567 86920677 85502055 84489028 83120603 81592879 [9] 80147074 78063945 Smallest eigenvalues: [1] 0.23402296 0.20905008 0.15574005 0.14781863 0.12052754 0.03904151 [7] -0.10691209 -0.23401472 -0.28549672 -0.99044935 Largest eigenvalues: [1] 99852865 96104803 89936406 85870498 85648658 83073587 82628393 80266874 [9] 79838077 77168405 Smallest eigenvalues: [1] 0.39287275 0.35641504 0.31726594 0.29033461 0.24813164 0.23218553 [7] 0.20493214 0.11985202 -0.09807594 -0.32267281 Largest eigenvalues: [1] 100785766 97954033 91459099 87305294 85739899 84749753 83584723 [8] 82068323 80623709 78907177 Smallest eigenvalues: [1] 0.44039214 0.38914058 0.33762984 0.27897675 0.25412127 0.22211749 [7] 0.17817647 0.15202289 0.01488218 -0.38695905 Largest eigenvalues: [1] 99035829 95416130 89679895 85535195 84195744 83664067 82045703 81058725 [9] 79311509 77559423 Smallest eigenvalues: [1] 0.40858082 0.40521180 0.30371451 0.29712132 0.27515423 0.25037619 [7] 0.24976230 -0.07136325 -0.11142482 -0.29703450 Largest eigenvalues: [1] 98290876 96847976 89861045 86704813 84829844 83418411 83184992 80727021 [9] 79849618 77473252 Smallest eigenvalues: [1] 0.50001869 0.48056690 0.45702531 0.42109877 0.35495694 0.33042460 [7] 0.26665534 0.20704247 0.04311262 -0.21360849 Largest eigenvalues: [1] 98458955 95819253 89130851 86173134 84160807 82613242 82450887 79972690 [9] 79304380 76704803 Smallest eigenvalues: [1] 0.41008871 0.36344470 0.34268481 0.29853210 0.25101946 0.24574792 [7] 0.22968143 0.04133598 -0.30323964 -0.44287712 Largest eigenvalues: [1] 98132036 96491732 90177666 87031928 84109503 83890086 82120280 80236934 [9] 79500776 76348342 Smallest eigenvalues: [1] 0.41635527 0.39643040 0.34462347 0.29699288 0.27856264 0.27633244 [7] 0.21301526 -0.03490948 -0.07132088 -0.14723872 Largest eigenvalues: [1] 100182234 97458515 90841058 87326625 85193836 83740341 83566000 [8] 81157167 80434009 78044381 Smallest eigenvalues: [1] 0.5011361 0.4473885 0.4085632 0.3734306 0.3569594 0.3425141 [7] 0.3147804 0.1579448 -0.1015685 -0.1517036 Largest eigenvalues: [1] 99997485 97337152 90526962 87366636 85435426 83885100 83615386 81339841 [9] 80533277 78148861 Smallest eigenvalues: [1] 0.26944587 0.26677659 0.25188427 0.19706187 0.19094033 0.16749463 [7] 0.04769111 -0.04008435 -0.10509525 -0.28368797 Largest eigenvalues: [1] 98566473 95915344 89453277 85926248 83534674 83381619 82784036 80750362 [9] 79692712 77439922 Smallest eigenvalues: [1] 0.2153345142 0.1939085964 0.1783041464 0.1749744866 0.1323146071 [6] 0.0185963799 0.0179228280 0.0001136309 -0.1547130021 -0.6087427639 Largest eigenvalues: [1] 99681387 97848433 91536831 87002576 86205368 84552707 83970519 81543450 [9] 80739268 78766264 Smallest eigenvalues: [1] 0.3573017 0.2914597 0.2488881 0.2255140 0.2112320 0.2087011 [7] 0.1851237 0.1510627 -0.1110930 -0.1696028 Largest eigenvalues: [1] 98206731 97225029 90111972 87011527 84788976 84212436 83524015 81557421 [9] 80208759 78308652 Smallest eigenvalues: [1] 0.39170285 0.38582195 0.36164078 0.34324168 0.24266822 0.18796943 [7] 0.16663398 0.12344121 -0.06960817 -0.24356689 Largest eigenvalues: [1] 99602379 95738048 90139200 85051029 85005273 83970663 82203712 81271847 [9] 79593405 78369460 Smallest eigenvalues: [1] 0.241406146 0.205457182 0.175996030 0.114242355 0.028364592 [6] -0.001623815 -0.040325178 -0.050156833 -0.105969594 -1.096258568 Largest eigenvalues: [1] 96473892 96445053 90300185 86560825 84074536 83788270 82943163 80813232 [9] 79930273 77412527 Smallest eigenvalues: [1] 0.3460029 0.3436308 0.2975445 0.2004709 0.1655647 0.1128766 [7] 0.1059864 0.0746796 -0.3253435 -0.3711266 Largest eigenvalues: [1] 99960749 95942548 89512582 85939005 85633281 83355638 82201548 80867582 [9] 79145410 77698468 Smallest eigenvalues: [1] 0.48700056 0.45409093 0.30948753 0.27380197 0.25708323 0.23950863 [7] 0.19118523 0.01871397 -0.03601040 -0.15158764 Largest eigenvalues: [1] 101933391 95814947 89992127 86156429 86049128 84311823 82828632 [8] 81791293 79972087 78492243 Smallest eigenvalues: [1] 0.37699948 0.37519356 0.35384173 0.27425011 0.17658792 0.13112822 [7] 0.10639095 0.06759279 -0.30924561 -0.31977748 Largest eigenvalues: [1] 99748655 96621129 90583358 86275206 85704672 83824880 83241075 81054063 [9] 80102118 78052289 Smallest eigenvalues: [1] 0.3486065 0.3483375 0.2722571 0.2378871 0.2126639 0.1877540 [7] 0.1561237 0.1462085 0.1169284 -0.7154846 Largest eigenvalues: [1] 100714671 96207745 90393997 85878802 85157288 84832759 82251210 [8] 81741992 80053172 78765077 Smallest eigenvalues: [1] 0.40945523 0.36068517 0.33821367 0.31492065 0.30492223 0.24771585 [7] 0.21971653 0.10456932 0.08611411 -0.53191484 Largest eigenvalues: [1] 100627244 97149857 90818865 86216991 86078127 83387766 82763225 [8] 80912453 79698911 77996692 Smallest eigenvalues: [1] 0.37616993 0.30844994 0.29948855 0.29302885 0.28062970 0.25498822 [7] 0.09802171 -0.17180103 -0.17929620 -0.26260563 Largest eigenvalues: [1] 100292963 94851270 88654424 85248640 85180907 82420885 81408968 [8] 79632993 78669713 76620845 Smallest eigenvalues: [1] 0.31929532 0.30962218 0.29295754 0.24546210 0.21094489 0.19175648 [7] 0.17828202 0.17541633 0.03272447 -0.22744769 Largest eigenvalues: [1] 100381947 99194313 92415504 88099414 86235582 85547398 84166551 [8] 82457502 80744271 79147537 Smallest eigenvalues: [1] 0.27281924 0.26796610 0.18828748 0.10242334 0.06776861 0.02514408 [7] -0.00851845 -0.05583437 -0.13812955 -0.69661165 Largest eigenvalues: [1] 99081514 96558866 90062751 87117164 85339180 84460402 83340506 81671399 [9] 80628647 78539530 Smallest eigenvalues: [1] 0.30717755 0.29788919 0.26579308 0.23907166 0.15675273 0.12863165 [7] 0.03914482 0.02203505 -0.12625111 -0.15345823 Largest eigenvalues: [1] 97482224 96098462 89463039 85843192 84518083 83108755 82502543 80586704 [9] 79379983 77319352 Smallest eigenvalues: [1] 0.4606964 0.4498573 0.4341361 0.4044638 0.3919605 0.3316422 [7] 0.2380871 0.1760859 0.1019369 -0.4003220 Largest eigenvalues: [1] 100604794 96812981 90701168 86606166 86605272 84628723 83045897 [8] 81737390 80209181 78645595 Smallest eigenvalues: [1] 0.30228558 0.25753183 0.22673132 0.21083375 0.20051458 0.18972953 [7] 0.05001417 0.02248299 0.01528388 -0.15330618 Largest eigenvalues: [1] 99188761 96610294 90349265 85927443 85134621 83987185 83304831 81333384 [9] 80259932 78479361 Smallest eigenvalues: [1] 0.42042496 0.38610917 0.38150603 0.33045975 0.25849543 0.24859809 [7] 0.23124638 0.14220413 0.02119718 -0.22765793 Largest eigenvalues: [1] 99944934 98200225 91945060 87390475 85814126 84375425 84051618 81818587 [9] 80967894 78799771 Smallest eigenvalues: [1] 0.38343928 0.33848989 0.30908607 0.30526491 0.20031416 0.11286690 [7] 0.08906204 0.03632128 -0.04255738 -0.45585753 Largest eigenvalues: [1] 102182210 96686791 90995083 87280922 85906787 83754025 83025937 [8] 81323481 80255935 78467902 Smallest eigenvalues: [1] 0.4750651 0.4068162 0.3756430 0.3544322 0.3413545 0.2973791 [7] 0.2837976 0.2378219 -0.2185010 -0.2210471 Largest eigenvalues: [1] 101140201 97438254 91063380 87163038 85714724 84884044 83065281 [8] 82030700 80455347 79198026 Smallest eigenvalues: [1] 0.32136750 0.21399019 0.18043269 0.15871306 0.14574535 0.14278759 [7] -0.07996082 -0.22705698 -0.94096321 -1.10915730 Largest eigenvalues: [1] 103055853 97258656 91779731 87641210 86572058 84846449 83524813 [8] 82503978 81026538 79412852 Smallest eigenvalues: [1] 0.23222786 0.22005381 0.18717196 0.17872592 0.16086927 0.09212912 [7] 0.08113099 0.04326307 -0.02664769 -0.86511128 Largest eigenvalues: [1] 99072419 95656343 89881616 85711273 84921930 83176239 82371409 80627638 [9] 79437988 77473306 Smallest eigenvalues: [1] 0.3327723 0.2615081 0.2528973 0.1895453 0.1799604 0.1628178 [7] 0.1122068 0.1076461 -0.5657305 -0.8363164 Largest eigenvalues: [1] 97856589 97555784 90034761 86781599 84638618 83504340 82633273 80300762 [9] 79648626 77383186 Smallest eigenvalues: [1] 0.22536684 0.22404784 0.20396321 0.18298110 0.15406155 0.15017093 [7] 0.07459641 -0.12694544 -0.16485056 -0.30890061 Largest eigenvalues: [1] 98642539 96418073 90315739 85953238 84734391 83532528 83346682 81336835 [9] 79894132 78001855 Smallest eigenvalues: [1] 0.318252765 0.292149770 0.281236994 0.280918317 0.221670301 [6] 0.187539017 0.019108335 -0.002302866 -0.033659372 -0.266602106 Largest eigenvalues: [1] 99154911 95670807 89216985 85470097 85323502 82882334 82723448 80424940 [9] 79083555 77042314 Smallest eigenvalues: [1] 0.48120013 0.43843719 0.38673201 0.37938179 0.34662840 0.32160201 [7] 0.26332508 0.12799789 0.02297657 -0.19224168 Largest eigenvalues: [1] 99818555 96095514 90240701 86108313 85073632 83941909 82376942 80907664 [9] 79513458 77962168 Smallest eigenvalues: [1] 0.19925156 0.19048414 0.17757749 0.16026219 0.08552460 0.04335418 [7] -0.12007095 -0.17869306 -0.18050936 -0.32592975 Largest eigenvalues: [1] 98135464 95340878 89123007 85453541 83474616 82613520 82222039 80257643 [9] 79035371 76923155 Smallest eigenvalues: [1] 0.28870140 0.27843684 0.26552235 0.25904209 0.25445189 0.14223807 [7] 0.13281769 0.11806811 -0.01231800 -0.05015492 Largest eigenvalues: [1] 99491554 97576782 91146108 86545697 84906426 84079424 83366713 81287722 [9] 80529554 78191431 Smallest eigenvalues: [1] 0.42556016 0.39155007 0.35295703 0.33511458 0.29968992 0.23966884 [7] 0.21359940 0.14313916 0.08460275 -0.02408846 Largest eigenvalues: [1] 100931028 98003410 91352237 87354120 85384000 84630653 83416583 [8] 81805581 80510207 78914111 Smallest eigenvalues: [1] 0.160722979 0.144748428 0.136866407 0.014927617 -0.001412761 [6] -0.056523043 -0.061078867 -0.239256716 -0.454745064 -0.581751132 Largest eigenvalues: [1] 99807441 96608260 90865118 85686586 85561036 83710720 82584821 80718669 [9] 80300226 77814264 Smallest eigenvalues: [1] 0.36234276 0.34660526 0.23632228 0.20939052 0.18651477 0.13723656 [7] 0.11044171 0.01413601 -0.11785535 -0.26152863 Largest eigenvalues: [1] 99389840 97641834 90995572 87360147 85782404 84407542 84065748 81640133 [9] 80720287 78736745 Smallest eigenvalues: [1] 0.35629740 0.32473997 0.31765388 0.28564839 0.27751105 0.24946310 [7] 0.16394921 0.09332484 0.05364107 -0.03790259 Largest eigenvalues: [1] 99571820 96472763 90178981 86741060 84820233 84156958 83077389 81496666 [9] 80520244 78698790 Smallest eigenvalues: [1] 0.39064716 0.37546323 0.35244183 0.28480280 0.28476617 0.22359175 [7] 0.17017990 0.10015471 -0.03243227 -0.12594887 Largest eigenvalues: [1] 100732499 97298912 90996749 86840039 85574160 84983889 83243074 [8] 81859287 80523171 78790227 Smallest eigenvalues: [1] 0.41563345 0.38329100 0.37926199 0.33635050 0.27179922 0.26776038 [7] 0.19182910 -0.05103619 -0.39895147 -0.56471587 Largest eigenvalues: [1] 100812333 96917794 90842963 87093805 86373138 84611564 83466561 [8] 81758990 80578012 78522752 Smallest eigenvalues: [1] 0.34737729 0.29420362 0.28489043 0.26263417 0.20039635 0.08699910 [7] 0.02964714 -0.02127512 -0.05699699 -0.35888419 Largest eigenvalues: [1] 100147469 95762190 89850309 85711668 84648001 83232160 82791093 [8] 80846581 79755876 77551271 Smallest eigenvalues: [1] 0.32936896 0.30372161 0.28639874 0.22515018 0.20464420 0.17621093 [7] 0.11744887 0.05547025 -0.24301547 -0.46635999 Largest eigenvalues: [1] 99324445 97247730 90687592 86969984 84428925 83492839 83329475 80942189 [9] 80147785 77811074 Smallest eigenvalues: [1] 0.32438539 0.29941732 0.24235070 0.22480898 0.17024942 0.15118652 [7] 0.10088109 0.05756656 0.01024561 -0.15598137 Largest eigenvalues: [1] 98549610 97600248 90612052 87268322 84593843 84212596 83829975 81374844 [9] 80445977 78036966 Smallest eigenvalues: [1] 0.22368749 0.20008031 0.19020969 0.17622172 0.15936609 0.03497386 [7] -0.17139976 -0.21479082 -0.48165974 -0.97830895 Largest eigenvalues: [1] 103768561 98002752 92704337 87863250 86891909 85394090 83834648 [8] 83092695 81282032 80324444 Smallest eigenvalues: [1] 0.29846452 0.29798040 0.29494894 0.28715100 0.22423160 0.22199886 [7] 0.13102250 0.08985633 0.06845518 -0.07427156 Largest eigenvalues: [1] 98620540 96003762 90086528 86596876 84103513 83348577 82386692 80904266 [9] 79690206 78029737 Smallest eigenvalues: [1] 0.32011884 0.30053309 0.26848868 0.24542315 0.19039616 0.18839554 [7] -0.02646633 -0.13935248 -0.20101674 -0.34284844 Largest eigenvalues: [1] 100293075 95324435 89988464 85411789 84424643 83556057 82320486 [8] 81294669 79347289 77999922 Smallest eigenvalues: [1] 0.30105920 0.28140832 0.27238707 0.25628928 0.23476222 0.17424607 [7] 0.15644698 0.05970213 -0.05346660 -0.41323885 Largest eigenvalues: [1] 100404962 97110757 90786915 86405772 86047936 84316539 82929739 [8] 81503491 80221304 78315313 Smallest eigenvalues: [1] 0.22598577 0.21445521 0.21257769 0.13307714 0.13199657 0.01155900 [7] -0.03719501 -0.14590301 -0.26088304 -0.33472360 Largest eigenvalues: [1] 100286439 97781764 91453710 87098836 85553875 83872049 83665515 [8] 81467068 80631218 78286592 Smallest eigenvalues: [1] 0.29032224 0.28855289 0.26282363 0.17125115 0.14116691 0.11350614 [7] 0.09050936 0.02684284 -0.22362210 -0.27603654 Largest eigenvalues: [1] 99484417 98162240 91258435 87795351 84801165 83976330 83734703 81265105 [9] 80664108 77824817 Smallest eigenvalues: [1] 0.35995603 0.33047329 0.32894565 0.26805780 0.22057293 0.15076656 [7] -0.01595369 -0.13517904 -0.41781460 -0.49061356 Largest eigenvalues: [1] 99834399 96394873 89549916 86725008 85396958 83054161 82409560 80277030 [9] 79629651 77646566 Smallest eigenvalues: [1] 0.440572888 0.392050526 0.380539404 0.323483267 0.274082681 [6] 0.219388090 0.085302929 0.074388317 0.006626811 -0.082493569 Largest eigenvalues: [1] 98558017 96682197 89926321 86566586 85325007 83088849 82938912 80542993 [9] 79608660 77204900 Smallest eigenvalues: [1] 0.38294816 0.38066726 0.32429630 0.32004647 0.25961218 0.25541012 [7] 0.18078584 0.11359822 0.05837036 -0.37177632 Largest eigenvalues: [1] 100212858 97158386 90520190 86597469 86037378 84892867 83135682 [8] 82143749 80126730 78843396 Smallest eigenvalues: [1] 0.482332156 0.464447794 0.456611013 0.388993918 0.378561311 [6] 0.347969702 0.285027003 0.123552149 0.004680041 -0.327349814 Largest eigenvalues: [1] 100740726 96812003 90522470 86970578 84931058 83449081 83278956 [8] 80887030 80341046 77767742 Smallest eigenvalues: [1] 0.34192816 0.33848486 0.31597353 0.30732485 0.25858441 0.25780066 [7] 0.19814994 0.15678728 -0.09072235 -0.36683178 Largest eigenvalues: [1] 100925719 97471814 91265856 87217066 87050841 85274634 83843689 [8] 82437694 80604936 78952684 Smallest eigenvalues: [1] 0.285809143 0.272496852 0.264854738 0.236057127 0.222256767 [6] 0.218822214 -0.007260748 -0.051954505 -0.128675267 -0.508773575 Largest eigenvalues: [1] 100188323 96523389 90521516 86467991 85542453 84125414 83139716 [8] 81733571 80268596 78302731 Smallest eigenvalues: [1] 0.31070614 0.30120851 0.22254950 0.14685084 0.12964470 0.11789596 [7] 0.10502754 0.05188713 -0.14477462 -0.16640862 Largest eigenvalues: [1] 99952725 96569244 89739423 85824251 85818433 83791477 82295301 80731608 [9] 79503524 77630535 Smallest eigenvalues: [1] 0.48705859 0.47855575 0.42951581 0.40513507 0.28474430 0.25147949 [7] 0.21732966 0.13657549 0.07933952 -0.41109732 Largest eigenvalues: [1] 100439337 96698042 90395635 86592191 86031332 83147978 82949924 [8] 80658073 79794977 77477865 Smallest eigenvalues: [1] 0.3934724 0.3689057 0.3640745 0.3520970 0.3458520 0.3453258 [7] 0.3137613 0.2217387 0.1270074 -0.1457992 Largest eigenvalues: [1] 98530727 96894582 90314404 86204884 84660381 83550466 82799419 80692281 [9] 79951152 77735957 Smallest eigenvalues: [1] 0.3758499 0.3308763 0.2931784 0.2589691 0.2572563 0.2486185 [7] 0.1277425 0.1015791 -0.2067078 -0.2563001 Largest eigenvalues: [1] 99792372 97095764 90472616 86272618 86196097 83759904 83120628 81132627 [9] 79939673 77789683 Smallest eigenvalues: [1] 0.29312602 0.25532621 0.25071290 0.16029843 0.12300439 0.11595944 [7] -0.08749474 -0.15135258 -0.22943554 -0.26699709 Largest eigenvalues: [1] 98755460 97097379 90267272 86943944 85573683 83711578 83131635 81101623 [9] 80541261 77703704 Smallest eigenvalues: [1] 0.37300520 0.34729712 0.33309853 0.25952996 0.24023835 0.20535809 [7] 0.19495173 0.08991581 -0.06080220 -0.21516376 Largest eigenvalues: [1] 100244353 96718973 90839770 86114660 84882537 84294235 82933442 [8] 81720044 80253604 78565605 Smallest eigenvalues: [1] 0.408900329 0.359104791 0.306862713 0.284010465 0.251176487 [6] 0.248207346 0.182228310 0.165924948 -0.007629804 -0.419598726 Largest eigenvalues: [1] 99782063 96229346 89711878 85878833 85285953 83999558 82541030 81351799 [9] 79723553 78201600 Smallest eigenvalues: [1] 0.37455898 0.36979165 0.36369826 0.34393633 0.30188863 0.18009467 [7] 0.17721636 0.09165441 -0.10767542 -0.24823568 Largest eigenvalues: [1] 99695079 96444418 90525937 86263861 85382900 83713314 82843075 80916788 [9] 80042707 78096870 Smallest eigenvalues: [1] 0.3404867 0.3269050 0.3183764 0.2898138 0.2886690 0.2229904 [7] 0.2086984 0.1589362 -0.2174432 -0.3429633 Largest eigenvalues: [1] 99766079 96514548 90663288 85437252 85168320 83102100 82424714 80546603 [9] 79596699 77688030 Smallest eigenvalues: [1] 0.1704127405 0.1479135358 0.1329266855 0.0539817197 0.0004596179 [6] -0.0302180883 -0.2925952864 -0.2990572104 -0.4613620406 -0.7795846016 Largest eigenvalues: [1] 99838491 94986761 88703523 85582885 85054651 83105792 81538577 80407305 [9] 78481908 77112431 Smallest eigenvalues: [1] 0.39341720 0.39137842 0.36600789 0.34876083 0.34712210 0.31338305 [7] 0.22653195 0.13162288 0.08894038 -0.18268360 Largest eigenvalues: [1] 99653649 97337399 90715213 86785401 85905448 85116427 83059783 82026067 [9] 80193403 78742340 Smallest eigenvalues: [1] 0.40544191 0.39270392 0.34488020 0.29564885 0.29119464 0.17988292 [7] 0.16777600 -0.02571681 -0.06720081 -0.20956030 Largest eigenvalues: [1] 101420733 96591345 90333904 86610655 85165072 83219828 82741592 [8] 80643886 80070446 77578321 Smallest eigenvalues: [1] 0.365549372 0.336342457 0.327276931 0.325600667 0.245103707 [6] 0.146167930 0.078552521 -0.003528213 -0.032648796 -0.248893136 Largest eigenvalues: [1] 99974780 96706051 90257919 86666479 85505143 83858032 83252173 81135345 [9] 79992340 77671213 Smallest eigenvalues: [1] 0.4087225 0.3553458 0.3122703 0.3079115 0.2989448 0.2790082 [7] 0.2089619 -0.2225661 -0.3132425 -0.4818820 Largest eigenvalues: [1] 101745770 97358429 91165051 86938146 86896739 85354391 83502420 [8] 82247328 80833195 79212337 Smallest eigenvalues: [1] 0.250289284 0.224418451 0.197426478 0.167028608 0.154578957 [6] 0.061015199 0.058019220 0.005735497 -0.056804080 -0.445752694 Largest eigenvalues: [1] 99032926 95655786 89953932 85471640 83743846 83085670 82503909 80754398 [9] 79683087 77522270 Smallest eigenvalues: [1] 0.398523547 0.326966080 0.304939195 0.266477505 0.253632628 [6] 0.219817412 0.208272397 0.193460432 0.004620064 -0.217424971 Largest eigenvalues: [1] 102134025 97561114 91144046 87042263 86828886 85464790 82888537 [8] 82364217 80430794 79524399 Smallest eigenvalues: [1] 0.4728044 0.4656492 0.4561668 0.3977354 0.3709171 0.3232007 [7] 0.1727159 0.1707283 0.1255730 -0.1470081 Largest eigenvalues: [1] 99137403 97361514 91155358 86865276 85350337 84065232 83681962 81421617 [9] 80454230 78353481 Smallest eigenvalues: [1] 0.510679527 0.503585171 0.489978859 0.468186197 0.388010467 [6] 0.204411722 0.176497312 0.077626287 -0.004377843 -0.109294510 Largest eigenvalues: [1] 101119507 96262378 90683449 86254096 85453929 84263209 82599357 [8] 81696451 80262742 78742735 Smallest eigenvalues: [1] 0.41712961 0.37808716 0.33390456 0.27718078 0.25251986 0.24656301 [7] 0.21192470 0.08193734 -0.08327945 -0.56399842 Largest eigenvalues: [1] 100232827 95666089 89985269 85387341 84828673 83624169 82221193 [8] 81208440 79380560 77889899 Smallest eigenvalues: [1] 0.31865111 0.27956852 0.27401201 0.18406549 0.12795188 0.10204782 [7] -0.04608224 -0.17698766 -0.71114611 -0.71669829 Largest eigenvalues: [1] 100722853 95629722 90117024 86209676 85260980 83086579 82739223 [8] 80661998 79516961 77511018 Smallest eigenvalues: [1] 0.35796167 0.34670746 0.32727107 0.31442367 0.28488570 0.20606400 [7] 0.14691519 0.08122901 -0.06728842 -0.07993234 Largest eigenvalues: [1] 97715761 97472371 90580325 87198539 84809247 84345815 83854582 81443009 [9] 80549672 78360682 Smallest eigenvalues: [1] 0.39807409 0.34964297 0.34798642 0.34723362 0.25903954 0.23996865 [7] 0.22856945 -0.03202365 -0.03421357 -0.09779054 Largest eigenvalues: [1] 101990746 96091454 90661284 85869882 85432075 83573266 82648774 [8] 81450918 80050383 78452292 Smallest eigenvalues: [1] 0.2873604 0.2406175 0.2061073 0.2011479 0.1902358 0.1536395 [7] 0.1124333 -0.2234221 -0.4596491 -0.6485345 Largest eigenvalues: [1] 99564501 96852184 90329734 86185316 86149131 84745531 83093047 82055684 [9] 80419288 79138111 Smallest eigenvalues: [1] 0.47004829 0.44956302 0.44267843 0.41641997 0.29400124 0.27615740 [7] 0.23620663 0.19153958 0.05505231 -0.28395448 Largest eigenvalues: [1] 101822799 95588151 89962860 85771998 85528959 84461459 82526882 [8] 81932156 79729073 78585406 Smallest eigenvalues: [1] 0.39988943 0.39573224 0.34824211 0.34144804 0.24589599 0.21536802 [7] 0.15810475 -0.04470396 -0.44130334 -0.48927460 Largest eigenvalues: [1] 100696277 97073120 91024100 86484220 86063969 83793930 83541767 [8] 81210780 80556301 78115354 Smallest eigenvalues: [1] 0.20243819 0.18510106 0.17889320 0.13828097 0.10988136 0.02487937 [7] -0.12089513 -0.16308249 -0.46969175 -0.59273974 Largest eigenvalues: [1] 96975298 96851230 90696985 85979179 84635902 83683700 82880403 80906835 [9] 79486018 77656533 Smallest eigenvalues: [1] 0.44000187 0.43291636 0.40586284 0.27166974 0.23015984 0.23014177 [7] 0.19486857 0.10130970 0.02942627 -0.14694322 Largest eigenvalues: [1] 101005444 96606843 90825138 86454296 85864228 85126736 82552402 [8] 82087973 80075289 79113881 Smallest eigenvalues: [1] 0.38337602 0.31651394 0.25776147 0.19781490 0.19752167 0.17745764 [7] 0.16425644 -0.01201535 -0.06950816 -0.18728402 Largest eigenvalues: [1] 100680856 96622146 89827767 86436023 85994600 83697388 82870635 [8] 81406986 79571289 78119638 Smallest eigenvalues: [1] 0.35876576 0.33979949 0.33836701 0.28337005 0.24039554 0.21917536 [7] 0.20099556 0.16876098 0.03103076 -0.22149992 Largest eigenvalues: [1] 99113266 97382714 90484455 86363318 85808817 83374894 83246100 80982902 [9] 79790139 77842249 Smallest eigenvalues: [1] 0.30704835 0.30059959 0.25458824 0.25182827 0.24333213 0.17932177 [7] 0.12094803 0.08543251 -0.21105746 -0.25820691 Largest eigenvalues: [1] 102719903 95426719 89809700 86750476 84965634 82797623 81655048 [8] 80375620 79100341 77381358 Smallest eigenvalues: [1] 0.42679419 0.32386659 0.29310488 0.29146631 0.27622499 0.25293305 [7] 0.21391153 0.18370350 0.02282517 -0.05050702 Largest eigenvalues: [1] 98550730 97114267 90287374 86880211 84634536 84423393 83019364 81748979 [9] 80006841 78405093 Smallest eigenvalues: [1] 0.3945600 0.3717346 0.3651580 0.3503336 0.3344669 0.2426653 [7] 0.2390838 0.2340258 0.2213380 -0.2072164 Largest eigenvalues: [1] 100292519 95593452 89802370 85482948 85023997 83494446 82969683 [8] 81247408 79493536 78058754 Smallest eigenvalues: [1] 0.41175699 0.38950545 0.37019013 0.27659328 0.22818304 0.22329321 [7] 0.17571895 0.16590123 -0.06489391 -0.13017483 Largest eigenvalues: [1] 100714880 96331880 90563322 85895636 85737579 83855689 83128647 [8] 81672731 80057270 78298742 Smallest eigenvalues: [1] 0.33259183 0.26277909 0.25582576 0.15664283 0.11910796 0.08702104 [7] 0.08638394 0.04786710 -0.02142092 -0.54841125 Largest eigenvalues: [1] 101079005 96226361 90560154 86781477 85781753 83419942 82610130 [8] 81135152 79510985 77827368 Smallest eigenvalues: [1] 0.29145410 0.28940441 0.28539643 0.27684333 0.24991573 0.17277188 [7] 0.14198307 0.13868467 -0.06712417 -0.34832525 Largest eigenvalues: [1] 99839585 97558645 91041026 86668962 85634480 83919678 83657479 81456298 [9] 80769672 78405713 Smallest eigenvalues: [1] 0.3659842 0.3102182 0.2757366 0.1942331 0.1621468 0.1327081 [7] 0.1161523 -0.1193468 -0.4714288 -1.1234355 Largest eigenvalues: [1] 100120411 95067585 89655472 85290975 84566217 82979898 82263876 [8] 80749480 79420574 77756921 Smallest eigenvalues: [1] 0.41803534 0.41721241 0.38583510 0.36892736 0.27840538 0.20295123 [7] 0.14769918 -0.08107825 -0.37907701 -0.56662463 Largest eigenvalues: [1] 101190582 97473309 91087423 87103766 86753855 84669109 83374669 [8] 81743584 80644548 78819328 Smallest eigenvalues: [1] 0.264440038 0.261302296 0.250507518 0.219007688 0.111351566 [6] -0.009447189 -0.060410237 -0.155182861 -0.214761296 -0.275850826 Largest eigenvalues: [1] 97300180 96496643 89569576 86302990 84445005 83679459 83399361 81090628 [9] 79716052 77759145 Smallest eigenvalues: [1] 0.351377848 0.322099500 0.258535921 0.227862233 0.192618418 [6] 0.077790198 0.002088115 -0.062672817 -0.072426539 -0.457051687 Largest eigenvalues: [1] 99161783 97043638 90640092 86870746 84568056 83674564 83509187 81141610 [9] 80561007 77723502 Smallest eigenvalues: [1] 0.26510224 0.24366621 0.23567284 0.20010371 0.19667448 0.09535692 [7] 0.05411813 0.05142078 -0.01293108 -1.32696707 Largest eigenvalues: [1] 98877560 96346937 90337112 86955955 84188119 83359184 83158510 80410901 [9] 79865629 77303655 Smallest eigenvalues: [1] 0.36294479 0.32656185 0.30063109 0.23799529 0.23594865 0.16724540 [7] 0.09899271 0.07269330 -0.10635215 -0.25563710 Largest eigenvalues: [1] 97943590 97658277 91337719 87510018 84578346 84350388 83904824 81545545 [9] 80892202 78356047 Smallest eigenvalues: [1] 0.36448038 0.36092519 0.30790760 0.19249257 0.16092006 0.13192366 [7] 0.12767409 -0.08773287 -0.19788144 -0.31153076 Largest eigenvalues: [1] 99118012 95927907 89643185 85769287 83928818 83213203 82669605 80719785 [9] 79747531 77614972 Smallest eigenvalues: [1] 0.37299605 0.37080168 0.34490453 0.23245295 0.16211870 0.11187644 [7] 0.09310969 0.05888227 0.02774412 -0.47810554 Largest eigenvalues: [1] 98847872 95704298 89929228 85668684 84324652 83150749 82135949 80373656 [9] 79393614 77241742 Smallest eigenvalues: [1] 0.3654140 0.3639396 0.2700087 0.2425750 0.2097143 0.1994774 [7] 0.1685570 0.1422004 -0.2465139 -0.8535758 Largest eigenvalues: [1] 101031270 97607230 91216830 87437073 87208573 85000879 83779530 [8] 82517317 81319962 79485477 Smallest eigenvalues: [1] 0.37756211 0.35707023 0.31013111 0.25855774 0.24972376 0.21986272 [7] 0.19937933 0.17107446 0.01772496 -0.38013997 Largest eigenvalues: [1] 100625497 96742162 90228993 86167595 86151306 84978859 82573800 [8] 82156086 79655341 78872017 Smallest eigenvalues: [1] 0.29637362 0.26541427 0.21256339 0.13147735 0.11995527 0.08847063 [7] 0.07888055 0.07576163 -0.15932322 -0.16633398 Largest eigenvalues: [1] 99629171 97178791 90142819 86637236 85506526 84884121 82594718 81708845 [9] 79900855 78551549 Smallest eigenvalues: [1] 0.36918140 0.33746030 0.30363949 0.25635045 0.22278268 0.15809756 [7] 0.11328799 0.10264674 0.09228072 -0.31414494 Largest eigenvalues: [1] 100237773 97468072 90975938 86529424 86491726 84490034 83128205 [8] 81620157 80264674 78614998 Smallest eigenvalues: [1] 0.48746975 0.42804782 0.38237090 0.35137848 0.23523077 0.19529961 [7] 0.18590550 0.11081368 -0.01036798 -0.05483418 Largest eigenvalues: [1] 101559603 96283142 90106012 86430813 85733876 84300694 82860232 [8] 81854428 80322220 79160084 Smallest eigenvalues: [1] 0.23069636 0.19847419 0.18645255 0.18342945 0.17660938 0.16117962 [7] 0.05844873 0.05785838 -0.14585089 -0.17686044 Largest eigenvalues: [1] 98797306 97225687 91113411 86562186 84381667 84118531 83850382 81578674 [9] 80791603 78784199 Smallest eigenvalues: [1] 0.31301908 0.28865658 0.23418857 0.21748037 0.20898878 0.19808066 [7] 0.08039183 -0.02541776 -0.31413862 -0.53179421 Largest eigenvalues: [1] 99016543 96395819 90037457 85934655 85717561 84060569 82631090 81492826 [9] 79555577 78113633 Smallest eigenvalues: [1] 0.29495076 0.26979096 0.16716006 0.15481753 0.14343851 0.09630921 [7] 0.08757449 0.03861197 -0.33909293 -0.70389865 Largest eigenvalues: [1] 100364994 99298096 91969083 88500661 85814875 84577894 84267616 [8] 81450962 81017860 78380314 Smallest eigenvalues: [1] 0.504165080 0.481779180 0.480484346 0.429342979 0.351170782 [6] 0.181205306 0.179632311 0.169740833 0.003942749 -0.415198764 Largest eigenvalues: [1] 100267166 96260307 90445915 86136702 85746688 83153787 82901198 [8] 80849151 79840261 77759292 Smallest eigenvalues: [1] 0.459367692 0.445354706 0.442430569 0.360310259 0.360070971 [6] 0.208156373 0.117585269 0.062752206 0.005082227 -0.055283008 Largest eigenvalues: [1] 100734725 96919100 90533411 86503961 86419019 83443070 82993396 [8] 80859570 79928987 77646468 Smallest eigenvalues: [1] 0.41883301 0.40392273 0.40272711 0.36922306 0.31088072 0.30017431 [7] 0.23915287 0.19467860 -0.00484238 -0.11970782 Largest eigenvalues: [1] 99048805 96857803 90395370 86433890 85509437 84099527 82986809 81235491 [9] 79853614 78054478 Smallest eigenvalues: [1] 0.37305885 0.34292566 0.31243975 0.29748108 0.28279151 0.28245676 [7] 0.20158352 0.10425514 0.09690102 -0.32276797 Largest eigenvalues: [1] 99266230 96646604 90314080 86210092 85521793 83125494 82459614 80408551 [9] 79981197 77427535 Smallest eigenvalues: [1] 0.25257677 0.24833787 0.24525369 0.22113854 0.17727591 0.14420024 [7] 0.02056847 -0.09038714 -0.22483375 -0.30338038 Largest eigenvalues: [1] 99784920 97063648 90513858 86349233 85343418 83373627 83271900 80836752 [9] 80070929 77852464 Smallest eigenvalues: [1] 0.29107821 0.26983041 0.24440567 0.24162767 0.15029000 0.13614359 [7] -0.01840315 -0.21758626 -0.22537564 -0.53432662 Largest eigenvalues: [1] 99338404 97091234 90730625 86977483 84429142 83533028 82913978 80358747 [9] 80157220 76910699 Smallest eigenvalues: [1] 0.24130045 0.20314681 0.19653209 0.16530125 0.05373587 -0.07767991 [7] -0.43888231 -0.46250494 -0.57706930 -0.59423605 Largest eigenvalues: [1] 100679651 96125329 90279822 86086794 85627394 82962730 82660767 [8] 80590934 79714757 77621774 Smallest eigenvalues: [1] 0.4513555 0.4395810 0.3989247 0.3163798 0.3141766 0.2624468 [7] 0.2529045 0.2158083 0.2142145 -0.2581155 Largest eigenvalues: [1] 99280284 96072349 89845912 85680086 84651303 83648126 82634971 81188130 [9] 79696445 78214870 Smallest eigenvalues: [1] 0.26327661 0.25086315 0.15826147 0.11698081 0.11205674 0.07093853 [7] 0.04307898 -0.04792343 -0.21239492 -0.27197809 Largest eigenvalues: [1] 98391139 98339029 91494569 87681283 84693217 84515827 83062952 81004947 [9] 80465181 77551276 Smallest eigenvalues: [1] 0.31059584 0.28013624 0.25760606 0.25069301 0.23275873 0.19809033 [7] 0.15495099 -0.09969918 -0.27102077 -0.86708071 Largest eigenvalues: [1] 99935203 95408417 89639282 85448136 84210873 82568516 82387424 80446297 [9] 79554764 77509883 Smallest eigenvalues: [1] 0.429791082 0.399800940 0.367065060 0.296889719 0.266736304 [6] 0.187573407 0.184407380 0.005299774 -0.371528840 -0.393313658 Largest eigenvalues: [1] 101397321 96915509 90898814 86580357 86520920 84233308 83077648 [8] 81728488 80163450 78542180 Smallest eigenvalues: [1] 0.178607060 0.168467081 0.152444934 0.132923045 0.094316349 [6] 0.045755101 0.008685834 -0.214910880 -0.309180505 -0.492545401 Largest eigenvalues: [1] 97000752 96469525 90796317 86195042 83851956 83583798 83512469 81443948 [9] 80187644 78178850 Smallest eigenvalues: [1] 0.39470246 0.35168882 0.34099159 0.31248679 0.27238824 0.24946498 [7] 0.24126221 0.08727550 0.04523319 -0.33821218 Largest eigenvalues: [1] 99834711 95388530 89635008 85725581 84232498 82903260 82040029 80462840 [9] 79198427 77383331 Smallest eigenvalues: [1] 0.390595698 0.353993018 0.352561443 0.301648010 0.241667049 [6] 0.230481264 0.112275392 0.040195216 0.007146699 -0.863131735 Largest eigenvalues: [1] 99860242 98444524 91387579 87946868 86565474 84792777 84324043 82014287 [9] 81247293 78580211 Smallest eigenvalues: [1] 0.39742498 0.37957379 0.37753286 0.34683340 0.31766746 0.25507606 [7] 0.10755867 0.01612215 -0.03687619 -0.52369557 Largest eigenvalues: [1] 99078373 97222478 90397259 86772349 85841832 83589852 83423184 80988049 [9] 80396912 77763608 Smallest eigenvalues: [1] 0.34055685 0.28053254 0.25944124 0.20635931 0.18468359 0.15524465 [7] 0.14931058 0.05787631 0.04978985 -0.23463472 Largest eigenvalues: [1] 101450361 95965016 89961918 85962548 85385783 83715332 83121423 [8] 81409335 80121723 78276711 Smallest eigenvalues: [1] 0.26751673 0.21974072 0.21838493 0.17946892 0.14986593 0.12942314 [7] 0.09194865 0.03147040 0.01433878 -0.91998753 Largest eigenvalues: [1] 100349084 97559250 91524516 86706315 86114605 83851137 83275845 [8] 81395244 80256047 78362904 Smallest eigenvalues: [1] 0.32559656 0.31924570 0.30633525 0.24005081 0.21683844 0.19756116 [7] 0.07209748 0.06429756 -0.24223085 -0.55130555 Largest eigenvalues: [1] 98141386 97694379 90660327 87431772 84997964 83863562 83662669 81007988 [9] 80368226 77761801 Smallest eigenvalues: [1] 0.31348287 0.29623303 0.25752401 0.25312998 0.20229314 0.19716505 [7] 0.12282798 0.01839462 -0.05453195 -0.07950966 Largest eigenvalues: [1] 99406667 96954899 90786031 86367413 85403798 85063129 83148989 81724834 [9] 80648340 79166536 Smallest eigenvalues: [1] 0.39560641 0.31463287 0.30129619 0.25235800 0.20560578 0.17392572 [7] 0.16633730 0.04815968 -0.08761367 -0.11713124 Largest eigenvalues: [1] 101888325 96645704 90571942 86675599 86629661 84612929 82992575 [8] 81703451 80438407 78645504 Smallest eigenvalues: [1] 0.43443319 0.38983099 0.38828640 0.38511926 0.28281465 0.26809482 [7] 0.13368367 0.08780331 -0.03263017 -0.36072287 Largest eigenvalues: [1] 102174629 96149205 90764896 86340185 86022945 84054468 82554362 [8] 81363195 79919745 78301673 Smallest eigenvalues: [1] 0.19988466 0.17372512 0.16045127 0.14436531 0.06499410 0.02886763 [7] 0.02220141 -0.01502777 -0.08168773 -1.04228761 Largest eigenvalues: [1] 98730711 98398034 91581949 87032003 85699460 84416650 84152274 81985147 [9] 80759685 78950237 Smallest eigenvalues: [1] 0.20339890 0.18280366 0.16854999 0.14735899 0.10550489 0.09107712 [7] 0.04560014 -0.02731637 -0.12814439 -1.11334461 Largest eigenvalues: [1] 99513541 98116917 90779729 87434985 86470169 84791865 83879004 82085772 [9] 80702896 78865795 Smallest eigenvalues: [1] 0.46227307 0.41995442 0.40845207 0.35688425 0.26812686 0.18647004 [7] 0.15733774 -0.01411357 -0.02026205 -0.12638831 Largest eigenvalues: [1] 101943157 96815399 91274154 86310206 86193948 84627394 83176234 [8] 82168123 80349328 79075514 Smallest eigenvalues: [1] 0.331410719 0.324665613 0.240219821 0.213022834 0.191196033 [6] 0.151736223 0.108498625 0.092559887 -0.009961564 -0.112796507 Largest eigenvalues: [1] 98137369 97715986 90708042 87843639 84871108 84681346 83764714 81807036 [9] 80748654 78978313 Smallest eigenvalues: [1] 0.38143199 0.31140571 0.29760754 0.27347634 0.23957733 0.16701707 [7] 0.12689540 0.03313372 -0.59249306 -0.67746960 Largest eigenvalues: [1] 101256029 96816315 90201478 87268076 85813543 84414550 83014006 [8] 81679726 80025982 78788737 Smallest eigenvalues: [1] 0.34067687 0.28775980 0.26414525 0.21414570 0.20163309 0.18085737 [7] 0.07917522 -0.12137968 -0.38725617 -0.68208733 Largest eigenvalues: [1] 101861278 96809971 91133423 86587790 85959178 84541025 82840449 [8] 82006674 80179007 79064039 Smallest eigenvalues: [1] 0.43372245 0.31659040 0.28499450 0.24518496 0.21852120 0.20446099 [7] 0.16948993 0.10645704 -0.06172721 -0.31112806 Largest eigenvalues: [1] 100764275 97248407 90530598 86547799 86418994 83747570 82661302 [8] 81147751 79958926 78334743 Smallest eigenvalues: [1] 0.39012743 0.38696761 0.34404646 0.31316234 0.25527803 0.23683761 [7] 0.11423121 0.09969124 -0.39028251 -0.78020804 Largest eigenvalues: [1] 100091193 97389485 90497342 87488863 86409875 84086532 83896798 [8] 81473909 80573273 78432231 Smallest eigenvalues: [1] 0.35585856 0.32410142 0.27363188 0.27126139 0.26717090 0.24941770 [7] 0.15436801 0.12444986 0.04458591 -0.21875618 Largest eigenvalues: [1] 98274014 96569642 90124448 85864282 84454531 83539953 83000264 80950603 [9] 79694661 77654519 Smallest eigenvalues: [1] 0.28133152 0.27686925 0.19555317 0.17725589 0.15588834 0.07969386 [7] -0.13463858 -0.13474443 -0.29868215 -0.34122695 Largest eigenvalues: [1] 100423814 97712812 91160801 86590597 86440211 84875792 83438980 [8] 81579099 80726140 78867894 Smallest eigenvalues: [1] 0.44267403 0.39947466 0.39250608 0.38838185 0.33379538 0.22413418 [7] 0.11791490 0.10812335 -0.03633909 -0.18620301 Largest eigenvalues: [1] 101254538 95959749 90592960 86338954 85366262 84241660 82868886 [8] 81737692 80385589 78512917 Smallest eigenvalues: [1] 0.058185343 0.045899067 -0.009036044 -0.095725922 -0.102067948 [6] -0.419780578 -0.490942268 -0.577191487 -0.619417892 -0.629020273 Largest eigenvalues: [1] 98745231 95751881 89881040 85754808 85326027 83279781 82531111 80654227 [9] 79443775 77523193 Smallest eigenvalues: [1] 0.3815785 0.3771295 0.3669656 0.2891872 0.2705186 0.2034987 [7] 0.1451879 -0.2175073 -0.4532708 -0.6015415 Largest eigenvalues: [1] 102334527 97444676 91470668 87787297 86232091 85113045 83968880 [8] 82644459 81392255 79485012 Smallest eigenvalues: [1] 0.33497666 0.33352712 0.28057664 0.25698945 0.24507983 0.20697409 [7] 0.08222553 0.02525762 -0.10619800 -0.25851396 Largest eigenvalues: [1] 100611638 96785725 90474451 86772944 85929264 84553506 82495070 [8] 81432507 80003968 78826244 Smallest eigenvalues: [1] 0.34431829 0.33498789 0.31293014 0.27834956 0.25846283 0.14380849 [7] 0.11407259 0.10549554 0.09734466 -0.58854530 Largest eigenvalues: [1] 98530229 95456355 89491894 85752857 83242262 82637660 82416853 79977600 [9] 79501800 77001605 Smallest eigenvalues: [1] 0.26914031 0.26043122 0.21459412 0.18736925 0.14845907 0.07874544 [7] 0.07784031 -0.07986671 -0.11959565 -0.56059877 Largest eigenvalues: [1] 100168323 96413539 90601393 86137388 85399523 83666577 82988120 [8] 81320765 79949432 77905892 Smallest eigenvalues: [1] 0.324614884 0.300514232 0.241329757 0.210709473 0.181934668 [6] 0.074295440 -0.003249435 -0.261985101 -0.745352569 -0.787918799 Largest eigenvalues: [1] 100872449 96125695 90148649 86504400 85893125 83542410 83344412 [8] 81473869 79951673 78172869 Smallest eigenvalues: [1] 0.4126539 0.3869167 0.3744963 0.3601519 0.2221537 0.2091842 [7] 0.1893213 0.1313180 0.0200826 -0.3045735 Largest eigenvalues: [1] 97502569 95960855 89958405 86134029 83986446 83671794 82740539 81221121 [9] 79782728 78024310 Smallest eigenvalues: [1] 0.43017845 0.37502626 0.33592130 0.32069081 0.26739616 0.15049299 [7] 0.13443244 0.11395836 0.09017143 -1.49593903 Largest eigenvalues: [1] 99560769 97625660 90787546 87559973 85534275 84317603 83400278 81148311 [9] 80563357 77676716 Smallest eigenvalues: [1] 0.29604206 0.28609854 0.27902571 0.18123724 0.15591815 0.15373248 [7] 0.14184828 0.08133732 -0.13209641 -0.14122370 Largest eigenvalues: [1] 99442783 98054270 90843246 87375130 85136854 84555745 83834471 81961115 [9] 80863790 79211299 Smallest eigenvalues: [1] 0.30215302 0.29498304 0.27217667 0.18138157 0.15288255 0.09410219 [7] 0.07540122 -0.01853222 -0.17238622 -0.65238838 Largest eigenvalues: [1] 98617735 97640564 90659621 87431634 84573203 84363064 83562997 81014055 [9] 80559671 77778796 Smallest eigenvalues: [1] 0.4719555 0.4191241 0.4017873 0.3946956 0.3100844 0.2386480 [7] 0.2080490 0.1821500 0.1732654 -0.1435028 Largest eigenvalues: [1] 100018414 96118663 90179985 85989212 85349571 83936897 83065475 [8] 81361935 80194895 78343777 Smallest eigenvalues: [1] 0.38092432 0.37331536 0.36546693 0.33524821 0.31116440 0.29576574 [7] 0.27999347 0.14919343 -0.04972975 -0.10721190 Largest eigenvalues: [1] 99341004 96720040 90125667 86525729 84743930 83263974 83109008 80556628 [9] 79890796 77481245 Smallest eigenvalues: [1] 0.3149938 0.2929249 0.2919076 0.2691387 0.2530930 0.2189553 [7] 0.1633777 -0.1250496 -0.1351757 -0.2087045 Largest eigenvalues: [1] 99214869 95374009 89099764 85327212 83988379 83052767 81965904 80396034 [9] 79026188 77137711 Smallest eigenvalues: [1] 0.38470707 0.36276823 0.32190500 0.31549949 0.24761274 0.19812443 [7] 0.18693791 0.17074537 0.06933354 -0.06727256 Largest eigenvalues: [1] 99385392 97297662 91560212 86507002 85558391 84630434 83751830 81861043 [9] 80840652 79188213 Smallest eigenvalues: [1] 0.4767251 0.4685349 0.4592432 0.4261618 0.3912516 0.1817691 [7] 0.1446941 0.1424519 0.1089849 -0.1850407 Largest eigenvalues: [1] 99707867 96429166 90404432 86623224 84995145 83766173 83280705 81274566 [9] 80399680 78260579 Smallest eigenvalues: [1] 0.2335448 0.2188832 0.1917935 0.1887423 0.1814929 0.1771487 [7] 0.1374852 0.1250975 0.0291889 -0.4680119 Largest eigenvalues: [1] 98273574 95556179 89645458 85187870 84717587 83354037 82165557 81011708 [9] 79350423 77963325 Smallest eigenvalues: [1] 0.24620507 0.21858558 0.16894975 0.16317197 0.11723825 0.11471277 [7] 0.07251718 0.03986858 -0.22640104 -0.67176309 Largest eigenvalues: [1] 100307190 99384901 91745488 88751023 86341941 84866710 84488179 [8] 82059309 81219494 78597738 Smallest eigenvalues: [1] 0.40935323 0.36159548 0.35488266 0.27146720 0.26311898 0.20870304 [7] 0.20025516 0.14263318 0.04805744 -0.37529690 Largest eigenvalues: [1] 98369697 97128000 90598943 86561343 84596563 83697747 82945593 80843120 [9] 79734379 77661114 Smallest eigenvalues: [1] 0.41175047 0.40325180 0.38193799 0.32003994 0.31042846 0.15598854 [7] 0.01868788 -0.16359973 -0.16971565 -0.42800350 Largest eigenvalues: [1] 100046220 96074520 90304809 86282093 85217762 83876506 82653421 [8] 81248500 79979128 77990133 Smallest eigenvalues: [1] 0.31383343 0.31346078 0.30712925 0.22542448 0.13625960 0.09530084 [7] 0.07769367 0.02423000 -0.05204557 -0.47005584 Largest eigenvalues: [1] 97444898 95450355 89190082 85364723 83621098 82385667 82116662 79651376 [9] 79031394 76281828 Smallest eigenvalues: [1] 0.3649556 0.3617310 0.3465880 0.3138276 0.2880125 0.2199215 [7] 0.1851893 0.1616141 0.1586361 -0.3439481 Largest eigenvalues: [1] 99209694 97291195 90361566 87057798 85288629 83809225 83634870 81373930 [9] 80299198 78520711 Smallest eigenvalues: [1] 0.3348225 0.2801413 0.2484938 0.2172986 0.1930259 0.1568888 [7] 0.1414990 0.1396131 -0.1103372 -0.2650043 Largest eigenvalues: [1] 100621004 98328826 91112993 87377093 86293644 84418602 83566065 [8] 81626027 80593884 78446852 Smallest eigenvalues: [1] 0.42444327 0.40028739 0.38148784 0.35453648 0.33268600 0.13847818 [7] 0.07952187 -0.11291591 -0.32223058 -0.38480346 Largest eigenvalues: [1] 100681739 96322714 89959821 86517018 85930799 83737572 83347117 [8] 81367308 79856829 78171240 Smallest eigenvalues: [1] 0.252656626 0.205776058 0.190594967 0.176824356 0.045604410 [6] 0.019306513 0.008340649 -0.361401912 -0.570848304 -0.730683188 Largest eigenvalues: [1] 99868714 96852705 90632588 86656771 85648597 83796916 83331936 81629172 [9] 80039851 78519484 Smallest eigenvalues: [1] 0.4593528 0.3893255 0.3766599 0.2768965 0.2762782 0.2307830 [7] 0.2254736 0.1759479 0.1135783 -0.4528005 Largest eigenvalues: [1] 100667360 97969492 91271475 87586299 86067439 84314707 84071188 [8] 81646420 80853880 78544220 Smallest eigenvalues: [1] 0.3510299 0.3385034 0.3071948 0.2622282 0.2389058 0.2286450 [7] 0.2059410 0.1711556 -0.1566071 -0.2463768 Largest eigenvalues: [1] 101135713 97331335 91088702 86463126 86217393 85231831 83052736 [8] 82441990 80273258 79246940 Smallest eigenvalues: [1] 0.38199830 0.36769959 0.34301811 0.27746184 0.24689443 0.20405738 [7] 0.13544772 0.09483139 0.02030478 -0.29501974 Largest eigenvalues: [1] 100070271 97831866 90674020 87372477 86161733 83547958 83443165 [8] 80634948 80082929 77361695 Smallest eigenvalues: [1] 0.37438582 0.36976021 0.36179464 0.29333067 0.26613039 0.17165153 [7] 0.10566550 -0.05698757 -0.35655390 -0.53352759 Largest eigenvalues: [1] 99754859 97038948 90564293 86860615 85797785 83472579 83331213 80749316 [9] 80108506 77673032 Smallest eigenvalues: [1] 0.25802055 0.23450663 0.19880209 0.12702044 0.04113767 -0.04967580 [7] -0.19115228 -0.47149969 -0.65365914 -0.93581442 Largest eigenvalues: [1] 101019653 95378962 89771927 86277076 85231362 83096589 82535764 [8] 81129720 79165978 77504679 Smallest eigenvalues: [1] 0.21278067 0.18949278 0.17242776 0.17118907 0.14233052 0.05991912 [7] -0.01893210 -0.09684069 -0.48836254 -0.50731041 Largest eigenvalues: [1] 101324263 97593997 91172686 86937931 86348242 84510021 83278593 [8] 81952751 80202144 78877555 Smallest eigenvalues: [1] 0.4208265 0.3639878 0.3512899 0.3200594 0.3047338 0.3015686 [7] 0.1895072 0.1145783 -0.1150118 -0.2139220 Largest eigenvalues: [1] 98304620 96803604 90375890 86727246 84451429 83412327 83214771 80882046 [9] 80019738 77655596 Smallest eigenvalues: [1] 0.281698680 0.281533700 0.256546252 0.226088006 0.223708356 [6] 0.114270740 0.042818163 -0.008678622 -0.110736070 -0.670415958 Largest eigenvalues: [1] 101185348 95931724 90257581 85508157 85226809 83616697 82490658 [8] 81426756 79604431 78339732 Smallest eigenvalues: [1] 0.41761241 0.41240658 0.40091710 0.38198660 0.32071976 0.20906311 [7] 0.20716043 0.06956320 -0.03745066 -0.28607350 Largest eigenvalues: [1] 100107626 95440889 89734629 85230717 85144758 83736904 81605045 [8] 81087241 79128540 77867393 Smallest eigenvalues: [1] 0.27061737 0.24703151 0.21959191 0.21580823 0.20473005 0.09554137 [7] 0.09530508 0.03834050 -0.00343953 -0.65423020 Largest eigenvalues: [1] 97373393 96531587 89583693 86630878 84122586 83154770 82961964 80584070 [9] 79549766 77363139 Smallest eigenvalues: [1] 0.45769452 0.45009303 0.38659504 0.37669354 0.31433898 0.30734342 [7] 0.20366714 -0.04075146 -0.05591965 -0.14335648 Largest eigenvalues: [1] 99188706 96982154 90366313 87330640 84912837 84207054 83155853 80761380 [9] 80219596 77161211 Smallest eigenvalues: [1] 0.22911217 0.21858659 0.20267879 0.19897631 0.16634976 0.16516647 [7] 0.08447713 -0.10646781 -0.29848244 -0.75932235 Largest eigenvalues: [1] 100997519 95839491 90022919 85331119 85081897 83519569 82181898 [8] 81148935 79458950 78014497 Smallest eigenvalues: [1] 0.26766870 0.19766377 0.17798173 0.13205080 0.08800957 0.06668416 [7] 0.02950838 -0.30796337 -0.39058239 -0.63176470 Largest eigenvalues: [1] 98400709 96399953 90571587 85834627 83960791 83487740 82802189 80871257 [9] 79688763 77709510 Smallest eigenvalues: [1] 0.21429646 0.17650710 0.09560023 0.08547053 0.04900958 -0.02548114 [7] -0.04340883 -0.09511792 -0.32107678 -0.52381986 Largest eigenvalues: [1] 98373351 97829063 91124969 87540051 84895878 84133526 83649371 81194542 [9] 80430064 77705409 Smallest eigenvalues: [1] 0.28248161 0.27376209 0.23778535 0.22887318 0.19865703 0.08801103 [7] 0.06218977 -0.02285149 -0.03258565 -0.21379139 Largest eigenvalues: [1] 99775512 95900627 89777322 85890169 84313045 83424790 82164998 80652110 [9] 79573174 77165731 Smallest eigenvalues: [1] 0.36781521 0.35982334 0.34962791 0.19485981 0.17790083 0.14009971 [7] 0.10921436 0.07310026 0.01995280 -0.26795094 Largest eigenvalues: [1] 99350483 96550470 90255423 86075781 85722055 84140992 82926836 81623876 [9] 79775301 78340079 Smallest eigenvalues: [1] 0.45371415 0.39124476 0.37421891 0.33444789 0.33157732 0.27601170 [7] 0.24610685 0.08682787 -0.23062857 -0.35493993 Largest eigenvalues: [1] 100327411 96759475 90697455 86292802 86045450 83552283 83337019 [8] 81348333 79960664 78119926 Smallest eigenvalues: [1] 0.046636993 0.035359558 0.017449824 0.015862257 0.003537427 [6] -0.032252855 -0.057342307 -0.230057749 -0.771263406 -1.590312342 Largest eigenvalues: [1] 98867425 97698841 90795929 86793252 86540610 84406671 83874382 81610980 [9] 80659906 78197657 Smallest eigenvalues: [1] 0.25804756 0.20071648 0.18647683 0.12117166 0.10024445 0.07416415 [7] -0.26325448 -0.28874537 -0.54908138 -0.56308618 Largest eigenvalues: [1] 102526834 97000175 91134028 87858330 85963653 84814061 83161686 [8] 82594866 80275596 79336479 Smallest eigenvalues: [1] 0.33775875 0.28745714 0.27183690 0.24930744 0.17070333 0.16259579 [7] 0.09871793 -0.07408996 -0.11719351 -0.38557054 Largest eigenvalues: [1] 101683941 96630367 91170559 87129730 85827565 84988288 83111650 [8] 82408866 80399078 79339477 Smallest eigenvalues: [1] 0.42968072 0.42110958 0.27611702 0.19894934 0.19619133 0.18425263 [7] 0.09758404 0.02732125 -0.03617361 -0.33772064 Largest eigenvalues: [1] 102347794 97012443 91408971 87163646 86707997 85616970 83160776 [8] 82520728 80953667 79679345 Smallest eigenvalues: [1] 0.28548938 0.25116030 0.24486995 0.16885419 0.16038230 0.05720970 [7] 0.04422642 -0.13743450 -0.17777822 -0.63440488 Largest eigenvalues: [1] 97395646 97316126 91209863 86695776 84558729 83838743 83675876 81342631 [9] 80230173 78057431 Smallest eigenvalues: [1] 0.442776082 0.391623751 0.382725334 0.381279589 0.363850334 [6] 0.345549336 0.009804477 -0.026025911 -0.105962376 -0.498362344 Largest eigenvalues: [1] 100614042 96615725 90226930 87168205 85422308 84184218 83317242 [8] 81496710 80456269 78427014 Smallest eigenvalues: [1] 0.42694793 0.35639499 0.35108276 0.29871305 0.28908353 0.22087682 [7] 0.15976578 -0.09342316 -0.30558180 -0.68065358 Largest eigenvalues: [1] 99334108 96674672 89862788 86993738 85068975 83904600 82886322 80664032 [9] 80266133 77517598 Smallest eigenvalues: [1] 0.4308011 0.4142717 0.3650295 0.2857384 0.2464918 0.2453967 [7] 0.1959111 0.0494940 -0.1635359 -0.2395798 Largest eigenvalues: [1] 101114828 95268029 89294177 85195923 84768918 83245343 81631967 [8] 80659045 78996872 77528946 Smallest eigenvalues: [1] 0.31449603 0.28985626 0.27663390 0.26592695 0.25166567 0.23601603 [7] 0.18660474 0.09371916 -0.03140952 -0.24225762 Largest eigenvalues: [1] 100782930 96312558 90388534 86503552 84976835 82939980 82667309 [8] 80232093 79705663 77225659 Smallest eigenvalues: [1] 0.31111033 0.29720889 0.23327700 0.20128001 0.16892894 0.16055564 [7] 0.15787289 0.13501886 0.04273853 -0.12985173 Largest eigenvalues: [1] 100255203 98760425 91698089 87815922 85382115 84930929 83717184 [8] 82113265 80877654 78963829 Smallest eigenvalues: [1] 0.3480369 0.2696630 0.2564487 0.2496769 0.1517936 0.1402594 [7] 0.1061727 0.1011491 -0.1454205 -0.1460305 Largest eigenvalues: [1] 100222935 97756015 90993038 87357335 86067421 83820499 83637554 [8] 80867492 80424331 77863631 Smallest eigenvalues: [1] 0.48081342 0.42919507 0.41925864 0.38888139 0.37344706 0.34659120 [7] 0.31291955 0.25326989 0.10653370 -0.04490726 Largest eigenvalues: [1] 100458943 96766794 90109848 86481009 85526355 83631147 82577029 [8] 80983043 79670597 77857202 Smallest eigenvalues: [1] 0.36236035 0.31721020 0.31392624 0.27677729 0.20533656 0.16221101 [7] 0.12907441 0.06818734 -0.40674266 -0.63878229 Largest eigenvalues: [1] 101319137 97773478 91592450 87673146 86144334 84143571 83948516 [8] 81581962 80763609 78613598 Smallest eigenvalues: [1] 0.4045498 0.3879079 0.3610878 0.3578397 0.2485032 0.1659034 [7] 0.1249912 0.1003893 -0.1786400 -0.4457197 Largest eigenvalues: [1] 99521787 96679611 90377359 86724952 85679579 84283571 83030569 81399752 [9] 80313216 78438244 Smallest eigenvalues: [1] 0.41404505 0.39003060 0.35982916 0.30239082 0.27486520 0.24478899 [7] 0.12962633 0.07244005 -0.02504669 -0.40874128 Largest eigenvalues: [1] 100712253 96385478 90780036 85742161 85702015 83942962 82912727 [8] 81655551 80211888 78999273 Smallest eigenvalues: [1] 0.3485337 0.3354698 0.3048705 0.3021327 0.2908771 0.2593732 [7] 0.2220939 0.1163274 -0.2397182 -0.6077688 Largest eigenvalues: [1] 99154721 97038249 90799939 86935918 85068815 83761234 83203080 81082837 [9] 80412269 77848777 Smallest eigenvalues: [1] 0.4233766 0.4147364 0.3510396 0.3332425 0.2905806 0.2784367 [7] 0.1803975 -0.3335088 -0.3669966 -0.5229525 Largest eigenvalues: [1] 100372986 96036649 89563607 86116582 85666577 83186631 83057644 [8] 80827217 79748104 77722181 Smallest eigenvalues: [1] 0.38983166 0.38487340 0.37208787 0.29054224 0.23320137 0.20777219 [7] 0.12504140 0.09933004 -0.19143744 -0.31194636 Largest eigenvalues: [1] 101281899 96173435 90944062 85988172 85939280 83550130 83153112 [8] 81393977 80269444 78406345 Smallest eigenvalues: [1] 0.347569103 0.327372172 0.321848328 0.307483784 0.156288232 [6] 0.154681260 0.058509231 0.017588019 -0.001766918 -0.033815865 Largest eigenvalues: [1] 100144452 96846882 90758827 86306564 84719137 83682019 83028101 [8] 81175517 80204826 78000990 Smallest eigenvalues: [1] 0.4090389 0.3627915 0.3476506 0.2782087 0.2762533 0.2727793 [7] 0.2249399 0.1626167 0.1073839 -0.1032556 Largest eigenvalues: [1] 99077168 96435042 90374970 85718440 84933027 84228130 82886459 81868980 [9] 80053463 78669893 Smallest eigenvalues: [1] 0.45102002 0.42739909 0.41265141 0.38966948 0.38052585 0.33418660 [7] 0.23188719 0.17593409 0.06790079 -0.10139031 Largest eigenvalues: [1] 99702125 95783662 89036761 86248118 85341539 82890255 82297361 80565432 [9] 79180315 77493682 Smallest eigenvalues: [1] 0.3942416 0.3892888 0.3819386 0.3360190 0.3339390 0.2560155 [7] 0.2171359 0.1761208 0.1394933 -0.1150816 Largest eigenvalues: [1] 98087575 97105412 90307908 86497525 85434288 83918838 83789166 81430940 [9] 80320173 78199214 Smallest eigenvalues: [1] 0.29877799 0.28556724 0.25028831 0.19129003 0.13790622 0.07852385 [7] -0.05774839 -0.14290567 -0.33090174 -0.60924416 Largest eigenvalues: [1] 101291665 97586212 91113511 86552832 86371197 83884344 82870623 [8] 81098482 79868608 78015487 Smallest eigenvalues: [1] 0.3266034 0.2723108 0.2449150 0.2311140 0.1198034 0.1179327 [7] 0.1075270 -0.1579041 -0.1602187 -0.7164355 Largest eigenvalues: [1] 99383581 98286507 91591050 87427128 86095739 84900683 83745485 81538270 [9] 80781832 78196081 Smallest eigenvalues: [1] 0.34855606 0.34089552 0.32322032 0.29137096 0.27673292 0.25805268 [7] 0.21791098 0.07110441 -0.14859563 -0.20484002 Largest eigenvalues: [1] 101274472 97595123 91036971 86858103 86441183 84799633 83100157 [8] 82292071 79960284 79035603 Smallest eigenvalues: [1] 0.27889303 0.27844637 0.25990528 0.13658687 0.01831973 -0.02484048 [7] -0.03088235 -0.06261795 -0.13665732 -0.34273962 Largest eigenvalues: [1] 100074790 95776483 90026420 85701913 85645614 84236822 83057760 [8] 81940416 79774724 78626849 Smallest eigenvalues: [1] 0.34981741 0.29878845 0.27855108 0.17326761 0.16220631 0.04052916 [7] -0.02611012 -0.15787457 -0.46048301 -0.89547548 Largest eigenvalues: [1] 101282510 96123958 90086878 86211614 86175111 84701277 83370964 [8] 81868580 80364939 79008676 Smallest eigenvalues: [1] 0.25906603 0.24811292 0.21993695 0.17488631 0.16174391 0.13402113 [7] 0.07151616 -0.12408328 -0.23128794 -0.31582863 Largest eigenvalues: [1] 98357885 97898636 91055033 87630008 84249133 84212096 83200764 80525443 [9] 80271323 77117444 Smallest eigenvalues: [1] 0.23641698 0.20624225 0.18525294 0.17828785 0.11896606 0.10187315 [7] 0.09210105 0.07195074 -0.34791008 -0.39390754 Largest eigenvalues: [1] 99279474 96983457 90290189 85953735 85443268 83968328 82975647 81413902 [9] 79719412 78205437 Smallest eigenvalues: [1] 0.4176070 0.3575368 0.3371788 0.3099605 0.2687841 0.2678587 [7] 0.2664475 0.2237560 0.1549113 -0.2692582 Largest eigenvalues: [1] 97899285 97087837 90624117 87204323 84559126 84362741 83237295 81828180 [9] 79855049 78508596 Smallest eigenvalues: [1] 0.4343852 0.3819684 0.3702191 0.3689260 0.3273773 0.2060304 [7] 0.1560160 0.1375543 0.1360155 -0.0694369 Largest eigenvalues: [1] 100596365 96241883 90286789 86486005 85636894 84608034 82696311 [8] 81814079 80096788 78693955 Smallest eigenvalues: [1] 0.37689905 0.34435708 0.32177875 0.31315594 0.29307640 0.17395796 [7] -0.05786294 -0.13821481 -0.47884541 -0.60791327 Largest eigenvalues: [1] 101828461 95977289 90461838 86693038 85907921 83882449 82858439 [8] 81562928 79926236 78434530 Smallest eigenvalues: [1] 0.410316943 0.381908199 0.345209941 0.305669916 0.280893197 [6] 0.250456104 0.244696198 0.002926307 -0.107938224 -0.138693776 Largest eigenvalues: [1] 101117928 96405711 90885059 86158471 86119029 84222275 82927994 [8] 81732255 80105695 78583906 Smallest eigenvalues: [1] 0.234059808 0.180942142 0.137386047 0.126149825 0.096684587 [6] 0.007760464 -0.100625359 -0.289805122 -0.609480439 -0.669918702 Largest eigenvalues: [1] 101062858 96805132 90903998 86473085 86108250 83979731 82866543 [8] 81496307 79945722 78378804 Smallest eigenvalues: [1] 0.3912443 0.3851973 0.3690836 0.3456639 0.3437930 0.3189483 [7] 0.2900501 0.1871427 0.1122719 -0.5214423 Largest eigenvalues: [1] 99491156 95950766 89387673 85990538 84566929 83501811 82155362 80685271 [9] 79356582 77568494 Smallest eigenvalues: [1] 0.3677983 0.3479690 0.3411484 0.2568955 0.2333802 0.2273164 [7] 0.1390135 0.1368217 -0.1093204 -0.1799333 Largest eigenvalues: [1] 100204052 97147167 90234945 87077710 85176039 84392041 83608051 [8] 81724587 80291790 78362499 Smallest eigenvalues: [1] 0.366966922 0.362717654 0.360335019 0.319582916 0.200745930 [6] 0.152922374 0.003352582 -0.266448190 -0.352148435 -0.417930394 Largest eigenvalues: [1] 98862982 97074532 90402106 86536506 85739899 84152294 83675610 81267876 [9] 80425882 78232969 Smallest eigenvalues: [1] 0.45191717 0.43950038 0.40385806 0.31130142 0.30891949 0.24313667 [7] 0.20693017 0.19572590 0.05756002 -0.26955153 Largest eigenvalues: [1] 100191604 97316183 90636333 86957543 85624644 83963100 83498253 [8] 81238812 80220408 77968545 Smallest eigenvalues: [1] 0.23397825 0.23241502 0.21649592 0.14441482 0.13952662 -0.05654203 [7] -0.05932610 -0.18019992 -0.26937088 -0.55667726 Largest eigenvalues: [1] 98077439 96837182 89745826 86305853 85808576 84771427 82953900 82168849 [9] 79855603 78859366 Smallest eigenvalues: [1] 0.27269166 0.22345738 0.21728267 0.19267097 0.14376271 0.13499501 [7] 0.12867720 0.06938402 -0.06350760 -0.67379346 Largest eigenvalues: [1] 98964379 98300823 91549033 87909320 85856434 84752260 84327194 81612079 [9] 81088527 78579785 Smallest eigenvalues: [1] 0.09957522 0.01537536 -0.03509050 -0.09849262 -0.19101268 -0.23046605 [7] -0.30163899 -0.35958915 -0.45000353 -0.88915703 Largest eigenvalues: [1] 100914053 97237217 91082370 87023629 85721450 84231415 83590468 [8] 81749584 80299963 78846282 Smallest eigenvalues: [1] 0.292016404 0.271769531 0.257989998 0.243381681 0.176269431 [6] 0.175803107 0.153864046 0.143341840 0.002725585 -0.602384881 Largest eigenvalues: [1] 99269626 96884936 90201947 86848869 84824305 83790576 83315979 81216337 [9] 80153990 77782459 Smallest eigenvalues: [1] 0.43850415 0.41442870 0.39690383 0.31029263 0.29555572 0.26145934 [7] 0.20976765 -0.02291559 -0.04284741 -0.13635327 Largest eigenvalues: [1] 100488694 97264099 90541710 86668662 85887328 84417592 83592227 [8] 81848523 80511793 78859929 Smallest eigenvalues: [1] 0.39471192 0.35063669 0.33547207 0.31752616 0.25248833 0.21683236 [7] 0.14449475 0.10680065 -0.01933623 -0.46130736 Largest eigenvalues: [1] 100714282 97595167 90849772 87053747 86745183 85106698 83634857 [8] 82408726 80519700 79249400 Smallest eigenvalues: [1] 0.31469041 0.28954432 0.28607079 0.23634182 0.21461819 0.17977594 [7] 0.04595727 -0.01096688 -0.06073514 -0.31440006 Largest eigenvalues: [1] 101740353 96052238 89905945 85822559 85731355 83648055 82538546 [8] 81118497 79552874 77860594 Smallest eigenvalues: [1] 0.4266116 0.4232172 0.3428957 0.2922577 0.2827195 0.2725651 [7] 0.2696178 0.1932111 -0.1911917 -0.7601754 Largest eigenvalues: [1] 101173753 97329449 91054267 87101393 86942104 85009815 83247482 [8] 81759686 80539331 78747386 Smallest eigenvalues: [1] 0.25483398 0.25440119 0.23748573 0.22084413 0.17672952 0.16243410 [7] 0.02964144 -0.04834645 -0.05541758 -0.24170052 Largest eigenvalues: [1] 99360354 96528295 90375623 85879135 85443810 83638858 83388456 81259125 [9] 80032915 77992215 Smallest eigenvalues: [1] 0.16150796 0.14893433 0.12487696 0.11568954 0.09019838 0.04326606 [7] -0.17314327 -0.32297092 -0.37563042 -0.91476655 Largest eigenvalues: [1] 101571118 96558076 91032209 86394127 85889716 84227305 83198967 [8] 82085763 80231043 78902193 Smallest eigenvalues: [1] 0.38059240 0.37732561 0.30066847 0.27935410 0.20453661 0.18769102 [7] 0.16705004 -0.02377098 -0.06607792 -0.15777434 Largest eigenvalues: [1] 97769102 96040358 89655288 85462809 84788605 82716880 82389853 80290862 [9] 79236402 77259572 Smallest eigenvalues: [1] 0.34634746 0.34456714 0.31802433 0.30331161 0.25942431 0.20890988 [7] 0.11439959 0.06513766 -0.05693716 -0.11050370 Largest eigenvalues: [1] 97163083 96693999 89776939 86245439 83854771 83526176 83134265 80874637 [9] 79826742 77696086 Smallest eigenvalues: [1] 0.3327129 0.2659533 0.2532687 0.2311225 0.1893002 0.1541538 [7] 0.1534513 -0.2784342 -0.3589102 -0.5319046 Largest eigenvalues: [1] 98857234 95325149 89070634 85749929 84193565 82773254 82649383 80221392 [9] 79692741 77003069 Smallest eigenvalues: [1] 0.34699249 0.32355695 0.26134788 0.26043983 0.24538748 0.11462200 [7] -0.01941008 -0.14688981 -0.38380129 -0.42099434 Largest eigenvalues: [1] 100877535 96950164 91136541 86613296 85924105 83512648 83299860 [8] 81277984 80381521 78392708 Smallest eigenvalues: [1] 0.35352883 0.34702510 0.28566263 0.26065976 0.25682427 0.21360104 [7] 0.19858020 0.13274861 0.04398071 -0.74566347 Largest eigenvalues: [1] 101152950 98571292 92099932 87450988 86815567 85309913 83897342 [8] 82538033 81000907 79556619 Smallest eigenvalues: [1] 0.23099717 0.19234303 0.19049139 0.17347833 0.14079204 0.10579074 [7] -0.04458064 -0.11949034 -0.18821758 -0.71881989 Largest eigenvalues: [1] 99149007 96423716 90537904 85998970 84346569 83400727 82734627 81071001 [9] 79948076 77831385 Smallest eigenvalues: [1] 0.40578246 0.40120171 0.36721794 0.29197626 0.26971145 0.24563370 [7] 0.19323597 0.16704558 0.02607803 -0.14519548 Largest eigenvalues: [1] 101094098 97456695 90817216 86939295 86357833 84231530 83308246 [8] 81530512 80419921 78530715 Smallest eigenvalues: [1] 0.43480910 0.43024832 0.34838111 0.34697034 0.31205261 0.27063612 [7] 0.24961073 0.09841438 0.03930832 -0.10974630 Largest eigenvalues: [1] 100410007 95976350 89771216 86088452 85320377 83678883 81978746 [8] 80686078 79253905 77664165 Smallest eigenvalues: [1] 0.12694587 0.11058854 0.09271166 0.04838720 -0.12021239 -0.34345029 [7] -0.36671085 -0.37713947 -0.57213810 -1.32014857 Largest eigenvalues: [1] 101692263 96698341 91559543 86348629 85602278 84743556 83027174 [8] 81845159 80408631 78734620 Smallest eigenvalues: [1] 0.30295159 0.24034660 0.18536516 0.14431746 0.07786097 0.05587312 [7] 0.01111916 -0.03639185 -0.53998312 -0.80037665 Largest eigenvalues: [1] 100508711 97044238 91670005 86100600 85731527 83901156 83543296 [8] 81738543 80527078 78656792 Smallest eigenvalues: [1] 0.52021728 0.42617878 0.38904175 0.38063202 0.37129728 0.36387846 [7] 0.26677558 0.20513106 -0.05435247 -0.06675711 Largest eigenvalues: [1] 98965763 96971076 90741985 87212870 84881984 83888714 83681774 81383664 [9] 80243575 78080073 Smallest eigenvalues: [1] 0.43839355 0.41715438 0.41245214 0.39575751 0.34503093 0.30450687 [7] 0.19916598 0.03750747 -0.13176149 -0.38965613 Largest eigenvalues: [1] 99573308 96204127 89716219 86118311 85478658 83099156 82622446 80610382 [9] 79593611 77458026 Smallest eigenvalues: [1] 0.44322180 0.42419448 0.38989221 0.38334586 0.28226819 0.26188999 [7] 0.19171159 0.05948086 0.03502478 -0.12676357 Largest eigenvalues: [1] 99096988 96959306 90650842 86678173 84879439 84109293 83414527 81296531 [9] 80353293 78258981 Smallest eigenvalues: [1] 0.5031935 0.3989250 0.3523077 0.2419549 0.1935245 0.1816304 [7] 0.1386767 -0.2046599 -0.2665340 -0.9005747 Largest eigenvalues: [1] 101811653 96421445 90087933 86874496 86140971 84036068 82219944 [8] 81227335 79629624 78153957 Smallest eigenvalues: [1] 0.49387907 0.48732465 0.41093407 0.34014672 0.30539747 0.30035957 [7] 0.22659959 0.20825811 0.17899060 -0.02690145 Largest eigenvalues: [1] 100462069 96442940 90685831 85980553 85882056 83677279 82570602 [8] 81045179 79710196 77872311 Smallest eigenvalues: [1] 0.372865009 0.350135488 0.326463316 0.286492580 0.275191241 [6] 0.205101118 0.163899184 0.026730037 -0.006885879 -0.047835749 Largest eigenvalues: [1] 99305474 96532758 90429288 85980661 85635220 83519321 82964695 81092529 [9] 79936555 77943309 Smallest eigenvalues: [1] 0.183239535 0.176508156 0.130695142 0.113508046 0.009426349 [6] -0.032568176 -0.105138535 -0.208262216 -0.404034721 -0.740318726 Largest eigenvalues: [1] 99122978 96826230 91160166 86329732 84955365 84484244 83330964 82133618 [9] 80283935 78694275 Smallest eigenvalues: [1] 0.38560188 0.38326858 0.30925081 0.30901290 0.28005665 0.27002888 [7] 0.21241842 0.12391159 -0.05900234 -0.06148758 Largest eigenvalues: [1] 100333631 96955965 90285904 86472662 85505195 84268466 82433271 [8] 81050267 79880259 78150643 Smallest eigenvalues: [1] 0.4919522 0.4479297 0.4265404 0.3869061 0.3124770 0.2323936 [7] 0.2064273 0.1780105 -0.1603598 -0.2175354 Largest eigenvalues: [1] 99772885 95187705 89557611 85534514 84364679 83027378 82448144 80532996 [9] 79621432 77417830 Smallest eigenvalues: [1] 0.37648509 0.35191103 0.30851276 0.24298059 0.19149177 0.04675491 [7] -0.04104796 -0.11084363 -0.15927765 -0.62363850 Largest eigenvalues: [1] 103600093 95505630 90364267 86619516 85529716 83770080 82524436 [8] 81749559 79696699 78564238 Smallest eigenvalues: [1] 0.24465153 0.21438791 0.16754235 0.15725125 0.15548894 0.09914795 [7] 0.06914302 -0.02671311 -0.59366857 -0.67332483 Largest eigenvalues: [1] 97593231 97100954 91290536 86250441 84521084 83732977 83569607 81068775 [9] 80385668 78071593 Smallest eigenvalues: [1] 0.31603021 0.25718825 0.24489518 0.21849013 0.11428810 0.09603519 [7] -0.11128751 -0.20718250 -0.29433289 -0.31132038 Largest eigenvalues: [1] 98202102 96764274 90308841 86543478 85294905 84179369 83892647 81906522 [9] 80044359 78418258 Smallest eigenvalues: [1] 0.43904139 0.43133331 0.40709788 0.37590294 0.33397495 0.32255071 [7] 0.29591741 0.27096567 0.04106674 -0.05712327 Largest eigenvalues: [1] 99274917 95867007 89981923 85547503 85104921 82963617 82438046 80870998 [9] 79513364 77919176 Smallest eigenvalues: [1] 0.46325498 0.46166157 0.41252004 0.37321712 0.28191879 0.24531393 [7] 0.12045733 0.11024800 -0.06605865 -0.24644531 Largest eigenvalues: [1] 99991117 96735833 89926256 87346369 85117088 84076131 83279852 81550169 [9] 80395504 78260830 Smallest eigenvalues: [1] 0.4330849 0.4020024 0.3748423 0.3565680 0.3196545 0.2676867 [7] 0.2016224 -0.1449578 -0.1619819 -0.1895933 Largest eigenvalues: [1] 100826966 96334744 90113451 86719380 85305835 84022201 82716086 [8] 81373764 80094463 78277733 Smallest eigenvalues: [1] 0.37326317 0.35846725 0.33249559 0.29447213 0.26408315 0.24215250 [7] 0.17350547 0.13258136 -0.03018616 -0.22135213 Largest eigenvalues: [1] 98672876 95550127 89031868 85314589 84821619 82649630 82264051 80302608 [9] 78897366 77093016 Smallest eigenvalues: [1] 0.30931218 0.22960786 0.20197239 0.17829339 0.16589960 0.15570694 [7] 0.14120589 0.08351061 0.08255726 -0.23851626 Largest eigenvalues: [1] 97380230 96461449 89803184 86526466 83796984 82897063 82702519 80203091 [9] 79389668 76746654 Smallest eigenvalues: [1] 0.3685795526 0.3436715158 0.3386713514 0.3251806977 0.3068118526 [6] 0.1570954217 0.1191157870 0.0959234791 -0.0001471406 -0.2346708568 Largest eigenvalues: [1] 98584082 97074468 90272150 87104656 84946612 83837832 83212349 80895421 [9] 80482347 77588447 Smallest eigenvalues: [1] 2.699266e-01 2.144292e-01 1.541071e-01 1.337610e-01 1.026406e-01 [6] 1.160841e-02 -5.443407e-05 -2.568958e-01 -2.684043e-01 -3.527842e-01 Largest eigenvalues: [1] 100053133 96130595 89871001 86291939 83713037 83591538 82574397 [8] 80998614 80034563 77576627 Smallest eigenvalues: [1] 0.4142776 0.3941530 0.3503994 0.3407098 0.3139414 0.2799652 [7] 0.1966966 0.1318278 -0.4223764 -0.8069486 Largest eigenvalues: [1] 101187856 97086018 91198856 86706254 86510063 83761188 83425056 [8] 81393989 80443295 78397806 Smallest eigenvalues: [1] 0.30941771 0.30524832 0.24366669 0.23749408 0.20493327 0.13285847 [7] 0.05133460 -0.03890257 -0.06084318 -0.71883526 Largest eigenvalues: [1] 100828793 97602180 90835926 87287453 87012492 85930345 83414172 [8] 82723922 80838955 79531443 Smallest eigenvalues: [1] 0.369029169 0.362691359 0.353588306 0.351764783 0.281286091 [6] 0.241423926 0.211884033 0.003464372 -0.158582853 -0.326647637 Largest eigenvalues: [1] 99680297 96454207 90543015 86500074 84885370 83790105 83199382 81344508 [9] 80110954 77972854 Smallest eigenvalues: [1] 0.3065613 0.2431831 0.2391782 0.2155183 0.2091817 0.1693003 [7] 0.1271607 -0.1995080 -0.4066203 -0.6307664 Largest eigenvalues: [1] 100736918 97179415 90516850 87000776 86405839 85212160 83163229 [8] 82302833 80445913 78931862 Smallest eigenvalues: [1] 0.29851823 0.28557206 0.27017650 0.26763524 0.24716206 0.13499916 [7] 0.05028756 -0.04307928 -0.09889282 -0.86216406 Largest eigenvalues: [1] 100182985 96941737 90878840 86562059 86087658 84230416 83401960 [8] 82014258 79990195 78720963 Smallest eigenvalues: [1] 0.3991817 0.3872397 0.3676609 0.3582896 0.2542244 0.2037604 [7] 0.1913263 -0.0472565 -0.0839502 -0.1719341 Largest eigenvalues: [1] 100383297 96503062 90378690 86093233 85765825 83773704 82515951 [8] 80920970 79955056 78090956 Smallest eigenvalues: [1] 0.30670780 0.20326089 0.19665993 0.08159352 0.01349483 -0.07291564 [7] -0.07379954 -0.15452279 -0.43753416 -0.79354714 Largest eigenvalues: [1] 100999884 97758210 90739158 87082463 86505883 83925578 83557227 [8] 81219474 80524907 78460703 Smallest eigenvalues: [1] 0.34253604 0.32545313 0.21630120 0.18977162 0.18198331 0.15796592 [7] 0.04390050 0.03035574 -0.19699336 -0.69375317 Largest eigenvalues: [1] 100340136 95827951 89074954 86099129 85926024 83820325 82560747 [8] 81277341 79579839 77787326 Smallest eigenvalues: [1] 0.39181683 0.36493295 0.32830043 0.29035042 0.27416137 0.14307365 [7] 0.05806362 0.03507854 -0.01639568 -0.35564321 Largest eigenvalues: [1] 100219678 96000098 90427975 85680377 85486644 83267441 82873168 [8] 81001057 79617517 77669430 Smallest eigenvalues: [1] 0.28810119 0.26425975 0.22160193 0.18028787 0.13756265 0.09173279 [7] 0.08807529 -0.02224719 -0.21659059 -0.57088636 Largest eigenvalues: [1] 98290070 97297714 90550965 86609295 84377950 83578526 83227989 80728442 [9] 80157389 77845012 Smallest eigenvalues: [1] 0.26401529 0.25813804 0.21829104 0.18125884 0.14915006 0.11737341 [7] 0.05911547 -0.03183136 -0.39064279 -0.74577689 Largest eigenvalues: [1] 99400100 96245545 90205652 86111153 84716775 83718335 83257677 81417377 [9] 79878080 78055283 Smallest eigenvalues: [1] 0.314146831 0.311850730 0.282658927 0.270622221 0.251437362 [6] 0.245090507 0.193428267 0.004988796 -0.084706632 -0.481487450 Largest eigenvalues: [1] 98820704 95808176 90287906 85149618 84254193 83955721 82333538 80875807 [9] 79932485 78220179 Smallest eigenvalues: [1] 0.32886736 0.29330735 0.25424508 0.24053868 0.13802277 0.10934938 [7] 0.10691209 -0.01604612 -0.25335859 -0.66526531 Largest eigenvalues: [1] 98344307 94573027 88820751 84807629 83326604 82914148 81831053 80239657 [9] 79073759 77121216 Smallest eigenvalues: [1] 0.326326924 0.317189115 0.199457293 0.174002643 0.152673245 [6] 0.122916336 0.094855930 0.088665521 -0.001178807 -0.070555217 Largest eigenvalues: [1] 99187907 97492326 91580242 86535210 84754837 83813793 83574985 81216735 [9] 80419874 78327326 Smallest eigenvalues: [1] 0.36695691 0.30716757 0.30560135 0.27392456 0.23536602 0.23473709 [7] 0.18030186 0.09647028 -0.02844927 -0.04304868 Largest eigenvalues: [1] 100996121 95881516 89901016 85548608 85544263 82925269 82075044 [8] 80319229 79352083 77309452 Smallest eigenvalues: [1] 0.4316303 0.4208347 0.4133128 0.3999564 0.3875765 0.3682845 [7] 0.2417644 0.1244756 -0.1259745 -0.2933479 Largest eigenvalues: [1] 100243806 96963715 90417763 87469165 84641066 83935936 83425260 [8] 80999256 80653669 77612974 Smallest eigenvalues: [1] 0.364297489 0.349647931 0.345258262 0.282858177 0.274275485 [6] 0.170002337 0.130009132 -0.009954598 -0.252593864 -0.333487135 Largest eigenvalues: [1] 101075882 97118586 91436235 86907756 85475047 85010052 83357766 [8] 82274281 80581721 78937387 Smallest eigenvalues: [1] 0.33993250 0.30180280 0.28043381 0.26909891 0.15660651 0.02907121 [7] 0.02043404 -0.11279720 -0.32588131 -0.35657728 Largest eigenvalues: [1] 102546257 95989900 90513981 87235312 85327544 83693600 82108944 [8] 81402140 79434442 78185465 Smallest eigenvalues: [1] 0.13374824 0.12737801 0.07047947 0.04598225 0.02741508 -0.07748124 [7] -0.18293921 -0.39316521 -0.75688512 -0.94082273 Largest eigenvalues: [1] 100435793 95682934 89327609 85997398 85536713 83341614 82840831 [8] 81174876 79395631 78082072 Smallest eigenvalues: [1] 0.30400737 0.27763694 0.27182902 0.21953290 0.13900133 0.06927903 [7] 0.02531365 -0.02921070 -0.07107304 -0.29811185 Largest eigenvalues: [1] 100803965 97284221 91030870 86848065 85460286 84452314 82993850 [8] 81851253 79995740 78540146 Smallest eigenvalues: [1] 0.36284994 0.35930795 0.29081657 0.28677139 0.27247123 0.23139737 [7] 0.00371644 -0.03468379 -0.04270706 -0.25026637 Largest eigenvalues: [1] 98644947 96013791 89642430 86044874 85497503 83341279 83253306 81119507 [9] 79537651 77764447 Smallest eigenvalues: [1] 0.41542279 0.40919142 0.32106334 0.29829831 0.25126733 0.20882237 [7] 0.16565436 0.15521824 0.04021373 -0.06157143 Largest eigenvalues: [1] 98434634 98312635 90868593 87791355 85197744 84544722 84065491 81618217 [9] 80794946 78728256 Smallest eigenvalues: [1] 0.32733372 0.30418752 0.29672656 0.25926005 0.24656299 0.18691614 [7] 0.08692670 0.02636084 -0.03448850 -0.65844271 Largest eigenvalues: [1] 98981019 95675266 89068969 86184630 84603629 83052050 82908943 80381501 [9] 79346067 77114293 Smallest eigenvalues: [1] 0.32821947 0.32414124 0.30149772 0.25790374 0.24369459 0.16258789 [7] 0.15852172 -0.01110554 -0.11072379 -0.33605135 Largest eigenvalues: [1] 99765026 97884729 91514202 87019737 85693192 84455431 83787676 81665821 [9] 80592654 78865850 Smallest eigenvalues: [1] 0.477988568 0.439918247 0.420547977 0.416711566 0.388852499 [6] 0.369853239 0.359176576 0.093815923 0.009193506 -0.187239575 Largest eigenvalues: [1] 102321485 96058157 90121770 86665887 85952561 83385499 82313344 [8] 81017521 79693527 77974300 Smallest eigenvalues: [1] 0.28042652 0.27298275 0.26165338 0.17415352 0.16970502 0.11993403 [7] 0.08453356 -0.06023711 -0.16631739 -0.64947397 Largest eigenvalues: [1] 98831808 97073287 90303978 87019229 85522093 84281777 83999382 81883623 [9] 80757423 78722295 Smallest eigenvalues: [1] 0.32248869 0.31578689 0.29279027 0.24579734 0.19024994 0.14878104 [7] 0.08520810 0.01025207 -0.09484912 -0.11261377 Largest eigenvalues: [1] 99867887 96849253 90443120 86820842 84560983 84159666 82857191 81326005 [9] 80112184 78032646 Smallest eigenvalues: [1] 0.35910779 0.29510038 0.23580913 0.19271113 0.18948207 0.17597670 [7] 0.12359647 0.08433964 -0.37427932 -1.22831509 Largest eigenvalues: [1] 102045698 96946137 91274498 86788916 86701640 84415063 83315986 [8] 81846463 80661233 79132255 Smallest eigenvalues: [1] 0.363616209 0.333862215 0.299872341 0.287371719 0.280834803 [6] 0.163472046 0.088348115 0.053377984 -0.001669046 -0.198216750 Largest eigenvalues: [1] 97952091 97308012 90802000 86852861 85124266 83682051 83488447 81009563 [9] 80472052 78041363 Smallest eigenvalues: [1] 0.270115388 0.262921215 0.244589065 0.233387432 0.194780113 [6] 0.043349180 -0.003913576 -0.022667061 -0.384858870 -1.387337587 Largest eigenvalues: [1] 102304323 96186394 90478927 86172171 85277837 84946744 82929901 [8] 82333781 80745454 79384467 Smallest eigenvalues: [1] 0.34068413 0.32926307 0.30087145 0.26145782 0.23951875 0.20125075 [7] 0.15595911 -0.07579312 -0.13727473 -0.40966281 Largest eigenvalues: [1] 100114791 96292819 90500274 86344339 85142094 84134377 83052809 [8] 81744618 80280563 78825498 Smallest eigenvalues: [1] 0.42491928 0.37954428 0.37297111 0.29147008 0.27333599 0.24918844 [7] 0.23339043 0.17011509 0.06384430 -0.09017256 Largest eigenvalues: [1] 99575642 96864583 90142779 85659676 85658192 83644555 82619231 81087148 [9] 79559156 77931575 Smallest eigenvalues: [1] 0.3939280 0.3377544 0.3215833 0.2963347 0.2746435 0.2677547 [7] 0.2015931 -0.2629492 -0.5839031 -3.8464995 Largest eigenvalues: [1] 100922082 97671625 91264838 87954535 86314430 84359730 84139855 [8] 81760624 81299610 78557200 Smallest eigenvalues: [1] 0.32088035 0.31744686 0.30103063 0.29481377 0.27594865 0.26108038 [7] 0.16518321 0.12722545 -0.08706957 -0.27501656 Largest eigenvalues: [1] 100273562 97121781 90838631 87419830 84787780 84043070 82983785 [8] 81227731 79960444 77983994 Smallest eigenvalues: [1] 0.24572507 0.23614287 0.21264002 0.19828196 0.16916035 0.13890045 [7] 0.09421075 -0.06775645 -0.31290185 -0.32677093 Largest eigenvalues: [1] 99405571 96076769 89929090 85829093 84054022 83149491 82967646 80633162 [9] 79905228 77307982 Smallest eigenvalues: [1] 0.37238334 0.35661176 0.33587332 0.29549755 0.26025956 0.22205667 [7] 0.20527115 0.09473500 -0.08733787 -0.13594070 Largest eigenvalues: [1] 101085009 95991368 89933883 85984642 85371243 83283580 82534865 [8] 80688811 79889005 77669161 Smallest eigenvalues: [1] 0.38325622 0.37433127 0.35638512 0.34526758 0.29069659 0.21939822 [7] 0.14711047 0.06178511 -0.16737429 -0.27145050 Largest eigenvalues: [1] 102456189 96914885 91040338 86575318 86246201 84851069 82918014 [8] 82082334 80506878 79062735 Smallest eigenvalues: [1] 0.38830062 0.36589516 0.30289503 0.28406847 0.25031188 0.22519916 [7] 0.17228382 0.09458279 -0.06773608 -0.54111833 Largest eigenvalues: [1] 101005871 97144376 91149610 87036393 85894894 85214494 83509107 [8] 82582804 80762431 79512342 Smallest eigenvalues: [1] 0.30592772 0.28896238 0.27320002 0.24951541 0.21908713 0.16324041 [7] 0.12205861 0.10553916 -0.08769211 -0.19439733 Largest eigenvalues: [1] 99800001 95795117 89620278 85284659 84669473 83213809 81827975 80585188 [9] 79196320 77552068 Smallest eigenvalues: [1] 0.25353134 0.24053701 0.23073527 0.20957257 0.06601571 0.04604083 [7] -0.02223759 -0.09850560 -0.16573659 -0.51260834 Largest eigenvalues: [1] 100776786 95631711 90409479 85456160 85336095 84229884 81973502 [8] 81224267 79504897 78599382 Smallest eigenvalues: [1] 0.4614451 0.4348184 0.3962426 0.3887389 0.3603514 0.3155989 [7] 0.2520493 0.2461396 0.2287887 -0.2481496 Largest eigenvalues: [1] 99701718 97512481 91147917 87292494 85569796 84748410 83365225 81979962 [9] 80290429 78835435 Smallest eigenvalues: [1] 0.3090049 0.3005691 0.2968760 0.2870542 0.2592391 0.1824990 [7] 0.1736249 0.1336746 0.1108898 -0.2203779 Largest eigenvalues: [1] 99368167 97309959 90002579 86841031 85346731 84870510 82260459 81221258 [9] 79615811 78285058 Smallest eigenvalues: [1] 0.36065884 0.33551938 0.33280822 0.32370304 0.24106259 0.21798514 [7] 0.16689562 0.03816438 -0.10593044 -0.50646967 Largest eigenvalues: [1] 101133501 96907438 90479610 87419778 86163932 84278151 83095809 [8] 81766994 80164837 78594944 Smallest eigenvalues: [1] 0.43527786 0.41320526 0.33337971 0.30641895 0.28805246 0.23480365 [7] 0.17088297 0.05456974 -0.22101630 -0.24807195 Largest eigenvalues: [1] 100620921 96347390 90487914 86304336 84519158 83933288 82844205 [8] 81496051 79854748 78143750 Smallest eigenvalues: [1] 0.37862062 0.37376140 0.37064563 0.33097662 0.31758120 0.21952049 [7] 0.13968060 0.11130327 -0.00912987 -0.08427104 Largest eigenvalues: [1] 100069182 96385364 90256717 86081809 85736345 84005751 83026416 [8] 81335926 80089040 78345930 Smallest eigenvalues: [1] 0.28301277 0.25694003 0.25320549 0.24988598 0.21796066 0.17372590 [7] 0.06343940 -0.02439735 -0.08598000 -0.16698327 Largest eigenvalues: [1] 99883796 95993256 90381932 85345268 84627389 83282699 82672981 80894983 [9] 79982998 77743056 Smallest eigenvalues: [1] 0.394588379 0.390381477 0.336382184 0.296214815 0.220447110 [6] 0.220320340 0.199348915 0.164899920 0.046990396 -0.001264787 Largest eigenvalues: [1] 100308045 95554374 89008297 85940560 85276677 82772401 81793295 [8] 80312709 78695704 76927181 Smallest eigenvalues: [1] 0.44616818 0.43960791 0.41195382 0.28453839 0.27981420 0.20707246 [7] 0.08480005 -0.02752333 -0.12172163 -0.50072316 Largest eigenvalues: [1] 100471635 95447019 89100818 86100794 85797561 82976443 81959392 [8] 80117094 79014002 76957356 Smallest eigenvalues: [1] 0.42099546 0.39497382 0.37298879 0.27331070 0.20722276 0.17317986 [7] 0.11844832 0.10351708 0.09758702 -0.14186559 Largest eigenvalues: [1] 98795512 95993503 90048666 85865312 84832881 83287406 82399807 80710592 [9] 79187092 77531886 Smallest eigenvalues: [1] 0.48712872 0.46427235 0.41083878 0.31821220 0.28871053 0.21946862 [7] 0.18450459 0.16148368 0.10439500 -0.03160107 Largest eigenvalues: [1] 99358770 96101435 89994107 86253701 84757307 83300231 82955629 80848946 [9] 79864016 77401440 Smallest eigenvalues: [1] 0.38754752 0.36931491 0.36142321 0.34325075 0.27382299 0.25633746 [7] 0.18681497 0.08162637 -0.03105068 -0.33989398 Largest eigenvalues: [1] 100864829 96430389 90953801 85840555 85293455 84349415 82871402 [8] 81962387 80243396 78823094 Smallest eigenvalues: [1] 0.24067772 0.23601800 0.23389428 0.22292071 0.19497830 0.17731891 [7] 0.05400771 0.03995535 0.03620340 -0.40447297 Largest eigenvalues: [1] 98788145 97536594 90660213 87389991 84648845 83752437 83207883 81067480 [9] 80226184 77605041 Smallest eigenvalues: [1] 0.33820942 0.27030640 0.25417173 0.24169389 0.23283821 0.21590241 [7] 0.11376314 -0.02883595 -0.36754236 -0.52181972 Largest eigenvalues: [1] 98714581 96619065 90177018 86330976 85087416 83535697 83397654 81047739 [9] 80317048 77769693 Smallest eigenvalues: [1] 0.39174009 0.32524347 0.28985309 0.20054168 0.19237940 0.19101722 [7] 0.08940818 -0.16670370 -0.36047134 -0.69079710 Largest eigenvalues: [1] 99933812 96941147 90721368 86553256 86308703 84021580 83779304 81701466 [9] 80165372 78247997 Smallest eigenvalues: [1] 0.18655005 0.16577837 0.16232250 0.14449290 0.13726420 0.13112099 [7] 0.04560549 -0.08578619 -0.26467629 -0.49880046 Largest eigenvalues: [1] 99435510 96448369 90309291 86130237 85275077 83390968 82995682 80821385 [9] 79946695 77931005 Smallest eigenvalues: [1] 0.43185323 0.42270272 0.35919220 0.35080242 0.25128398 0.22136257 [7] 0.20891948 0.18867283 0.03289081 -0.07837342 Largest eigenvalues: [1] 98227670 97430090 90584809 87115553 84484684 84093028 83699023 81379141 [9] 80377975 78157463 Smallest eigenvalues: [1] 0.21032160 0.20371226 0.19698221 0.17061765 0.16168591 0.11740691 [7] 0.08660657 0.07002979 -0.10805552 -0.34508916 Largest eigenvalues: [1] 97897138 97844230 90883487 87200596 84399309 83941594 83668966 81248549 [9] 80312936 77879668 Smallest eigenvalues: [1] 0.4118170 0.4008201 0.3674775 0.2898745 0.2822209 0.2502554 [7] 0.1976928 0.1682335 0.1251252 -0.1704450 Largest eigenvalues: [1] 97546410 96201668 89523473 85630605 84643386 83212585 83049254 80791726 [9] 79651894 77824843 Smallest eigenvalues: [1] 0.44186199 0.42570971 0.39274271 0.37123195 0.34994851 0.28412068 [7] 0.27076251 0.19424168 0.01129769 -0.01776899 Largest eigenvalues: [1] 100065712 95659183 89647526 86140537 84547486 83502801 82186782 [8] 80715714 79542008 77738227 Smallest eigenvalues: [1] 0.32713925 0.30784757 0.29809931 0.25883863 0.21649066 0.18439788 [7] 0.16696320 0.13225522 0.08932447 -0.51157525 Largest eigenvalues: [1] 99056474 97901050 90941608 86907480 85943776 84056548 83838397 81504439 [9] 80534993 78485352 Smallest eigenvalues: [1] 0.4576806 0.4543102 0.3405121 0.3332690 0.3051610 0.2015817 [7] 0.1932974 0.1443592 -0.2023058 -0.5885060 Largest eigenvalues: [1] 99461250 96593725 90747950 86917715 84744431 84146285 83510223 81733760 [9] 80488536 78311084 Smallest eigenvalues: [1] 0.32506477 0.31850666 0.29879996 0.27480250 0.23378666 0.21813274 [7] 0.10411059 0.05257262 -0.16681207 -0.54536420 Largest eigenvalues: [1] 101515212 97973693 91925690 87233013 86740063 84159941 83903875 [8] 81658078 80668435 78680359 Smallest eigenvalues: [1] 0.276156753 0.262510726 0.243310284 0.174719473 0.090094527 [6] 0.080125926 0.009127941 -0.023264543 -0.049654436 -0.250950890 Largest eigenvalues: [1] 97035674 94675517 88018423 85020305 84023748 82244669 81925478 79716882 [9] 78317532 76419387 Smallest eigenvalues: [1] 0.375420251 0.331734607 0.292932432 0.255818150 0.182293959 [6] 0.143995165 0.081662550 -0.004589589 -0.315916134 -0.369067254 Largest eigenvalues: [1] 99956406 96929096 89844489 86778996 85067232 83608526 82739479 80589682 [9] 79990646 77277768 Smallest eigenvalues: [1] 0.45135554 0.45099710 0.44210050 0.41641268 0.29732456 0.25091161 [7] 0.23932332 0.23155627 -0.05122225 -0.27781981 Largest eigenvalues: [1] 99443371 96233487 89679343 86206202 85366398 83828236 82464618 80993610 [9] 79639737 77883084 Smallest eigenvalues: [1] 0.322345994 0.311841269 0.306704379 0.227729906 0.181674396 [6] 0.142532968 0.036632283 0.018214785 0.001388422 -0.135509565 Largest eigenvalues: [1] 97642845 96213358 89542657 85702869 84271301 82836222 82292405 79811486 [9] 79482891 76532962 Smallest eigenvalues: [1] 0.28481610 0.28279875 0.25455030 0.21957068 0.21225153 0.10422880 [7] -0.01635793 -0.05413075 -0.13564742 -0.37879992 Largest eigenvalues: [1] 98729612 96217519 89388901 86163221 84532864 83021909 82487956 80266098 [9] 79640379 77147473 Smallest eigenvalues: [1] 0.37861828 0.36425935 0.33924189 0.33146964 0.32595628 0.28190339 [7] 0.12957517 0.07153319 -0.09206744 -0.10984948 Largest eigenvalues: [1] 98290129 97119354 90094559 86151959 85602654 83825482 82819916 80355804 [9] 80040197 77390833 Smallest eigenvalues: [1] 0.4690518 0.3944267 0.3436349 0.3237457 0.2576546 0.2271785 [7] 0.2166449 0.1462338 -0.1338530 -0.2791152 Largest eigenvalues: [1] 99745942 95761893 89811844 85351340 85159813 82896329 82737409 80588156 [9] 79647884 77657118 Smallest eigenvalues: [1] 0.29853507 0.25527026 0.24421619 0.23673835 0.15038527 0.13882399 [7] 0.12645394 0.02038824 -0.11947001 -0.37218149 Largest eigenvalues: [1] 98859117 97848875 90957788 86655989 86240604 84116248 83918632 81556170 [9] 80358538 78391958 Smallest eigenvalues: [1] 0.373135740 0.364616979 0.353102074 0.337331571 0.270222883 [6] 0.242042927 0.202188157 0.162763061 -0.005018144 -0.456501178 Largest eigenvalues: [1] 98772103 94478806 88636212 84634983 83927568 82266229 81781790 80078692 [9] 78626520 76820664 Smallest eigenvalues: [1] 0.40022422 0.37522604 0.37412534 0.35527681 0.29493933 0.18039555 [7] 0.14180878 0.12389672 -0.02528634 -0.11756021 Largest eigenvalues: [1] 100035885 96529283 89963471 86057691 85557221 83309737 82823923 [8] 80821231 79664571 77824054 Smallest eigenvalues: [1] 0.22886423 0.20446361 0.19565306 0.15979919 0.13168703 0.07282501 [7] 0.06773439 0.05458765 -0.07287387 -0.98799769 Largest eigenvalues: [1] 98658511 96782287 90077766 86141917 85984971 83820536 83569788 81659254 [9] 79784013 78330633 Smallest eigenvalues: [1] 0.27403230 0.24682704 0.23881421 0.20939585 0.13549206 0.10028434 [7] -0.05113872 -0.05811827 -0.13349633 -0.25240867 Largest eigenvalues: [1] 100494618 96114754 89715203 86428956 85337232 83775297 83045281 [8] 80904438 80126143 77817060 Smallest eigenvalues: [1] 0.3798479 0.3688158 0.3364864 0.3303298 0.3272489 0.3162162 [7] 0.1992480 0.1259659 -0.1398778 -0.3440427 Largest eigenvalues: [1] 100410882 95396757 88751964 85551621 85523489 82527769 82090999 [8] 80395773 78800558 77129034 Smallest eigenvalues: [1] 0.33297422 0.29790431 0.29286483 0.28843265 0.25235799 0.22673159 [7] 0.21263566 0.19600496 0.19542258 -0.06945186 Largest eigenvalues: [1] 98837058 97123615 89886140 86308816 84865807 84574869 82123122 81249554 [9] 79580641 78345490 Smallest eigenvalues: [1] 0.355077112 0.350719211 0.326042181 0.296514661 0.208291617 [6] 0.189387299 0.161544620 0.102807617 0.077319575 -0.001189006 Largest eigenvalues: [1] 100476566 96798950 91026950 86171653 85485491 84370204 82689733 [8] 81447276 80029234 78216619 Smallest eigenvalues: [1] 0.38835580 0.36551427 0.35402454 0.29785552 0.21562170 0.21157276 [7] 0.17981580 0.12157408 -0.08894265 -0.08937981 Largest eigenvalues: [1] 99460731 97427927 90684120 86734363 85572392 83707485 83369576 80970686 [9] 80153589 78089272 Smallest eigenvalues: [1] 0.27768815 0.27614297 0.24100552 0.11418914 0.10189489 0.02029595 [7] -0.02409096 -0.14590894 -0.18412974 -0.32071125 Largest eigenvalues: [1] 100438388 94792822 89591775 85614689 84710004 82994653 82410232 [8] 81137004 79061385 77677454 Smallest eigenvalues: [1] 0.3453203 0.3397317 0.3233700 0.3120832 0.2959284 0.1813801 [7] 0.0192316 -0.1195605 -0.2008387 -0.3420154 Largest eigenvalues: [1] 101743458 97013015 91185443 87005154 86364388 84297600 83431535 [8] 81759283 80858983 78797023 Smallest eigenvalues: [1] 0.43650886 0.36076152 0.33759084 0.29757485 0.22891426 0.20259403 [7] 0.18813998 0.05711445 -0.43878317 -0.79299022 Largest eigenvalues: [1] 102500640 97062974 91394395 86936944 86672340 84427104 83425725 [8] 81707388 80408492 78657733 Smallest eigenvalues: [1] 0.410386588 0.381209301 0.349629899 0.323425522 0.286472190 [6] 0.256594317 0.210740097 0.101591392 -0.002145321 -0.198620150 Largest eigenvalues: [1] 98348808 97535945 90524133 87179178 85127526 84475930 83523867 81460911 [9] 80536335 78396110 Smallest eigenvalues: [1] 0.29651045 0.29356453 0.26481037 0.26069759 0.16710442 0.12839739 [7] 0.11130759 0.09198345 -0.03437715 -0.33216658 Largest eigenvalues: [1] 97735531 96710453 89789093 86520798 84310691 83303824 82935331 80645597 [9] 79612318 77186769 Smallest eigenvalues: [1] 0.33984843 0.32673202 0.30049812 0.25743596 0.24022707 0.11653070 [7] 0.04049596 -0.07248766 -0.68144113 -1.00090193 Largest eigenvalues: [1] 100224721 96583178 90816691 86393696 85818164 84171253 83367723 [8] 81615367 80343922 78501805 Smallest eigenvalues: [1] 0.4136193 0.4011755 0.3677415 0.3121629 0.2756345 0.2629066 [7] 0.0394471 -0.2190153 -0.2527221 -0.7285935 Largest eigenvalues: [1] 100047612 95239824 89660937 85294714 85252926 83022023 82581871 [8] 80638899 79502001 77710669 Smallest eigenvalues: [1] 0.40839468 0.39874306 0.39242510 0.37805145 0.33232260 0.32985684 [7] 0.28811633 0.23303703 0.10330107 -0.09094716 Largest eigenvalues: [1] 99920097 95761768 89767763 85597931 85256643 82640229 82485340 80371137 [9] 79358807 77271808 Smallest eigenvalues: [1] 0.45961726 0.40703058 0.39448133 0.37865704 0.37068883 0.27373200 [7] 0.26225922 0.22040196 0.20106544 -0.06478495 Largest eigenvalues: [1] 99473641 96127134 89231087 86246488 85487092 82988827 82206553 80180493 [9] 79336506 77040230 Smallest eigenvalues: [1] 0.36595581 0.34903232 0.30691141 0.26846925 0.23379219 0.21200380 [7] 0.15083474 0.09010609 -0.32297292 -0.57526093 Largest eigenvalues: [1] 99273030 97166982 90932544 87166389 84974173 83357313 83194497 80603215 [9] 80000309 77510943 Smallest eigenvalues: [1] 0.3851452 0.3818509 0.3426629 0.3245424 0.2641816 0.2208535 [7] 0.1760051 0.1186726 -0.0736515 -0.1440016 Largest eigenvalues: [1] 101024706 96609214 89835452 86425978 85679366 83785716 82723426 [8] 81123755 79930253 77985604 Smallest eigenvalues: [1] 0.30920410 0.27671668 0.25686651 0.19981567 0.18665654 0.18423982 [7] 0.16198289 0.06473794 -0.31880380 -0.39032891 Largest eigenvalues: [1] 98885397 96726960 90846854 86643201 84929480 84044000 83294322 81110266 [9] 80447717 78276114 Smallest eigenvalues: [1] 0.39838245 0.35036614 0.32766634 0.22231630 0.20469045 0.16577983 [7] 0.09912122 -0.34726823 -0.42791126 -0.48356249 Largest eigenvalues: [1] 101783620 97825931 91225498 87376845 86751437 84032473 83789608 [8] 81763826 80532478 78700246 Smallest eigenvalues: [1] 0.42040981 0.36646895 0.35148799 0.33581034 0.29017098 0.24382018 [7] 0.10913589 0.06364797 0.05196649 -1.03644202 Largest eigenvalues: [1] 99183696 96667653 90524013 86984337 84353734 84188920 83192301 81747855 [9] 80229049 78362409 Smallest eigenvalues: [1] 0.182744795 0.097649252 0.086594991 0.061893819 0.057781883 [6] -0.007763881 -0.011758081 -0.323473398 -0.556873650 -3.093486907 Largest eigenvalues: [1] 98399192 97328123 91161008 86824054 85043315 84196868 83707796 81356709 [9] 80823293 78308159 Smallest eigenvalues: [1] 0.49664862 0.38861652 0.38490686 0.37964142 0.36688734 0.29506705 [7] 0.20537207 0.09283510 -0.02305328 -0.19663247 Largest eigenvalues: [1] 99538386 96697275 90867385 86634980 85116349 83496136 82969194 80824288 [9] 80265036 77748292 Smallest eigenvalues: [1] 0.45764204 0.43522455 0.40738049 0.40663933 0.40575750 0.39548711 [7] 0.30030275 0.23288669 -0.03119384 -0.10216182 Largest eigenvalues: [1] 98636406 96078335 89843206 86388961 84214265 83234529 82815918 80948985 [9] 79898731 77914697 Smallest eigenvalues: [1] 0.38020826 0.36753675 0.28338110 0.25377733 0.20129663 0.19264840 [7] 0.18565038 0.09461722 -0.03626982 -0.04946334 Largest eigenvalues: [1] 101838993 96756288 91169957 86382049 86148593 84748967 82988664 [8] 81982233 80531681 79136495 Smallest eigenvalues: [1] 0.426044550 0.410347850 0.346535148 0.327959055 0.291376013 [6] 0.223830945 0.138596016 0.008732714 -0.043980602 -0.313279641 Largest eigenvalues: [1] 99847941 97026909 90541133 86800764 85684510 84102053 83394529 81539170 [9] 80447749 78171220 Smallest eigenvalues: [1] 0.31350510 0.28915371 0.27987674 0.23052247 0.21965724 0.14746622 [7] 0.11539168 -0.04531777 -0.24138083 -0.24578704 Largest eigenvalues: [1] 99933756 96594597 89929089 86458027 84871533 84273391 82672712 81484442 [9] 79936598 78273130 Smallest eigenvalues: [1] 0.2799180 0.2444111 0.2295801 0.2174750 0.1938087 0.1440567 [7] 0.1356819 -0.2966907 -0.4874643 -1.0039626 Largest eigenvalues: [1] 98198057 96973988 90197533 86245645 85054755 84136976 82180519 81155417 [9] 79155553 78190695 Smallest eigenvalues: [1] 0.46066893 0.44394651 0.43858698 0.43055836 0.42919192 0.32624550 [7] 0.28120610 0.22569189 0.09295630 -0.05083171 Largest eigenvalues: [1] 100831147 96830649 90607187 86372222 85972076 83372078 82759171 [8] 80874713 79708634 77627111 Smallest eigenvalues: [1] 0.42829647 0.40999005 0.39722576 0.35849593 0.34251641 0.30043016 [7] 0.28943356 0.09552253 0.07680635 -0.13672731 Largest eigenvalues: [1] 98621220 97086252 90344941 87141851 84485112 83825264 83147559 80724761 [9] 80123649 77406472 Smallest eigenvalues: [1] 0.18389503 0.18372193 0.12822900 0.12504277 0.08795327 0.07601556 [7] 0.06962724 0.03393597 -0.17476871 -0.21304736 Largest eigenvalues: [1] 97054864 96267448 90271226 87015051 84342747 83583121 83479696 81762372 [9] 80575122 78320702 Smallest eigenvalues: [1] 0.54647024 0.50914350 0.47300351 0.39829130 0.35744543 0.30066341 [7] 0.21865488 0.15150680 0.10686805 -0.03764187 Largest eigenvalues: [1] 100177717 97149296 90919394 86903117 85598857 83859986 83713001 [8] 81314877 80531967 78210634 Smallest eigenvalues: [1] 0.36188095 0.33154497 0.28084677 0.27027198 0.25349816 0.23266924 [7] 0.16157990 -0.08828979 -0.09259169 -0.15250096 Largest eigenvalues: [1] 99508726 95689348 89370252 85700586 83901788 83123438 82806295 80739396 [9] 79483378 77428633 Smallest eigenvalues: [1] 0.33630454 0.30777249 0.30537957 0.28594531 0.19288364 0.16615106 [7] 0.09010590 0.05899619 -0.10405405 -0.34019080 Largest eigenvalues: [1] 99332276 95920113 90030227 86067077 83662528 83536728 82451170 81046350 [9] 79893757 77975274 Smallest eigenvalues: [1] 0.39276363 0.35040358 0.32994772 0.32001891 0.29454848 0.16857480 [7] 0.12142075 0.07432521 0.01099322 -0.29693436 Largest eigenvalues: [1] 100299555 96759039 90566330 86307629 85931863 83694099 83024913 [8] 81075841 80356558 78067487 Smallest eigenvalues: [1] 0.21893762 0.19593698 0.18543051 0.14873324 0.14516919 0.13645890 [7] 0.11023235 -0.02897616 -0.14211528 -0.16044410 Largest eigenvalues: [1] 100431057 95961096 89341427 86642375 85186878 83183779 82061555 [8] 80101802 79347220 77445793 Smallest eigenvalues: [1] 0.2602365 0.2570870 0.2388784 0.2053796 0.1995073 0.1046424 [7] -0.1621127 -0.2250190 -0.2843639 -0.3168477 Largest eigenvalues: [1] 99647172 96916163 90640776 86239395 85470397 83579807 83328086 80822148 [9] 80163657 77952000 Smallest eigenvalues: [1] 0.40400429 0.36604617 0.30860037 0.28677286 0.28115367 0.22716540 [7] 0.04393261 -0.05833318 -0.11548213 -0.47605436 Largest eigenvalues: [1] 101649014 95522373 90100448 85653832 85473953 83194115 82216662 [8] 81115959 79330155 77859028 Smallest eigenvalues: [1] 0.37558747 0.36683486 0.31083082 0.22741827 0.21773171 0.11644854 [7] 0.07298194 0.07005614 -0.41328467 -0.65295298 Largest eigenvalues: [1] 102148664 97614896 91630564 87671115 86884646 85794834 83672506 [8] 83012664 80790557 79753091 Smallest eigenvalues: [1] 0.51971322 0.50236056 0.48731704 0.45929382 0.45197303 0.38667543 [7] 0.37841139 0.33527757 -0.03335841 -0.08405912 Largest eigenvalues: [1] 99655885 96744856 90161402 86840470 85157421 83588651 83260994 80827890 [9] 80257875 77936108 Smallest eigenvalues: [1] 0.43942356 0.40974277 0.39342205 0.36772868 0.29667184 0.29486481 [7] 0.13749098 -0.02550308 -0.18765960 -0.27126923 Largest eigenvalues: [1] 100636001 96151021 90344495 86105475 85282811 83325189 82874150 [8] 80650549 79995501 77380646 Smallest eigenvalues: [1] 0.43776415 0.38631081 0.29806117 0.29448067 0.28620525 0.28405758 [7] 0.28110522 0.16351536 -0.04610377 -0.24788462 Largest eigenvalues: [1] 99272851 96419933 90717019 86045286 85116829 84428760 82978278 81984611 [9] 79943126 78876023 Smallest eigenvalues: [1] 0.5509046 0.5457060 0.5062425 0.4487377 0.4130501 0.3349153 [7] 0.3257687 0.1665704 0.1453993 -0.1944866 Largest eigenvalues: [1] 99710199 97256160 90470268 87257597 85442606 83810170 82954597 80691333 [9] 80276279 77766906 Smallest eigenvalues: [1] 0.22922968 0.21369999 0.20204880 0.18203972 0.15649445 0.09370964 [7] -0.04422377 -0.08416410 -0.08849072 -0.45506529 Largest eigenvalues: [1] 99619219 96888235 91079179 86104055 84816616 83456118 83312997 80852636 [9] 80289936 78000833 Smallest eigenvalues: [1] 0.393891474 0.368868367 0.365145559 0.330822180 0.264080828 [6] 0.263617170 0.259932186 0.137141252 0.001561397 -0.344528383 Largest eigenvalues: [1] 100970049 95705926 89944456 86153788 84956462 83054093 82572837 [8] 80673284 79605524 77463145 Smallest eigenvalues: [1] 0.3113159 0.2756453 0.1911906 0.1798713 0.1717007 0.1586581 [7] 0.1500908 0.1007756 -0.3973729 -0.7090370 Largest eigenvalues: [1] 100207484 95748029 89844841 85332900 84837122 83780557 82282207 [8] 81352604 79617378 77938945 Smallest eigenvalues: [1] 0.40223768 0.39144923 0.36552822 0.31730640 0.27804525 0.17950052 [7] 0.16813610 0.11463871 -0.04986981 -0.32003184 Largest eigenvalues: [1] 99596151 96556998 90134915 86154525 85877594 83598114 83105399 81157801 [9] 80066606 78360035 Smallest eigenvalues: [1] 0.38516375 0.35856738 0.35664409 0.34413946 0.28296176 0.22722562 [7] 0.18128588 0.12341308 -0.06084001 -0.57956965 Largest eigenvalues: [1] 99943402 96453675 89793614 86457386 85402811 83129530 82427586 80566073 [9] 79726739 77550637 Smallest eigenvalues: [1] 0.3761855 0.3746307 0.3255401 0.2959918 0.2527528 0.1944826 [7] 0.1570679 0.1247068 -0.2664169 -0.6922870 Largest eigenvalues: [1] 98606790 96276700 90175078 85858342 85118926 83127152 82596470 80645223 [9] 79490738 77445099 Smallest eigenvalues: [1] 0.37924129 0.30634121 0.26664416 0.20665351 0.19501598 0.11445113 [7] 0.02504388 -0.01858016 -0.36288679 -0.47341315 Largest eigenvalues: [1] 100681860 96008258 90031237 86153295 86135000 84138442 83281297 [8] 81845217 80091499 78713334 Smallest eigenvalues: [1] 0.42865001 0.38990625 0.36763473 0.35062993 0.28735282 0.26719084 [7] 0.18972497 0.10848164 0.08819804 -0.25454027 Largest eigenvalues: [1] 99766283 96853515 90420953 86632539 85688765 84137676 82793902 81313784 [9] 79926007 78404812 Smallest eigenvalues: [1] 0.25595105 0.22639834 0.22466148 0.18638676 0.14432052 0.11389366 [7] 0.06940228 -0.33635245 -0.58425217 -0.68676949 Largest eigenvalues: [1] 99510124 96771213 90629724 86650092 85341574 84012763 83365452 81783816 [9] 80174278 78695313 Smallest eigenvalues: [1] 0.4285852254 0.3997891407 0.3969092617 0.3712435518 0.3664479509 [6] 0.3549069316 0.1300255951 0.0731919449 0.0380002154 -0.0006040823 Largest eigenvalues: [1] 100364487 96160140 90431147 85580724 84944369 82997627 82528999 [8] 80440018 79946214 77468090 Smallest eigenvalues: [1] 0.46776230 0.45988348 0.45474318 0.44117380 0.40999107 0.30586253 [7] 0.24687362 0.20382624 0.08107048 -0.35598098 Largest eigenvalues: [1] 99029449 97009562 90557522 86998871 85211551 83767014 83006087 80692745 [9] 80284306 77657956 Smallest eigenvalues: [1] 0.34728103 0.33471874 0.30801816 0.29508497 0.22548739 0.12634063 [7] 0.12631132 0.09962885 -0.12022322 -0.97869459 Largest eigenvalues: [1] 100469475 95876078 89979992 85869378 84699315 83095235 82597882 [8] 80831290 79884327 77675066 Smallest eigenvalues: [1] 0.44706944 0.39920568 0.38985087 0.38958923 0.25891558 0.18416717 [7] 0.15265301 0.14701494 0.08483516 -0.12834914 Largest eigenvalues: [1] 100271850 95025032 89019897 85345507 84621904 82838048 81581391 [8] 80368487 78668508 77202431 Smallest eigenvalues: [1] 0.47215679 0.39479868 0.34281193 0.33326029 0.29871603 0.23902886 [7] 0.20912750 0.20871301 0.08198655 -0.08068304 Largest eigenvalues: [1] 99333755 96743208 90837950 86361918 84596958 84446254 82755116 81852648 [9] 79799114 78791922 Smallest eigenvalues: [1] 0.35998541 0.24171326 0.23265200 0.23159816 0.17045843 0.15681433 [7] -0.07185973 -0.25306503 -0.28851923 -0.51593553 Largest eigenvalues: [1] 100212223 96788515 90527247 87568042 84999210 84115242 83754942 [8] 81059640 80616070 77720318 Smallest eigenvalues: [1] 0.43752264 0.43465960 0.43031536 0.32962370 0.32276997 0.27011194 [7] 0.16963925 0.08553073 -0.11178122 -0.20050478 Largest eigenvalues: [1] 99138418 96584437 89887545 86572127 84646997 83243397 82991443 80473208 [9] 80073227 77419974 Smallest eigenvalues: [1] 0.20043427 0.16173165 0.14849818 0.04248158 0.03502653 -0.02527992 [7] -0.02737679 -0.10294468 -0.19073288 -0.48769691 Largest eigenvalues: [1] 96965417 96822366 90658075 86010713 84167454 83493425 83065549 80584530 [9] 79777801 77470917 Smallest eigenvalues: [1] 0.314275122 0.284166683 0.284143168 0.268311125 0.152286799 [6] 0.141677021 0.119435624 0.111505918 0.003968222 -0.239445632 Largest eigenvalues: [1] 98020104 96050530 89620544 85472708 83752495 83069269 82848614 80624445 [9] 79517959 77406359 Smallest eigenvalues: [1] 0.26293799 0.22792776 0.18670991 0.16475471 0.14428839 0.12266500 [7] 0.08996917 -0.20903127 -0.62081804 -1.45886878 Largest eigenvalues: [1] 100657250 96917723 90829997 87242993 85322828 84391765 84028328 [8] 81985538 80922661 78700272 Smallest eigenvalues: [1] 0.43378311 0.37363816 0.35481855 0.34296215 0.29283867 0.23132859 [7] 0.18172462 0.08693672 -0.12029571 -0.24043411 Largest eigenvalues: [1] 98294759 96319160 89798418 86356281 84383428 83157465 83028146 80636073 [9] 79804024 77343655 Smallest eigenvalues: [1] 0.49396069 0.38615448 0.34757115 0.31180418 0.27055155 0.20844742 [7] 0.17181707 0.11385935 0.01217052 -0.06995956 Largest eigenvalues: [1] 101294337 95492743 89634942 85869682 85568152 83603315 82530069 [8] 80906557 79686247 77812945 Smallest eigenvalues: [1] 0.1526260314 0.1311212752 0.1014911600 0.0979826409 0.0373865808 [6] 0.0349146992 -0.0004025047 -0.0521226967 -0.4723957994 -0.7229358658 Largest eigenvalues: [1] 101893790 97244837 90812424 87115832 86693676 85898778 82935662 [8] 82444550 80784605 79199158 Smallest eigenvalues: [1] 0.14384739 0.08788012 0.08777941 0.02201911 -0.04388965 -0.23056977 [7] -0.30866149 -0.52467144 -0.75183837 -0.90022854 Largest eigenvalues: [1] 98023175 97487943 91364914 86462944 85372742 84248844 83734940 81182009 [9] 80406336 78317018 Smallest eigenvalues: [1] 0.4530279 0.3534015 0.3061967 0.2845028 0.2399986 0.1968493 [7] 0.1812347 0.1071914 -0.2455290 -0.3969593 Largest eigenvalues: [1] 98975078 96608261 90288001 86348950 85085949 83305422 83109169 80795737 [9] 79822024 77816369 Smallest eigenvalues: [1] 0.343317748 0.339378521 0.271306168 0.265682309 0.262015729 [6] 0.254886949 0.163092072 0.083546179 -0.007327227 -0.453658290 Largest eigenvalues: [1] 101186982 95847778 90160713 86656954 85252703 84153975 82222508 [8] 81421827 79650678 78453483 Smallest eigenvalues: [1] 0.40731401 0.37668139 0.33959024 0.26674997 0.23655481 0.15124796 [7] 0.13885303 0.06057001 -0.55934292 -0.63713510 Largest eigenvalues: [1] 101268224 96547217 91192230 86637955 85882631 84559945 82962242 [8] 82162655 80263228 79313609
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 19.50949 | 0.6735958 | 1821.112 | 0.05 | 2.281469 | 2.326024 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)/
(GET_results[[5]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ air pressure + noise
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(air_pressure = airpressure_fd,
noise = noise_fd
)
path_plot <- 'figures/model_HR_airpress_noise_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 30. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 172 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.15845393 0.15456730 0.15323569 0.15309657 0.15263615 0.15138328 [7] 0.15056304 0.07148425 0.07130301 -0.15743932 Largest eigenvalues: [1] 18484502 18333396 18120823 18065769 17986287 17761297 17622487 17535008 [9] 17467479 17328246 Smallest eigenvalues: [1] 0.17853850 0.17663013 0.17544969 0.17417858 0.17227721 0.17139890 [7] 0.15289376 0.09391307 0.07861465 -0.11685164 Largest eigenvalues: [1] 18497405 18345455 18101366 18048431 17963927 17857263 17678093 17601874 [9] 17508740 17392413
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.784591 | 0.401951 | 6.733928 | 0.04 | 0.6636861 | 0.6926779 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ air pressure + noise + air temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(air_pressure = airpressure_fd,
noise = noise_fd,
temperature = temperature_fd
)
path_plot <- 'figures/model_HR_airpress_noise_temp_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 25. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 262 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.10049050 0.09870038 0.09683498 0.09604983 0.09565113 0.09325221 [7] 0.09139448 0.05526609 0.04407148 -0.32047288 Largest eigenvalues: [1] 16355053 16198674 16132178 15903323 15792269 15611790 15471286 15345177 [9] 15263289 15199542 Smallest eigenvalues: [1] 0.10760275 0.10682632 0.10317115 0.10090800 0.09703859 0.09303815 [7] 0.08418235 0.06159548 0.04931716 -1.22004555 Largest eigenvalues: [1] 16361221 16100095 15977299 15853573 15809618 15699875 15574450 15511030 [9] 15414523 15261930 Smallest eigenvalues: [1] 0.13587619 0.13276008 0.13207705 0.12912577 0.12441757 0.12243005 [7] 0.09461737 0.07095360 0.06942470 -0.22605266 Largest eigenvalues: [1] 16254373 16132921 16014237 15926807 15820685 15699559 15536213 15475377 [9] 15326802 15241950 Smallest eigenvalues: [1] 0.082537385 0.081961386 0.079301818 0.078346931 0.076345831 [6] 0.073700496 0.068863082 0.043700523 0.031455814 -0.009860154 Largest eigenvalues: [1] 16404595 16215084 16190676 15860716 15797660 15695601 15490967 15395130 [9] 15287997 15235032 Smallest eigenvalues: [1] 0.0579022118 0.0560362018 0.0546029674 0.0532622023 0.0514941030 [6] 0.0510026453 0.0487051856 0.0471930905 0.0278328470 -0.0001433643 Largest eigenvalues: [1] 16432027 16160121 16156371 15928699 15903793 15677388 15561430 15426807 [9] 15346551 15292998
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.724708 | 0.4400124 | 9.678972 | 0.21 | 1.179298 | 0.9076917 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + acc + Sex
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_Sex_N200'
basis_params <- list(beta_0 = list(nbetabasis = 60, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 60, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 60, norder = 4, lambda = 1e4),
acceleration = list(nbetabasis = 60, norder = 4, lambda = 1e4),
Sex = list(nbetabasis = 60, norder = 4, lambda = 1e4))
factors <- list(Sex = participant_info$Sex |> as.factor())
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params,
factors = factors)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |>
substr(4, 9))] |> as.numeric())
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
if(!is.na(factors[1])) {for (fact in names(factors)) {
assign(paste0(fact, '_BS'),
factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |>
as.numeric())}}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
formula_BS <- as.formula(formula_BS)
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 31. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 450 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.9688860 0.7923770 0.7839802 0.7089242 0.7061079 0.7004947 [7] 0.5701982 0.4222949 0.4087865 -0.5678656 Largest eigenvalues: [1] 135256038 131203586 122990816 117887683 114015726 113315527 113149768 [8] 110015403 109084873 105696629 Smallest eigenvalues: [1] 0.9544816 0.9361034 0.8328902 0.8091576 0.7739644 0.7606454 [7] 0.7575709 0.7553243 0.1693061 -1.5115225 Largest eigenvalues: [1] 137501025 131427866 122889632 118097765 116624626 113193359 113001944 [8] 110026587 108756610 105629481 Smallest eigenvalues: [1] 0.9614418 0.9225914 0.6914412 0.5924914 0.5497382 0.4885853 [7] 0.4144111 0.3878296 0.1064785 -0.4911248 Largest eigenvalues: [1] 137094604 131113312 123628899 116688854 116595749 114057268 112946378 [8] 110814368 108618032 106607737 Smallest eigenvalues: [1] 1.1564350 1.1338316 1.0377003 1.0259619 0.9665639 0.9647546 [7] 0.8127989 0.6185221 0.3791011 -0.7589908 Largest eigenvalues: [1] 136164340 132656839 124259577 118533944 115847823 114388485 113266284 [8] 110231758 109759032 105893395 Smallest eigenvalues: [1] 1.1505863 1.1160754 1.0165090 0.9922383 0.7094019 0.6516838 [7] 0.6134164 0.6052341 0.5655830 -0.6573829 Largest eigenvalues: [1] 133436218 130976030 122381334 118328235 114037347 112576615 112408328 [8] 109260710 108780920 104773053 Smallest eigenvalues: [1] 1.1185887 1.0582716 1.0201250 0.9637271 0.7956847 0.7826604 [7] 0.6542965 0.5654786 0.4072251 -2.3559232 Largest eigenvalues: [1] 130885760 130852944 122800509 118881715 114030886 113204217 112216022 [8] 109642554 109304156 105369724 Smallest eigenvalues: [1] 1.0545992 1.0354944 0.9779019 0.9233780 0.8905897 0.5518688 [7] 0.4873694 0.4469574 0.3539931 -0.3402065 Largest eigenvalues: [1] 137221285 132919786 123981982 118234497 117328678 113931463 113638093 [8] 110702506 109484838 106761073 Smallest eigenvalues: [1] 1.2248888 1.1887652 1.0533451 0.9403865 0.9210631 0.9103510 [7] 0.8423889 0.6573866 0.5516138 -0.1483955 Largest eigenvalues: [1] 135967218 133801548 124451848 119797832 115847951 114282065 113843866 [8] 110629861 110098930 106579426 Smallest eigenvalues: [1] 1.30813749 1.23787645 1.11359816 1.08186806 0.99086914 0.98551032 [7] 0.74845577 0.74071083 0.73728535 -0.01505082 Largest eigenvalues: [1] 134207169 132134609 124319846 119466943 113807668 113757586 113304155 [8] 110364240 109728413 106183448 Smallest eigenvalues: [1] 0.9093957 0.8429204 0.8335873 0.7220211 0.6488800 0.6238243 [7] 0.5957890 0.4801154 0.4549419 -0.2964439 Largest eigenvalues: [1] 133564077 130973207 123187379 117847002 113721761 113522829 112256016 [8] 109508175 109079325 104938910 Smallest eigenvalues: [1] 1.1379407 1.1350288 1.0406986 1.0160823 0.9563521 0.8142150 [7] 0.7077676 0.5935217 0.5108063 -0.5471780 Largest eigenvalues: [1] 135589123 131853370 123504640 118080264 115528579 113263608 112991338 [8] 109711348 108986896 105540395 Smallest eigenvalues: [1] 0.9958364 0.9658244 0.9067076 0.6886484 0.6639905 0.6244460 [7] 0.3789718 0.1823708 -0.1282827 -0.2723373 Largest eigenvalues: [1] 135899280 131617753 122651526 117517101 117307561 113063232 112617621 [8] 110270841 108429819 105988203 Smallest eigenvalues: [1] 1.2189650 1.1226973 1.0456972 0.9896847 0.9072902 0.8142459 [7] 0.7862135 0.7627543 0.4311736 -0.3123060 Largest eigenvalues: [1] 135784267 132040516 124005747 118895274 115183729 113834466 113179370 [8] 110398891 109733851 106098447 Smallest eigenvalues: [1] 1.0673985 1.0276958 0.9202925 0.7714554 0.7674908 0.7567785 [7] 0.6805751 0.5179251 0.4594829 -1.0889680 Largest eigenvalues: [1] 136233676 131115345 123195429 117389036 116851635 114412764 113143992 [8] 111196341 109291964 107197555 Smallest eigenvalues: [1] 1.0690837 0.9603471 0.9035975 0.8955947 0.8855373 0.8298453 [7] 0.4307876 0.3166552 0.2495788 -0.3645691 Largest eigenvalues: [1] 137555695 131472385 123296996 116795616 116522479 113675823 112757097 [8] 110610289 108553828 106126259 Smallest eigenvalues: [1] 1.0245585 0.8950231 0.8644307 0.8083248 0.7798005 0.7499528 [7] 0.7214333 0.6622987 0.3735917 -0.2413907 Largest eigenvalues: [1] 135227207 132767734 124313537 118755259 115391844 114112100 113805937 [8] 110217395 109610881 105566847 Smallest eigenvalues: [1] 1.0029995 0.9328319 0.9327370 0.7864304 0.7034891 0.6673939 [7] 0.4594537 0.4216955 0.2183513 -1.0060318 Largest eigenvalues: [1] 137521867 131754185 123571527 118107671 115551061 113946805 113279981 [8] 111044078 109348892 106127866 Smallest eigenvalues: [1] 0.9994690 0.9923605 0.8979505 0.8552854 0.8415888 0.7673291 [7] 0.7044542 0.5943836 0.2936434 -1.3660862 Largest eigenvalues: [1] 135827267 131919435 123966458 118766214 115619043 113775048 112836485 [8] 110178249 109410240 105749460 Smallest eigenvalues: [1] 1.0396130 0.9961151 0.9130125 0.9100908 0.7780031 0.6903398 [7] 0.6894318 0.4253155 0.2656445 -0.9492245 Largest eigenvalues: [1] 133952093 132103118 123966949 119337988 115274875 114228599 112678706 [8] 110388789 109685854 105674388 Smallest eigenvalues: [1] 1.1463728 1.1153447 1.1106684 0.9843023 0.8711505 0.5423673 [7] 0.4561904 0.4381777 0.1650653 -0.3194171 Largest eigenvalues: [1] 135367953 132887135 124382054 119161115 115521159 114612291 113575311 [8] 111124531 110241836 106783026 Smallest eigenvalues: [1] 0.9599534 0.9208488 0.7784240 0.7152306 0.6778071 0.6279480 [7] 0.6182952 0.5785797 0.3802319 -2.1925345 Largest eigenvalues: [1] 135813654 131088733 123695233 117728555 115143708 113937891 113646450 [8] 110764971 109238901 106156772 Smallest eigenvalues: [1] 0.8289328 0.7574264 0.7193836 0.6006725 0.5094471 0.4480233 [7] 0.4358892 0.3556260 0.1490550 -0.3459324 Largest eigenvalues: [1] 136451616 133599516 125078740 119203866 116952202 115594046 114341390 [8] 111603666 109920607 107468866 Smallest eigenvalues: [1] 0.9456964 0.8166213 0.7219202 0.6977297 0.6921685 0.6267455 [7] 0.3664069 0.3627567 0.2819279 -1.7848098 Largest eigenvalues: [1] 131782468 131683019 123643540 119056495 114902359 112664850 112160452 [8] 109723501 109237765 104993065 Smallest eigenvalues: [1] 1.08574416 1.04379105 0.87243525 0.76919023 0.75698360 0.74917196 [7] 0.71926067 0.55608833 0.32192858 -0.07440743 Largest eigenvalues: [1] 137204189 133698370 123653770 118320912 115980438 114927605 113702543 [8] 110894210 109558845 106495311 Smallest eigenvalues: [1] 1.05120787 1.04194036 1.01487272 0.84994413 0.82884007 0.73016267 [7] 0.67209992 0.38022451 0.01509145 -0.55404841 Largest eigenvalues: [1] 139545221 133719550 125097865 118921985 118548854 115112308 114227798 [8] 111756446 110199741 108045089 Smallest eigenvalues: [1] 1.03882583 1.03589737 1.00296502 0.99136485 0.95654367 0.68156244 [7] 0.56062695 0.48393081 0.06807012 -0.05950702 Largest eigenvalues: [1] 134660729 132528232 123727535 118831674 115788801 113922877 113733353 [8] 110572639 109714521 106738489 Smallest eigenvalues: [1] 1.0396135 0.9658589 0.9288576 0.8188947 0.7920223 0.5702712 [7] 0.5405805 0.4809489 0.4721227 -0.7104762 Largest eigenvalues: [1] 134391282 131590394 123112441 117596800 114973951 113143452 112762835 [8] 109797770 108418449 105431644 Smallest eigenvalues: [1] 1.0985861 1.0472141 0.8957156 0.8647416 0.8581900 0.7825575 [7] 0.7382876 0.5735613 -0.1684700 -1.5405825 Largest eigenvalues: [1] 138094351 132871277 124701353 118682935 117156566 114227129 113443152 [8] 110656295 109328286 106572389 Smallest eigenvalues: [1] 0.98827770 0.91802702 0.89916978 0.83174811 0.77879069 0.74220782 [7] 0.45411217 0.42020081 0.09615512 -1.35473343 Largest eigenvalues: [1] 137226580 129641131 122202867 116765239 116068150 112224765 111172666 [8] 109438196 107429670 105315868 Smallest eigenvalues: [1] 1.0626611 1.0403723 0.9546409 0.8719927 0.8703990 0.8472838 [7] 0.7625131 0.5842803 0.4190668 -0.5842997 Largest eigenvalues: [1] 134865388 133264740 124233541 118695796 115644771 114050208 113853054 [8] 110472404 109398206 106439372 Smallest eigenvalues: [1] 1.1326700 1.0922024 0.9600027 0.9551540 0.8502791 0.8476822 [7] 0.5703527 0.4598740 0.2663142 -1.3852334 Largest eigenvalues: [1] 134036097 131231871 122870296 117969399 115053098 114155375 112021342 [8] 109643866 109089247 105379549 Smallest eigenvalues: [1] 0.9432775 0.9171678 0.8801126 0.6817939 0.6409919 0.5686675 [7] 0.5499618 0.4847470 0.4839770 -0.3029676 Largest eigenvalues: [1] 133336389 131671868 122921902 117829257 114511870 113480728 112057007 [8] 109110659 108697995 104527953 Smallest eigenvalues: [1] 1.0441547 0.8622080 0.8376512 0.6449458 0.4220183 0.4127773 [7] 0.3766716 0.2891900 0.2540777 -2.3349884 Largest eigenvalues: [1] 135409978 130621350 123305525 116890769 115116988 112917597 111904457 [8] 109522498 108680530 105452550 Smallest eigenvalues: [1] 1.1737463 1.0370897 1.0367004 1.0018156 0.9337256 0.5546521 [7] 0.5498891 0.5392489 0.4780433 -0.1168439 Largest eigenvalues: [1] 136678006 131110370 122902021 117295611 114960874 113692034 112107141 [8] 110766592 108301375 105927461 Smallest eigenvalues: [1] 1.09287956 1.06839714 0.96582559 0.83378381 0.80879817 0.80785344 [7] 0.76328510 0.75127011 0.09723270 -0.04897159 Largest eigenvalues: [1] 134024766 132152890 123201687 118187585 114776757 113813751 113674088 [8] 110447327 109389374 106170001 Smallest eigenvalues: [1] 1.0373517 0.9628217 0.8235005 0.7981366 0.7436669 0.7305748 [7] 0.6893718 0.3580972 0.3278450 -0.2480008 Largest eigenvalues: [1] 134068829 130328346 122216629 116461162 114767052 112616520 112410744 [8] 109313265 108378882 105618944 Smallest eigenvalues: [1] 0.94239969 0.91631954 0.85648240 0.83564551 0.75669972 0.58620550 [7] 0.57479169 0.06901803 -0.24964130 -0.92038140 Largest eigenvalues: [1] 136697646 132135761 123686622 117715904 116929739 113115981 112892445 [8] 109880688 108866536 105911807 Smallest eigenvalues: [1] 1.03191434 1.01720133 0.97081175 0.79336619 0.79227968 0.68027693 [7] 0.64973896 0.58258275 0.31591576 -0.09416299 Largest eigenvalues: [1] 135764860 133313011 124941669 119811243 116457258 114435615 113282294 [8] 110689677 109964691 106310896 Smallest eigenvalues: [1] 1.0102334 1.0053290 0.9922848 0.9440762 0.9420984 0.7800463 [7] 0.6185816 0.6145541 0.3906510 -0.1893042 Largest eigenvalues: [1] 134168773 132413407 123483919 118725487 115450878 113973195 113267006 [8] 110043069 109115099 106326255 Smallest eigenvalues: [1] 1.0382794 0.9507924 0.8870887 0.8596301 0.8197861 0.6592628 [7] 0.4005770 0.3394154 0.2245226 -0.1000553 Largest eigenvalues: [1] 133454860 133243296 123388221 118452104 114077892 113646217 112838495 [8] 110064391 109218737 105580077 Smallest eigenvalues: [1] 1.0167987 1.0067789 0.9547590 0.8825125 0.7061137 0.5148236 [7] 0.4051440 0.3832299 0.3774022 -0.6660513 Largest eigenvalues: [1] 136470553 131583617 124097831 117671681 115680492 113881169 113251208 [8] 110353641 109572124 106185007 Smallest eigenvalues: [1] 1.14044774 1.07652696 1.05616281 0.98110823 0.86910508 0.84694068 [7] 0.75258935 0.74457466 0.02533093 -0.32940363 Largest eigenvalues: [1] 134572855 131091376 123161126 118091908 113544916 113360274 113168853 [8] 110228013 109265994 105826947 Smallest eigenvalues: [1] 1.0621701 0.9427645 0.9051551 0.7601148 0.7127552 0.6917281 [7] 0.6727694 0.6178408 0.5034638 -0.3369336 Largest eigenvalues: [1] 135478646 131436911 123378303 118212557 115176749 114316871 112839297 [8] 110765987 109095546 106718081 Smallest eigenvalues: [1] 1.0812048 1.0747398 1.0736365 0.9934737 0.8520125 0.6980457 [7] 0.5633948 0.5116939 0.4333273 -1.1274514 Largest eigenvalues: [1] 135882265 131209793 122888194 117444421 114638127 112831917 112129557 [8] 109628140 108460250 104829513 Smallest eigenvalues: [1] 1.03732870 1.00664470 0.84059559 0.77478882 0.76739547 0.67184545 [7] 0.58217521 0.57531073 0.09229861 -0.05517217 Largest eigenvalues: [1] 137095448 131407432 123822762 117517416 116024738 114572931 112648701 [8] 110800203 109088975 106965861 Smallest eigenvalues: [1] 1.1185494 0.9618374 0.8826793 0.8400191 0.7787778 0.6220969 [7] 0.5899111 0.3627868 0.3621359 -1.8165766 Largest eigenvalues: [1] 137128564 132715349 124609803 119839915 116826845 114198047 113939538 [8] 110891242 110178742 106996164 Smallest eigenvalues: [1] 1.0300828 1.0123090 0.9680805 0.9600012 0.8598882 0.7299005 [7] 0.7035601 0.4769452 0.3803877 -0.3507494 Largest eigenvalues: [1] 138199497 131383770 123316687 117794606 115208842 113152572 112741264 [8] 110383742 108698402 105728821 Smallest eigenvalues: [1] 1.15855795 1.03425798 1.00420820 0.95886997 0.95464209 0.78459917 [7] 0.76063053 0.70590603 0.15621349 -0.09697355 Largest eigenvalues: [1] 136527333 133215622 124499265 119061136 116017097 114439462 113995372 [8] 111017571 110179199 107271217 Smallest eigenvalues: [1] 1.0899275 0.9415549 0.8288436 0.7935858 0.7935681 0.6617445 [7] 0.5165707 0.4647370 0.4446136 -1.1766939 Largest eigenvalues: [1] 136813978 131908882 123877553 117981861 116710636 113872231 113408480 [8] 110501043 109354994 106521405 Smallest eigenvalues: [1] 0.9798561 0.9364494 0.9043078 0.7296532 0.7047301 0.5731803 [7] 0.4850737 0.3515605 -0.1347396 -0.7692006 Largest eigenvalues: [1] 137165980 132241603 124655682 118218050 117543621 115257665 113489925 [8] 111406701 109504037 107381322 Smallest eigenvalues: [1] 1.1299150 0.9825307 0.9790333 0.9624829 0.8022683 0.7206804 [7] 0.6934415 0.6221411 0.3919681 -0.1552567 Largest eigenvalues: [1] 137694879 131383995 123206519 116574538 116432181 113597009 112774664 [8] 110386153 108939718 106362020 Smallest eigenvalues: [1] 0.9894955 0.8810198 0.8657774 0.7079470 0.6990686 0.6798601 [7] 0.5330665 0.4387386 0.4039624 -2.5682382 Largest eigenvalues: [1] 135216382 133459996 124724070 120336564 115554988 115366952 114665146 [8] 111217857 110798478 106730976 Smallest eigenvalues: [1] 1.0029979 0.9894337 0.9657951 0.8931327 0.8164346 0.6385867 [7] 0.5978628 0.4032887 0.1920436 -0.4420922 Largest eigenvalues: [1] 137303389 133358960 124970971 119030667 117398001 114759806 114555708 [8] 111195691 110457642 107281242 Smallest eigenvalues: [1] 1.1706722 1.1636130 1.0101147 0.9820114 0.7333357 0.6732234 [7] 0.6613315 0.5527298 0.5316512 -0.4742273 Largest eigenvalues: [1] 132158494 130575865 122426208 117641221 113374585 112834698 112040247 [8] 109352560 108647544 105236386 Smallest eigenvalues: [1] 1.0713429 0.9447356 0.9297435 0.8098997 0.7529481 0.6839599 [7] 0.5237067 0.5076790 0.1330335 -0.3192479 Largest eigenvalues: [1] 138112927 132166960 124182609 117773864 117595566 113885243 113202295 [8] 111378240 109075657 107139664 Smallest eigenvalues: [1] 1.0078198 0.9884496 0.8281396 0.8240012 0.7819829 0.7271506 [7] 0.6248498 0.5160166 0.3270552 -0.6627981 Largest eigenvalues: [1] 136172368 132725773 123921939 118333364 116155954 113587555 113447898 [8] 110328728 108856619 105632767 Smallest eigenvalues: [1] 1.0803471 1.0787975 0.9374415 0.9142182 0.7968931 0.7776288 [7] 0.7272637 0.3873496 -0.3064515 -0.3781777 Largest eigenvalues: [1] 135214937 131037347 122740232 117913818 114517981 113125097 112252269 [8] 109615174 108564016 104600437 Smallest eigenvalues: [1] 1.15468054 1.13827933 1.10157035 1.04311364 1.02172702 0.70618442 [7] 0.65712530 0.65160852 0.47955042 -0.09350394 Largest eigenvalues: [1] 139268878 131214833 123639789 118037519 116924485 114191276 112706295 [8] 111163310 108946403 106738930 Smallest eigenvalues: [1] 1.1500913 1.0903491 1.0377948 1.0226323 0.9639596 0.8951181 [7] 0.7722534 0.6654304 0.3544484 -0.7270938 Largest eigenvalues: [1] 134807524 129555422 122004078 116805208 113507606 112732081 111911925 [8] 109055639 108317510 104663642 Smallest eigenvalues: [1] 1.1705832 1.0630012 0.9594253 0.8926407 0.7998752 0.7619922 [7] 0.7162435 0.6524585 0.5284527 -0.4569586 Largest eigenvalues: [1] 135508113 131861201 124082315 118831952 115768962 114193954 113317044 [8] 110673094 109547710 106682237 Smallest eigenvalues: [1] 1.1668380 1.0706558 0.9716204 0.8585883 0.8583195 0.7228779 [7] 0.5798090 0.5079012 0.4785799 -0.6842266 Largest eigenvalues: [1] 136679991 131923202 124405717 118085272 116062159 114726834 113626859 [8] 110897825 109701668 106968195 Smallest eigenvalues: [1] 0.939367915 0.885596297 0.870563838 0.837719439 0.786857291 [6] 0.621768854 0.565269996 0.411356303 0.073933769 -0.006983568 Largest eigenvalues: [1] 139077174 132124672 123980267 118349442 118117583 114096803 113003819 [8] 111077288 109107279 106815214 Smallest eigenvalues: [1] 1.11616284 1.09019475 0.95782270 0.93344345 0.76680151 0.76044917 [7] 0.56072419 0.49844045 0.44558962 -0.06395638 Largest eigenvalues: [1] 134037434 133412526 124965521 119618047 115376964 114849933 113401577 [8] 110916067 110260571 106364627 Smallest eigenvalues: [1] 1.0638062 1.0204108 1.0201889 0.9741826 0.9173209 0.7768200 [7] 0.7477912 0.6002204 0.3250965 -0.1614133 Largest eigenvalues: [1] 137470031 132773397 124687420 118780808 116541311 114334022 114118409 [8] 110909022 109786086 106460132 Smallest eigenvalues: [1] 1.161057641 1.139323340 1.119134342 1.077427176 0.951895774 [6] 0.850399296 0.501310214 0.442614923 0.247149976 -0.007004209 Largest eigenvalues: [1] 138114071 131246382 122993093 117257180 117232495 113249107 112317609 [8] 110083531 108571560 106190741 Smallest eigenvalues: [1] 1.03379506 1.00044033 0.98587366 0.92724962 0.90234853 0.80694965 [7] 0.43928140 0.41782564 0.35778457 -0.02320456 Largest eigenvalues: [1] 136334834 132832534 124200620 118463890 116046464 114364309 113383480 [8] 110862490 109141477 106925725 Smallest eigenvalues: [1] 1.0396085 0.9816794 0.9353829 0.8728415 0.7665449 0.7195809 [7] 0.6814536 0.5571039 0.1449074 -0.9692659 Largest eigenvalues: [1] 135364810 132251770 124065318 118426680 116119556 113825123 113576465 [8] 110483721 109563995 106287467 Smallest eigenvalues: [1] 0.9254435 0.8949878 0.8869167 0.7865337 0.6624205 0.6541863 [7] 0.6275214 0.5222385 0.1541507 -0.6593987 Largest eigenvalues: [1] 138704012 133142230 124778197 118805116 118412541 114297735 113748114 [8] 111209987 109654377 106805201 Smallest eigenvalues: [1] 0.9774613 0.9400363 0.9262829 0.7432793 0.7073598 0.6508125 [7] 0.6235384 0.4389632 -0.0403218 -3.5779398 Largest eigenvalues: [1] 135264930 133019006 124636691 118960397 115540945 114608832 113027163 [8] 110340612 109921951 105900412 Smallest eigenvalues: [1] 1.1194456 0.9408376 0.9391890 0.9048962 0.9040624 0.5934157 [7] 0.5779869 -0.1388906 -0.2294558 -0.2961695 Largest eigenvalues: [1] 135351701 132503924 123840160 118485643 116001148 113942287 112821885 [8] 110238416 108582737 106026739 Smallest eigenvalues: [1] 0.9733772 0.9475114 0.9039902 0.8221547 0.7985379 0.7923911 [7] 0.7133250 0.2374300 0.1609382 -0.4256023 Largest eigenvalues: [1] 138658952 133370194 124677304 118205339 117806051 114559949 113596193 [8] 111127738 109909377 107218546 Smallest eigenvalues: [1] 1.1523276 1.0727685 0.9417707 0.8766789 0.8642186 0.6458429 [7] 0.6127939 0.5895132 0.4473188 -0.1236023 Largest eigenvalues: [1] 138442094 131847172 124019996 117443441 117308575 114539258 113032983 [8] 111128537 109470399 107388397 Smallest eigenvalues: [1] 1.1489040 1.1019013 1.0462988 0.9444421 0.8721010 0.7637375 [7] 0.5163876 0.4070077 0.1835515 -0.4694777 Largest eigenvalues: [1] 136736763 131526730 122963932 118254279 115894535 113300732 112543831 [8] 109973278 108793453 105357982 Smallest eigenvalues: [1] 1.1312476 1.0080637 1.0018752 0.9978000 0.9618659 0.7797975 [7] 0.6260164 0.4672589 0.2929586 -0.1255885 Largest eigenvalues: [1] 137588856 132736714 124211896 118623875 117267608 114148667 113529875 [8] 110618015 109372782 106897298 Smallest eigenvalues: [1] 1.0185650 0.9224327 0.8358586 0.7332705 0.7184736 0.5636534 [7] 0.4657152 0.1213703 -0.5094281 -0.6227698 Largest eigenvalues: [1] 138104365 132748751 124292918 118005706 117389329 115911964 113983794 [8] 111844393 109938123 107693840 Smallest eigenvalues: [1] 1.1389064 1.1194827 1.0602250 1.0239757 0.9224550 0.8925552 [7] 0.6883756 0.5754431 0.4100234 -0.6709451 Largest eigenvalues: [1] 135666698 132792273 124242028 118879952 115418687 114117573 113902735 [8] 110496266 109938114 106402326 Smallest eigenvalues: [1] 1.140632608 1.092645038 1.090132805 0.947767067 0.860220262 [6] 0.795300162 0.726303306 0.654235165 0.156476362 -0.009928531 Largest eigenvalues: [1] 136056041 130440720 122097944 117164727 115859815 113418367 112512702 [8] 110316008 108333230 105955024 Smallest eigenvalues: [1] 1.1626412 1.1377907 0.9018100 0.8872660 0.8651979 0.8102843 [7] 0.7785115 0.5679260 0.3282432 -0.3858834 Largest eigenvalues: [1] 134842687 130160538 121970545 116709344 114824686 112854681 111930818 [8] 110049615 107825324 105688420 Smallest eigenvalues: [1] 0.9467027 0.9344285 0.9128206 0.8793134 0.8229584 0.7172003 [7] 0.4629851 0.4395434 0.3896888 -0.2694351 Largest eigenvalues: [1] 134584027 130636848 121809879 116876073 116032135 112804070 112179017 [8] 109622442 108012773 105233956 Smallest eigenvalues: [1] 0.9920661 0.9556303 0.9429426 0.9273824 0.8202346 0.6476825 [7] 0.6057444 0.5363126 0.5177233 -0.4422573 Largest eigenvalues: [1] 135231824 131932056 124450265 118474375 115744029 114244324 113792893 [8] 110906920 109500186 106756262 Smallest eigenvalues: [1] 0.9891930 0.9660190 0.8836175 0.8081286 0.7950407 0.7269758 [7] 0.6339289 0.6085802 0.4587375 -1.0288509 Largest eigenvalues: [1] 136760097 132539224 124927148 118607346 116438162 114816379 114585336 [8] 111446077 110101114 107043899 Smallest eigenvalues: [1] 1.17805466 1.08685419 1.01508059 0.90591219 0.79288098 0.77678451 [7] 0.70242775 0.69695614 0.39463342 -0.08891716 Largest eigenvalues: [1] 136815119 131655007 123290803 118629720 115897039 113336981 113072924 [8] 110238640 109122433 105906429 Smallest eigenvalues: [1] 1.1951818 1.1468847 1.1365253 0.9713300 0.8909258 0.7750622 [7] 0.5643882 0.5238809 0.1732544 -0.3450903 Largest eigenvalues: [1] 134550263 130386870 122775230 117400578 113470701 112950527 111617268 [8] 109187017 108689410 104469553 Smallest eigenvalues: [1] 1.0734417 0.9908388 0.9189598 0.8508919 0.7110209 0.6407004 [7] 0.5944665 0.3382000 -0.1875544 -0.2892285 Largest eigenvalues: [1] 137386476 131938257 124076635 117534570 117226370 113532647 112661568 [8] 110062268 109085950 106456943 Smallest eigenvalues: [1] 1.12448430 1.08428395 1.00088508 0.94199478 0.76755438 0.70106879 [7] 0.61489198 0.59903763 0.30084487 -0.02584492 Largest eigenvalues: [1] 136476153 131443483 123709735 117800125 114850395 113162448 112635437 [8] 109832834 108946491 105662583 Smallest eigenvalues: [1] 1.04972246 1.02070746 0.99070188 0.97510889 0.86771419 0.83804821 [7] 0.69861209 0.69429875 0.33455010 -0.09572964 Largest eigenvalues: [1] 136410923 131233477 122772426 118234786 115965776 114024465 112638416 [8] 110678158 108726545 106627176 Smallest eigenvalues: [1] 0.8870807 0.8350603 0.7537281 0.6871759 0.6801307 0.5319542 [7] 0.5129123 0.4828997 0.2478617 -0.1038163 Largest eigenvalues: [1] 136207429 132987934 123556191 118317096 117194264 114673331 114144973 [8] 110729926 109780598 106688378 Smallest eigenvalues: [1] 1.0451253 1.0198112 0.9709212 0.8929643 0.7286408 0.7119554 [7] 0.6767607 0.3768106 0.2641183 -0.3429396 Largest eigenvalues: [1] 133330612 131423598 123327066 118010895 114919944 113881784 112757857 [8] 109967866 109114314 105773268 Smallest eigenvalues: [1] 1.0251317 0.8462031 0.8286233 0.7594445 0.6191225 0.5088844 [7] 0.3982119 0.3302044 0.0692134 -0.7669854 Largest eigenvalues: [1] 136606330 132169759 123776772 118378432 116438924 114511608 113387366 [8] 111132497 109158997 106186212 Smallest eigenvalues: [1] 1.1159767 1.0990815 0.9757286 0.9481750 0.8609663 0.7677819 [7] 0.6912020 0.6865107 0.5992712 -0.0877039 Largest eigenvalues: [1] 134296836 133342673 124668678 119947870 115297766 114666704 113803740 [8] 110484060 109927542 106125472 Smallest eigenvalues: [1] 1.03136331 0.93132714 0.90225052 0.77323007 0.75986151 0.71989671 [7] 0.59324172 0.40434595 0.09217178 -2.15644924 Largest eigenvalues: [1] 136867281 131260557 123317783 117285307 115639016 113508969 112926740 [8] 110841135 108777015 106256351 Smallest eigenvalues: [1] 1.0973832 1.0241306 0.8782204 0.8405039 0.8163045 0.7780373 [7] 0.7372148 0.6885016 0.5990339 -1.3667574 Largest eigenvalues: [1] 135863194 132574410 124625111 118614630 115902032 114766756 113979118 [8] 111324725 109779369 106905766 Smallest eigenvalues: [1] 1.1230325 1.1047961 1.0752721 1.0207528 0.9992266 0.9191325 [7] 0.7282923 0.6650337 0.3576889 -0.1807112 Largest eigenvalues: [1] 136097531 130810524 122975854 117447009 115846513 113711003 112949949 [8] 110384045 108991892 106356184 Smallest eigenvalues: [1] 1.0288400 1.0095087 1.0057071 0.9747426 0.7791183 0.6868027 [7] 0.5204124 0.4368311 0.1049893 -0.5382668 Largest eigenvalues: [1] 135624526 130367454 122735719 118211509 116205766 113588177 112576700 [8] 110522025 108869951 106633052 Smallest eigenvalues: [1] 1.1674445 1.0240108 0.9640820 0.9590423 0.9284936 0.7813545 [7] 0.6966257 0.5217715 0.3947093 -0.8671934 Largest eigenvalues: [1] 135369181 132618799 123845043 119583023 115134503 114325934 113944121 [8] 110623377 109903829 106508636 Smallest eigenvalues: [1] 1.1984974 1.1748076 1.1406129 1.0869761 1.0421804 0.9440269 [7] 0.8823381 0.8298928 0.5048125 -0.2724884 Largest eigenvalues: [1] 135228843 131001067 123172022 117407262 114724822 113525947 112395265 [8] 110208998 108537676 105991114 Smallest eigenvalues: [1] 1.0884185 1.0326757 1.0155812 0.9271647 0.9078090 0.7644290 [7] 0.7067695 0.5544309 0.4498260 -1.1355492 Largest eigenvalues: [1] 132899651 130426270 122390315 118245434 113329684 112826955 112060763 [8] 109428086 108925104 105054404 Smallest eigenvalues: [1] 0.9516667 0.7914653 0.7638693 0.7460755 0.7175364 0.6906613 [7] 0.5071603 0.4262511 0.2476806 -0.1450733 Largest eigenvalues: [1] 137734421 133570970 125429114 119062996 116812287 114499194 114263514 [8] 111108704 110317877 107440074 Smallest eigenvalues: [1] 0.9721431 0.8012526 0.7359061 0.6706211 0.6601480 0.6252495 [7] 0.5656663 0.3330420 0.2391079 -0.2682998 Largest eigenvalues: [1] 133118204 129246232 121604393 116258335 113453271 112163743 112019736 [8] 109121491 107799092 105220406 Smallest eigenvalues: [1] 1.02299413 0.92619474 0.84507185 0.76140619 0.67339652 0.52095106 [7] 0.48050942 -0.04923667 -0.18329085 -0.91614320 Largest eigenvalues: [1] 137119298 131287858 122838959 117123867 116618885 113575833 112897754 [8] 110709801 108715514 106472629 Smallest eigenvalues: [1] 1.16444102 0.98223638 0.96022756 0.94234237 0.91371043 0.71855750 [7] 0.68984883 0.67665249 0.33828438 -0.08746629 Largest eigenvalues: [1] 134273581 131329145 123293412 117021129 113748904 113271704 112966340 [8] 110752466 108898424 106024281 Smallest eigenvalues: [1] 1.065287179 1.041477481 0.998169554 0.984279234 0.810966236 [6] 0.745708417 0.681727266 0.500262255 0.405207790 -0.005957367 Largest eigenvalues: [1] 138264372 131625221 123165725 117337269 116907042 113579614 112390428 [8] 110393190 108405828 106131073 Smallest eigenvalues: [1] 1.1013091 1.0018530 0.9878088 0.9433219 0.8061246 0.7666738 [7] 0.7503725 0.6898731 0.4191194 -0.4062362 Largest eigenvalues: [1] 136441308 132079017 123904208 118523120 115271083 114449921 113287499 [8] 111230394 109382441 106887599 Smallest eigenvalues: [1] 1.1243010 1.0683696 0.9778119 0.9029492 0.8604403 0.8081882 [7] 0.6770519 0.6295505 0.5576291 -0.1758463 Largest eigenvalues: [1] 135819666 132069852 123502718 118365220 115281534 113303449 113108897 [8] 110011170 108938363 105847620 Smallest eigenvalues: [1] 1.0834586 0.9339904 0.8307919 0.8274291 0.7797233 0.7457566 [7] 0.5526795 0.5526047 0.4070128 -0.1907547 Largest eigenvalues: [1] 135250675 132457856 124310215 118346890 114712484 114271673 113815785 [8] 110824101 109908392 106746116 Smallest eigenvalues: [1] 1.0674725 1.0463354 0.9577353 0.9209438 0.7593151 0.6831467 [7] 0.6489527 0.6238522 0.5595071 -0.8519290 Largest eigenvalues: [1] 136562107 132264080 123935648 118411242 116178752 114770419 113568068 [8] 111479767 109482573 106840688 Smallest eigenvalues: [1] 1.07471232 1.05422917 1.00280112 0.97110287 0.97018141 0.90518340 [7] 0.66409443 0.65071087 0.52992902 -0.03140993 Largest eigenvalues: [1] 135306596 133094840 124395524 119729185 115416436 115151230 114517802 [8] 111544165 110561374 107596312 Smallest eigenvalues: [1] 1.0791689 1.0778712 1.0308044 0.9709707 0.8055795 0.7877484 [7] 0.7823670 0.7549878 0.4521996 -0.6812339 Largest eigenvalues: [1] 134593500 131166176 122401515 118536090 114771480 114034002 112249168 [8] 109633479 109048214 105262744 Smallest eigenvalues: [1] 1.0874851 1.0123813 0.9746583 0.8677117 0.8027323 0.7816284 [7] 0.6702468 0.4923499 0.4519261 -0.9243272 Largest eigenvalues: [1] 135936453 133209744 124683858 118927807 115768401 114494334 113853301 [8] 111043306 110025074 106402378 Smallest eigenvalues: [1] 1.0119422 0.9791951 0.7639759 0.7606874 0.7547262 0.6753445 [7] 0.5382947 0.4630023 0.3518115 -0.9520252 Largest eigenvalues: [1] 134236915 134167652 124681259 119672695 116041916 114981995 113609443 [8] 110399201 109962014 105919794 Smallest eigenvalues: [1] 1.06562058 1.02892398 0.98292482 0.94893836 0.90037480 0.71464507 [7] 0.68182895 0.66333554 0.38184958 -0.06201706 Largest eigenvalues: [1] 133254037 130657142 123120104 117436445 113513428 113253508 112958400 [8] 109736932 109214721 105951445 Smallest eigenvalues: [1] 0.9377315 0.9169039 0.9166504 0.8768386 0.6206026 0.6110003 [7] 0.5853355 0.5578546 -0.1678941 -0.1946190 Largest eigenvalues: [1] 137666164 131122123 123445549 117430348 117286391 115150476 113057360 [8] 111373622 109290998 107618751 Smallest eigenvalues: [1] 0.97662034 0.95050752 0.92040757 0.78450358 0.70894762 0.70374400 [7] 0.50616102 0.50264093 0.20342701 -0.07540777 Largest eigenvalues: [1] 134928976 132132724 123219343 118282508 115533485 114044413 112906917 [8] 110076155 108896279 105332906 Smallest eigenvalues: [1] 1.09686659 0.83797395 0.83724003 0.82588658 0.67891249 0.50850710 [7] 0.49984932 0.34855186 -0.05394257 -0.19309521 Largest eigenvalues: [1] 137751950 130312207 123066953 116733279 115916945 113016498 111273137 [8] 109636828 107737729 105812548
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.668593 | 0.5548134 | 12.21568 | 0.195 | 1.257246 | 1.071169 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + speed + Sex
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
speed = speed_fd)
path_plot <- 'figures/model_HR_alt_speed_Sex_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
Sex = list(nbetabasis = 80, norder = 4, lambda = 1e3))
factors <- list(Sex = participant_info$Sex |> as.factor())
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params,
factors = factors)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |>
substr(4, 9))] |> as.numeric())
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
if(!is.na(factors[1])) {for (fact in names(factors)) {
assign(paste0(fact, '_BS'),
factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |>
as.numeric())}}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
formula_BS <- as.formula(formula_BS)
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 47. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 500 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 1.1781640 1.1346809 1.1146184 0.8654722 0.7578887 0.6003548 [7] 0.5576528 0.5394753 0.4745520 -5.7280285 Largest eigenvalues: [1] 149590000 141780953 134185261 129504683 127893292 124292907 121372067 [8] 119917159 118139682 117320293 Smallest eigenvalues: [1] 1.3187540 1.2534301 1.1642820 1.0235925 0.9119360 0.9064681 [7] 0.7091962 0.5859837 0.4572523 -7.0889327 Largest eigenvalues: [1] 148160290 141296343 133762539 128975099 128516111 124927929 120378765 [8] 119386591 118165962 117240667 Smallest eigenvalues: [1] 1.36405751 1.22228365 1.18786766 1.07988584 1.02677005 0.77947244 [7] 0.77873041 0.68768944 0.49510563 -0.01505912 Largest eigenvalues: [1] 149017513 142560121 134692549 130836886 128841489 124655181 120831532 [8] 120696007 119676855 117503360 Smallest eigenvalues: [1] 1.18460164 1.11650549 1.07755792 0.93144211 0.90962915 0.80811594 [7] 0.57973552 0.55787425 0.48535873 -0.04310089 Largest eigenvalues: [1] 148297472 141175379 132341435 128248523 127778904 124436227 120213673 [8] 118444663 118142425 116617546 Smallest eigenvalues: [1] 1.2945462 1.1691853 1.1622388 0.8758997 0.8595341 0.8106490 [7] 0.7410779 0.7266192 0.4030367 -1.3535300 Largest eigenvalues: [1] 149303155 141302696 133796017 130663810 128202506 124960250 120659543 [8] 119738357 118180862 116318403 Smallest eigenvalues: [1] 1.6624388 1.4599492 1.2697815 1.1601602 0.9192361 0.9029982 [7] 0.8854069 0.8695371 0.7843537 -0.2452722 Largest eigenvalues: [1] 149389330 140579687 133410327 128283290 127854013 123567059 119814335 [8] 119068707 117682411 116096158 Smallest eigenvalues: [1] 1.4054855 1.3187594 0.8976240 0.8742945 0.8008566 0.7547644 [7] 0.6148409 0.3120185 0.2711259 -2.8259375 Largest eigenvalues: [1] 147283928 142656542 133991712 128748635 128378003 125466443 120782776 [8] 118443362 118308851 116891374 Smallest eigenvalues: [1] 1.1107011 0.8671631 0.8482472 0.8185048 0.6363300 0.5259692 [7] 0.4595736 0.3374729 0.3083746 -2.9191520 Largest eigenvalues: [1] 148216997 141543776 133306305 129361066 128307698 124582093 120404402 [8] 119725084 118358360 116461766 Smallest eigenvalues: [1] 1.12287587 0.96214433 0.86950738 0.80735512 0.68341585 0.66271969 [7] 0.47118475 0.44982958 -0.05296173 -2.91914208 Largest eigenvalues: [1] 147946186 143143036 133385140 130553807 129040444 125374886 120971050 [8] 120075677 119105695 117093054 Smallest eigenvalues: [1] 1.5155546 1.3898472 1.3875458 1.2195079 1.0167413 1.0006485 [7] 0.9476630 0.7764376 0.6618371 -2.7221814 Largest eigenvalues: [1] 148749372 142782114 134090142 129119629 128722738 124682308 120093595 [8] 119386462 119071311 117071997 Smallest eigenvalues: [1] 1.2238397 1.1643391 1.0616039 1.0439030 1.0287803 0.7962047 [7] 0.7639633 0.6588083 0.1679842 -2.0741316 Largest eigenvalues: [1] 153070872 140862952 133102113 130030721 127978209 123526345 120866812 [8] 119944728 119558285 117576209
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.265521 | 0.6803457 | 12.40876 | 0 | 0.7130665 | 1.890904 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + steps + Sex
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
steps = steps_fd)
path_plot <- 'figures/model_HR_alt_steps_Sex_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
Sex = list(nbetabasis = 80, norder = 4, lambda = 1e3))
factors <- list(Sex = participant_info$Sex |> as.factor())
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params,
factors = factors)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |>
substr(4, 9))] |> as.numeric())
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
if(!is.na(factors[1])) {for (fact in names(factors)) {
assign(paste0(fact, '_BS'),
factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |>
as.numeric())}}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
formula_BS <- as.formula(formula_BS)
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 39. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 396 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.308018 | 0.7106202 | 11.9561 | 0 | 0.7517159 | 2.119495 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + acc
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 432 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.9739181 0.9070555 0.9044741 0.8227855 0.7871775 0.5797282 [7] 0.5447441 0.5304211 0.1462120 -0.3233728 Largest eigenvalues: [1] 107757898 102082451 95875388 93692545 92991159 90103538 87300144 [8] 87123994 86805321 85850434 Smallest eigenvalues: [1] 0.9600672 0.7639749 0.7222864 0.6831188 0.5820995 0.4457554 [7] 0.4429751 0.4157449 0.3607366 -0.3871306 Largest eigenvalues: [1] 106461459 102714673 96523396 93752390 93550486 90720069 87770294 [8] 87276932 86752277 85605894 Smallest eigenvalues: [1] 1.12144307 1.06242080 0.87649874 0.79347665 0.74439217 0.66350438 [7] 0.60190233 0.55378957 0.51711597 -0.02045023 Largest eigenvalues: [1] 105829349 103394034 97749405 93653001 93095508 91441423 88374627 [8] 88050165 86682215 86102144 Smallest eigenvalues: [1] 0.9973730 0.8630682 0.8204420 0.7664982 0.7029154 0.5189685 [7] 0.5145405 0.5063051 0.2355076 -1.1446937 Largest eigenvalues: [1] 106262500 101803413 96408942 93325711 93038505 90436544 88368260 [8] 87122424 86188854 85614843 Smallest eigenvalues: [1] 0.9380506 0.9057991 0.7974583 0.7854969 0.7488043 0.6271615 [7] 0.6157394 0.5951337 0.4298249 -0.1027140 Largest eigenvalues: [1] 105888788 103182592 97000905 93468480 93316605 91022840 88196838 [8] 87249699 86366499 85750471 Smallest eigenvalues: [1] 0.9959630 0.9587178 0.8511334 0.7057276 0.6709490 0.6441068 [7] 0.5804226 0.5782194 0.2786083 -1.2692560 Largest eigenvalues: [1] 108097038 101658959 96210444 93879148 92044067 89873924 87499400 [8] 87105833 86999861 85447673 Smallest eigenvalues: [1] 1.0602412 0.9374022 0.9279722 0.8926586 0.7895102 0.7717937 [7] 0.7001134 0.5497410 0.4865444 -0.6337533 Largest eigenvalues: [1] 105569136 102515039 96393532 93228582 92611669 90551635 87551044 [8] 87399116 85880860 85533123 Smallest eigenvalues: [1] 1.0522998 0.9887746 0.9156795 0.8701023 0.8261606 0.7990901 [7] 0.7593079 0.7167662 0.3340540 -0.5894481 Largest eigenvalues: [1] 107082135 102200653 96209165 93509252 92524823 90588967 87853406 [8] 87276167 86071986 85207164 Smallest eigenvalues: [1] 0.9342266 0.9163383 0.7692761 0.6682715 0.6471987 0.5963400 [7] 0.5617708 0.4187039 0.1625168 -0.2475219 Largest eigenvalues: [1] 106501411 101930061 95686593 93077685 92859929 90129501 87533204 [8] 86946163 85672585 85317158 Smallest eigenvalues: [1] 0.9954587 0.9656373 0.8385163 0.8183769 0.7468686 0.6036963 [7] 0.5662285 0.4359675 0.4074427 -0.1552247 Largest eigenvalues: [1] 107088196 99984352 95383721 92982159 91605599 89076474 86263273 [8] 86181958 85876111 84957046 Smallest eigenvalues: [1] 0.7824925 0.7510949 0.6095060 0.5779382 0.5731246 0.5522463 [7] 0.4849424 0.4824695 0.1987788 -0.6091327 Largest eigenvalues: [1] 106546940 102558831 96903721 93204445 92896778 90696179 88422239 [8] 87555852 86250195 85709403 Smallest eigenvalues: [1] 0.93256259 0.78722467 0.74130118 0.73611676 0.69867149 0.58071432 [7] 0.58037770 0.33130211 0.27698438 -0.08817705 Largest eigenvalues: [1] 105273231 101492058 96093008 93039779 92595070 90284383 87895010 [8] 87259920 86134106 85754897 Smallest eigenvalues: [1] 1.0254990 0.9100123 0.8884040 0.8660469 0.8539111 0.6463336 [7] 0.5813533 0.4988011 0.2079018 -1.3079552 Largest eigenvalues: [1] 107247314 101561558 96239419 93415521 92490345 90227034 87886485 [8] 86957699 86542579 85578622 Smallest eigenvalues: [1] 0.8154282 0.7877572 0.6802313 0.6671185 0.5109802 0.4850972 [7] 0.4836900 0.4629582 0.3260486 -0.7163060 Largest eigenvalues: [1] 108469806 103343989 96547874 94687313 93766980 90407563 87987230 [8] 87847784 87623981 86167216 Smallest eigenvalues: [1] 0.9456455 0.8984036 0.8866654 0.8832891 0.6631040 0.6600169 [7] 0.5796109 0.5008270 0.2935479 -0.6530128 Largest eigenvalues: [1] 109676154 102844716 96957559 94695928 93532279 90818974 88235819 [8] 87967576 87890004 86409684 Smallest eigenvalues: [1] 1.0483063 0.8318142 0.8043516 0.7301932 0.7110074 0.6254776 [7] 0.5638472 0.3718597 0.3240146 -0.1978363 Largest eigenvalues: [1] 105316952 102459779 96476288 92681962 92509315 90220461 87594586 [8] 86441673 85771783 84897398 Smallest eigenvalues: [1] 1.09141225 1.07669232 1.01665677 0.95552947 0.88231725 0.87835712 [7] 0.67359767 0.63757596 0.60719812 -0.01507027 Largest eigenvalues: [1] 106739727 102068652 96163577 93570663 92969149 90671731 87256747 [8] 87163185 86163665 85607077 Smallest eigenvalues: [1] 1.1193088 1.1184372 1.0164019 0.8572574 0.8291404 0.7187604 [7] 0.6574832 0.6528185 0.5952092 -0.4579073 Largest eigenvalues: [1] 106539673 102642731 96460135 93646440 93437770 90865029 87464845 [8] 87428334 86687024 85779571 Smallest eigenvalues: [1] 1.0188610 0.7415235 0.7170481 0.6089356 0.5346981 0.4727927 [7] 0.3380275 0.2920763 -0.1335225 -0.8869777 Largest eigenvalues: [1] 106558703 100221025 95320206 92834115 91450142 88326528 87130785 [8] 86452796 86020181 85313657 Smallest eigenvalues: [1] 1.1361328 1.0545885 0.9298457 0.8439620 0.6850588 0.6830385 [7] 0.5856037 0.5693867 0.4086119 -0.5385280 Largest eigenvalues: [1] 107256592 101498566 96535298 94008026 92603884 90202423 87387895 [8] 87069620 86620373 85870043 Smallest eigenvalues: [1] 0.6890101 0.6524320 0.6485062 0.5782830 0.5497101 0.3645368 [7] 0.3133968 0.2086596 -0.2817090 -1.9828159 Largest eigenvalues: [1] 108480312 100853582 96589590 93113610 92255329 89341376 87134928 [8] 86562125 86355509 85727803 Smallest eigenvalues: [1] 1.0955902 1.0409376 0.9183825 0.8478418 0.7498295 0.6879591 [7] 0.5251165 0.5117385 0.3928066 -0.2432927 Largest eigenvalues: [1] 105371754 100416913 95027949 92137122 92118418 89287405 86990511 [8] 86118875 85278386 84780001 Smallest eigenvalues: [1] 0.8654643 0.8501803 0.6557305 0.5953598 0.5876937 0.5624438 [7] 0.3403873 0.3399493 0.2272461 -0.2142548 Largest eigenvalues: [1] 108756210 102682611 97522858 95741999 93430264 90957393 88257961 [8] 88173520 87932791 86326087 Smallest eigenvalues: [1] 0.9306975 0.8753051 0.7986481 0.7878632 0.7436808 0.5883950 [7] 0.5191112 0.2534280 0.1071440 -0.2756760 Largest eigenvalues: [1] 108704297 103010102 97278702 95999986 93890698 91396459 88522334 [8] 88095321 87615291 86411240 Smallest eigenvalues: [1] 1.0399542 0.9155670 0.8671659 0.8337449 0.7370843 0.6036512 [7] 0.5964418 0.5219686 0.2235807 -0.3133140 Largest eigenvalues: [1] 106550292 101841994 96294820 93131214 92786668 90355335 88269321 [8] 86948202 86243817 85548646 Smallest eigenvalues: [1] 1.1321073 1.0896680 1.0208217 0.9838445 0.8353567 0.8005417 [7] 0.7259968 0.6940746 0.5083624 -0.6082429 Largest eigenvalues: [1] 108733158 101307471 96119582 93759244 92736810 89999366 87644581 [8] 87069819 86996291 86205278 Smallest eigenvalues: [1] 0.8549064 0.7923236 0.7761904 0.7292166 0.6752019 0.6499100 [7] 0.5727572 0.5258840 -0.2340326 -0.6195309 Largest eigenvalues: [1] 107800389 102038357 97031044 94184788 92623989 90196274 88117397 [8] 87752913 87406320 86562664 Smallest eigenvalues: [1] 0.84665529 0.79642648 0.66157459 0.59468960 0.59095047 0.44760698 [7] 0.43947429 0.41525945 0.29558469 -0.07780902 Largest eigenvalues: [1] 107486780 102397613 96246139 94955101 92493242 90317269 87811284 [8] 87600492 87218129 85772277 Smallest eigenvalues: [1] 1.0399587 1.0004180 0.7030955 0.6702356 0.6508857 0.6409989 [7] 0.5537590 0.5534124 0.4161613 -0.9415906 Largest eigenvalues: [1] 105226174 101384146 96207126 92667623 91916540 90129115 87578087 [8] 86834390 85760947 85265229 Smallest eigenvalues: [1] 1.0740236 0.9699365 0.9257382 0.8976239 0.8814413 0.8189048 [7] 0.7087698 0.5209375 0.4943526 -0.6475468 Largest eigenvalues: [1] 105432599 101961961 96632200 93200940 92903891 90942382 88527626 [8] 86921735 85813932 85438444 Smallest eigenvalues: [1] 0.9613563 0.8535764 0.8520412 0.8291887 0.7795163 0.6968560 [7] 0.5084520 0.4892364 0.3059006 -0.0407415 Largest eigenvalues: [1] 108389100 101563713 96232884 94956012 92782694 90057687 87408472 [8] 87205428 86912569 85714317 Smallest eigenvalues: [1] 0.9539057 0.9133985 0.8185856 0.6942262 0.6925654 0.4889985 [7] 0.4595531 0.4110463 0.1071997 -0.1582165 Largest eigenvalues: [1] 109272464 102640614 96526103 95468141 93805268 90601919 88419732 [8] 88145744 87126209 86505585 Smallest eigenvalues: [1] 0.8484347 0.6440976 0.6061702 0.5426354 0.5336470 0.4505841 [7] 0.4443875 0.2906917 -0.3276361 -1.4825787 Largest eigenvalues: [1] 108071369 102573761 96562558 94781465 92606132 90093096 87891813 [8] 87851695 86869427 85747906 Smallest eigenvalues: [1] 1.02355361 0.96973626 0.90924679 0.89008064 0.83161944 0.72567351 [7] 0.58141891 0.58048383 0.44611625 -0.08229867 Largest eigenvalues: [1] 106467640 100899267 95673039 93050578 92103650 89236240 87316141 [8] 87098983 86233727 85986087 Smallest eigenvalues: [1] 0.7859443 0.7827471 0.7658371 0.6862303 0.6082995 0.5313227 [7] 0.5001402 0.4797584 0.4562193 -0.8163203 Largest eigenvalues: [1] 106338183 101741941 96582443 92904785 92145666 90014135 86924138 [8] 86333393 86194225 84856749 Smallest eigenvalues: [1] 1.070407878 0.933948588 0.898295072 0.860893853 0.810180977 [6] 0.655686908 0.562261570 0.557175728 0.550095770 -0.001107183 Largest eigenvalues: [1] 106724776 101722385 96206922 93328293 93124718 90456090 87294056 [8] 86751106 86173386 85034085 Smallest eigenvalues: [1] 0.8775099 0.8684947 0.7630967 0.6250612 0.5756749 0.5541340 [7] 0.3185507 0.3141688 0.1140295 -1.1804514 Largest eigenvalues: [1] 105311288 99680273 94926540 91728595 90973605 88726663 86707190 [8] 86238942 85344718 85008989 Smallest eigenvalues: [1] 1.0698727 0.9825964 0.9636048 0.7260857 0.6620844 0.6241240 [7] 0.4912535 0.4525449 0.3955901 -2.3864842 Largest eigenvalues: [1] 105085125 100817852 95057283 92591380 92386877 89547713 87597386 [8] 85899385 85526899 84540699 Smallest eigenvalues: [1] 1.0582997 1.0423215 0.9252621 0.9156458 0.8376192 0.8134114 [7] 0.7389213 0.6342170 0.5806265 -0.6904383 Largest eigenvalues: [1] 106831057 102251934 96516194 93007097 92784583 90216579 87734029 [8] 86941752 86198545 85166290
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.588232 | 0.5394108 | 9.702973 | 0.115 | 0.8661495 | 0.6864926 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + speed
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
speed = speed_fd)
path_plot <- 'figures/model_HR_alt_noise_speed_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e4),
speed = list(nbetabasis = 90, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 39. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 544 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.7617205 0.7477865 0.7148203 0.6362117 0.6162146 0.5815881 [7] 0.4405483 0.4055886 0.3600405 -1.1965898 Largest eigenvalues: [1] 116195483 111748288 104405966 103957144 101468990 98773121 97195470 [8] 96652661 94691486 94210649 Smallest eigenvalues: [1] 1.3277775 1.2388246 1.1172145 0.9280693 0.8347739 0.8189306 [7] 0.7396110 0.5954559 0.4854317 -0.1209143 Largest eigenvalues: [1] 117031665 110973293 105196308 102837568 102040803 99426680 96859116 [8] 96308938 95242173 94478992 Smallest eigenvalues: [1] 1.1823724 1.1108130 1.0793316 0.8427276 0.7413642 0.7232134 [7] 0.6714152 0.6341284 0.4915158 -0.4899471 Largest eigenvalues: [1] 116016852 110373411 104330249 102880584 101093227 98753164 95712715 [8] 95535870 93438738 92535885 Smallest eigenvalues: [1] 1.3060250 1.1933808 1.1234077 0.8447658 0.8172104 0.8119259 [7] 0.7403245 0.6913732 0.4060425 -0.8774854 Largest eigenvalues: [1] 116006302 110127656 104729619 102547274 101106888 98319509 95913736 [8] 95617937 93720703 92832685 Smallest eigenvalues: [1] 1.0454655 1.0143675 0.7880554 0.6915586 0.5744043 0.5365012 [7] 0.4478798 0.4113546 0.3630624 -0.4475338 Largest eigenvalues: [1] 116542938 111400603 105761488 103844782 102185038 99622962 96861277 [8] 96527788 95739488 94112863 Smallest eigenvalues: [1] 1.0071717 0.9666416 0.8214861 0.8111498 0.7295765 0.6971859 [7] 0.5772700 0.4873467 0.4853716 -0.3726666 Largest eigenvalues: [1] 118069780 110500665 105037548 103894359 101778252 98702108 96927996 [8] 96550989 94040509 93565290 Smallest eigenvalues: [1] 1.0008711 0.8523772 0.8399589 0.8079212 0.7063454 0.6960455 [7] 0.6703585 0.5626612 0.5393766 -0.1002940 Largest eigenvalues: [1] 116516685 110204796 104193436 104059149 100961974 98821671 96797762 [8] 95451787 93945153 92469406 Smallest eigenvalues: [1] 1.0112000 0.9618017 0.9064340 0.8582519 0.6792072 0.6680352 [7] 0.6153928 0.5642197 0.5199594 -0.2248893 Largest eigenvalues: [1] 116927792 111808947 104805722 103778860 102053412 99321668 96978883 [8] 96642421 94435142 93401997 Smallest eigenvalues: [1] 0.94540766 0.94382542 0.81604349 0.69587258 0.66378513 0.60491167 [7] 0.59868370 0.56132766 0.19148445 -0.00150778 Largest eigenvalues: [1] 118205206 110717090 105044120 104933350 101210560 98764973 97528989 [8] 95862060 94996876 93353379 Smallest eigenvalues: [1] 1.0273973 1.0232075 0.9348405 0.8387037 0.7966725 0.6588555 [7] 0.6273982 0.6228426 0.4017236 -0.6066088 Largest eigenvalues: [1] 117574604 111401120 104723078 103775184 102040651 99638705 96911850 [8] 96578545 94416633 93560895 Smallest eigenvalues: [1] 1.35408259 1.21672034 1.07850898 1.01682658 0.73816501 0.70915603 [7] 0.59119856 0.58812883 0.54719432 -0.02990621 Largest eigenvalues: [1] 114859831 110649623 104172487 102050223 101168907 98680257 95964751 [8] 94817062 92990487 92530528 Smallest eigenvalues: [1] 1.25613265 1.16853182 1.01505033 1.01502712 0.91905730 0.78134201 [7] 0.77978246 0.63800900 0.58140982 -0.06894696 Largest eigenvalues: [1] 114186660 110262741 104280233 101813294 101443436 98903388 96142401 [8] 95356358 94268113 93270392
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.373718 | 0.760873 | 12.6287 | 0 | 0.8301466 | 2.496647 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + steps
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
steps = steps_fd)
path_plot <- 'figures/model_HR_alt_noise_steps_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 90, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 440 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 1.1183631 1.0176210 0.9297772 0.8452723 0.7416317 0.7239285 [7] 0.6755437 0.6392289 0.4596060 -7.0519949 Largest eigenvalues: [1] 97342625 89767749 85927968 85393823 82761422 80416058 79617758 77874284 [9] 77830476 76648885 Smallest eigenvalues: [1] 0.8210996 0.7967740 0.7775604 0.6622976 0.5964201 0.4700285 [7] 0.3924557 0.3526923 0.2299710 -1.9672223 Largest eigenvalues: [1] 97687654 91789160 86679747 86363060 83441144 81363035 81221010 79222884 [9] 77766615 76801490 Smallest eigenvalues: [1] 0.7809085 0.7613850 0.7280797 0.6448397 0.6044466 0.5885938 [7] 0.3637156 -0.3397471 -0.4689503 -0.9617772 Largest eigenvalues: [1] 94616108 92014319 87189576 84496714 83900342 82116066 79681349 78839727 [9] 78226421 77210041 Smallest eigenvalues: [1] 0.8790409 0.8762651 0.8668854 0.8083423 0.6172791 0.4986781 [7] 0.4639298 0.4487909 0.3879823 -83.8401403 Largest eigenvalues: [1] 95013428 90569749 85918908 84249953 83632789 81235229 79313667 79022815 [9] 77538099 77432421 Smallest eigenvalues: [1] 0.8182690 0.6401740 0.5501843 0.5120892 0.4566674 0.4324881 [7] 0.3822173 0.3785554 0.3085159 -0.2504592 Largest eigenvalues: [1] 96966908 91255816 86770080 85821377 83067470 81559868 80487231 78717159 [9] 77957178 76823548 Smallest eigenvalues: [1] 0.8443321452 0.7014341727 0.5375279694 0.4550888811 0.4201822598 [6] 0.4051580069 0.3375296354 0.1761667111 0.0007127554 -0.0165973187 Largest eigenvalues: [1] 96806438 91300290 86815235 86162579 83218191 81217851 80537921 78963757 [9] 78268287 77282901 Smallest eigenvalues: [1] 0.9823531 0.8947998 0.8728813 0.8447557 0.8135737 0.6899906 [7] 0.6732836 0.5242621 0.4675930 -1.3404609 Largest eigenvalues: [1] 95451019 91570758 86104006 85195379 83155760 80992776 79440481 78670863 [9] 78018942 76633417 Smallest eigenvalues: [1] 1.0390931 0.9529703 0.9339237 0.8237270 0.7792322 0.7282763 [7] 0.6451593 0.5112481 0.3376959 -28.3220241 Largest eigenvalues: [1] 95834393 90947640 85769393 83874098 83688641 81565216 78836824 78824626 [9] 77592514 76924571 Smallest eigenvalues: [1] 1.0335811 0.9599569 0.8353745 0.7895177 0.7619191 0.6985246 [7] 0.6390835 0.5487342 0.3134193 -0.1837513 Largest eigenvalues: [1] 96205870 90409373 85933555 85664122 83076060 80855113 80097453 78266143 [9] 77974082 76646107 Smallest eigenvalues: [1] 0.8848091 0.8357054 0.8175768 0.6723973 0.6027441 0.5282721 [7] 0.4208806 0.3864270 -0.5034857 -1.3005486 Largest eigenvalues: [1] 96600178 90314570 84956974 84778438 83021410 81098185 79706643 77985859 [9] 77523600 76252610 Smallest eigenvalues: [1] 0.9727185 0.8713698 0.8211615 0.8076140 0.7866359 0.5450408 [7] 0.4848952 0.3819790 0.3526645 -0.6073986 Largest eigenvalues: [1] 98159840 91550927 86406960 85948383 83750655 81535491 80511086 79445043 [9] 78057025 76963392 Smallest eigenvalues: [1] 0.7994454 0.7980990 0.7727976 0.7306752 0.6654204 0.5804071 [7] 0.4938032 0.4620601 0.3854601 -5.2689323 Largest eigenvalues: [1] 96236424 89930310 85186737 85037654 82927329 80801786 79964170 78108661 [9] 76365710 75632436 Smallest eigenvalues: [1] 0.9987405 0.8282154 0.7820841 0.7083499 0.7068107 0.6720074 [7] 0.6550574 0.5963241 0.3904962 -26.0125030 Largest eigenvalues: [1] 95897137 90277161 86094230 85415539 83015600 80970027 79298922 78717499 [9] 77342657 76535222 Smallest eigenvalues: [1] 0.9106482 0.8725599 0.8068087 0.7525102 0.6446547 0.5736019 [7] 0.5572219 0.4385993 0.3041376 -0.1036589 Largest eigenvalues: [1] 94785674 89700105 84956515 84689601 81917125 80247314 79217789 77990231 [9] 76801161 76283336 Smallest eigenvalues: [1] 0.8493593 0.7656852 0.7633727 0.6794515 0.6147809 0.5883757 [7] 0.4586596 0.4099439 0.2995486 -0.2556937 Largest eigenvalues: [1] 94698839 89899913 85030277 83892467 82941184 80746361 78672462 77918520 [9] 77092099 76206674 Smallest eigenvalues: [1] 0.7597501 0.7359965 0.6113205 0.5533182 0.4643636 0.4331087 [7] 0.4169669 0.2676231 -1.2904106 -7.4245328 Largest eigenvalues: [1] 96694596 90550331 85791487 85504495 83231538 81174834 80138656 78776778 [9] 77743858 76746502 Smallest eigenvalues: [1] 0.8096768 0.8080229 0.6192397 0.5808576 0.5696829 0.5216424 [7] 0.4242342 0.3107008 0.2545836 -4.0480507 Largest eigenvalues: [1] 97234301 91336989 87023326 86981303 83801467 81663531 80789482 79297968 [9] 78308457 76932022 Smallest eigenvalues: [1] 0.8345835 0.7678830 0.7280397 0.6273266 0.6126059 0.5681748 [7] 0.4992526 0.4169739 0.2130704 -1.1686863 Largest eigenvalues: [1] 97173752 91673607 87080868 86734701 84034652 82325471 81185718 79060794 [9] 78263298 76991975 Smallest eigenvalues: [1] 0.70745480 0.63708534 0.62267342 0.52474762 0.49496496 0.41734368 [7] 0.40898477 0.32801835 0.09583426 -2.29334387 Largest eigenvalues: [1] 92521415 89854653 85216031 82706697 82653520 81250894 78875544 76959270 [9] 76841184 76474316 Smallest eigenvalues: [1] 0.9656954 0.9408413 0.8876182 0.7705218 0.7403162 0.6023363 [7] 0.5968584 0.2868750 0.2190016 -0.2576864 Largest eigenvalues: [1] 97038967 89604736 85449932 85242478 82450162 79980244 79463271 78075041 [9] 76964527 76154970 Smallest eigenvalues: [1] 0.8880987 0.8879066 0.8675313 0.7690868 0.6384597 0.5964105 [7] 0.5667384 0.4505765 0.4454542 -6.3000596 Largest eigenvalues: [1] 97086238 90234362 85995703 85770637 83112879 81081677 81039049 78791957 [9] 77757862 76853844 Smallest eigenvalues: [1] 0.8777975 0.8357658 0.7048800 0.6263099 0.5689071 0.5550204 [7] 0.4405208 0.4316264 0.4193840 -0.1576789 Largest eigenvalues: [1] 96700338 92147228 86839380 86180997 83471622 81246164 80646263 79252846 [9] 78243911 77133471 Smallest eigenvalues: [1] 0.7569901 0.6930407 0.6167104 0.5166723 0.4608167 0.3336871 [7] 0.2862939 0.1773101 -0.2638416 -1.8712947 Largest eigenvalues: [1] 97862004 91019788 86122981 85669038 83412634 81367364 80406622 78584223 [9] 78086890 76877454 Smallest eigenvalues: [1] 1.006842016 0.803337527 0.760850995 0.742796120 0.711957733 [6] 0.682263884 0.532263495 0.398594162 0.001300631 -0.056494873 Largest eigenvalues: [1] 93189303 91116267 85755306 83621079 82556698 81711333 78863027 77549826 [9] 77484557 76886579 Smallest eigenvalues: [1] 0.9254361 0.8677790 0.6952662 0.6213181 0.5171152 0.4233124 [7] 0.4127589 0.3896964 0.3616560 -20.0647939 Largest eigenvalues: [1] 97517421 90887275 86741133 86308801 83738187 81727076 80767522 79247290 [9] 78308366 77071954 Smallest eigenvalues: [1] 0.9221112 0.6273579 0.6017540 0.5419971 0.4840735 0.3566440 [7] 0.3321478 0.3161846 0.2590900 -5.8431321 Largest eigenvalues: [1] 98336627 90609523 86826911 86802791 83156548 80831082 80515045 78748336 [9] 77845632 76744263 Smallest eigenvalues: [1] 1.0152904 0.9485014 0.8074888 0.7356652 0.7132664 0.5698418 [7] 0.5522237 0.5110457 0.3421706 -1.6223099 Largest eigenvalues: [1] 96436714 90775402 86565474 85370198 83043566 80878595 80146647 79007926 [9] 78213492 77122380 Smallest eigenvalues: [1] 0.6262398 0.6030298 0.5897837 0.5417284 0.4639333 0.4227664 [7] 0.3858953 0.1800709 0.1686028 -0.1691043 Largest eigenvalues: [1] 96109951 91196818 85990241 85785450 82846540 81125703 80281543 78891487 [9] 77473128 76810432 Smallest eigenvalues: [1] 0.9225509 0.9007225 0.8430807 0.7667531 0.7384909 0.6761920 [7] 0.6278637 0.4378571 0.4051111 -0.4958256 Largest eigenvalues: [1] 94926675 90415114 85419204 84769461 82684548 80510406 79162966 78518963 [9] 77207221 76592112 Smallest eigenvalues: [1] 0.89785602 0.79423905 0.65984252 0.64846354 0.59898882 0.51796339 [7] 0.44763014 0.32853625 0.23615514 -0.09008767 Largest eigenvalues: [1] 96760475 91025403 85965696 85347750 83328351 81417932 80083727 78734951 [9] 76977323 76886583 Smallest eigenvalues: [1] 0.8579348 0.8448779 0.7492269 0.6510432 0.5938614 0.5244255 [7] 0.4847245 0.4549396 0.2810066 -10.8838739 Largest eigenvalues: [1] 96582844 91841933 86374739 85300909 83113508 81140530 79398771 78749502 [9] 77522302 76396169 Smallest eigenvalues: [1] 0.9813092 0.8430597 0.6818274 0.5987037 0.5922118 0.5200347 [7] 0.4079037 0.3899331 0.3627472 -0.1262698 Largest eigenvalues: [1] 94178693 88700630 84615615 83088373 81502142 79580880 77815670 77771354 [9] 76629914 75973029 Smallest eigenvalues: [1] 0.8986536 0.8660044 0.7985145 0.7141116 0.6439741 0.5981077 [7] 0.4698929 0.4130062 0.1723396 -0.4823159 Largest eigenvalues: [1] 94888908 91178708 85724452 84807081 83789787 81504809 79743807 79626801 [9] 77364800 77146917 Smallest eigenvalues: [1] 0.8245662 0.8212721 0.7058040 0.5876186 0.5287688 0.4516459 [7] 0.3917832 0.3289544 0.3176127 -54.4242583 Largest eigenvalues: [1] 95537133 88814399 84941291 83430609 82419458 80144807 77745157 77230520 [9] 77136002 76392147 Smallest eigenvalues: [1] 0.7935410 0.7711320 0.7223435 0.5948197 0.5520337 0.5169339 [7] 0.5151069 0.3901845 0.3163592 -3.5536421 Largest eigenvalues: [1] 94931478 91268911 85460407 85458955 83142289 81245998 79212731 78801384 [9] 77537339 77066987 Smallest eigenvalues: [1] 0.738303921 0.718467994 0.696675291 0.657685616 0.563580808 [6] 0.449522496 0.374952228 0.258969352 0.186110053 -0.004662431 Largest eigenvalues: [1] 95568795 92218054 87347682 85337592 84414188 82440341 80068791 79232920 [9] 78757811 77819859 Smallest eigenvalues: [1] 0.83487953 0.80007875 0.65175969 0.61502176 0.58914868 0.54243355 [7] 0.50488690 0.22633978 0.16764347 -0.01283282 Largest eigenvalues: [1] 97871149 90012619 86656062 85658486 82504679 80649890 80352807 78139276 [9] 77199974 76007852 Smallest eigenvalues: [1] 0.9063662 0.8437767 0.6882514 0.6507760 0.5958862 0.4931903 [7] 0.4465234 0.4002606 0.2787049 -11.0352552 Largest eigenvalues: [1] 95831899 91329581 86490907 85397769 83382993 81706383 80070057 79095968 [9] 77735560 76838843
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 8.555006 | 0.7180601 | 11.37672 | 0 | 0.9351964 | 2.043492 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + acc + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 642 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.3572400 0.3241591 0.3175724 0.2539564 0.2211844 0.1429275 [7] 0.1386985 -0.1192288 -0.1583929 -4.0563352 Largest eigenvalues: [1] 64057025 60144807 57579659 55680452 55075247 53420479 52147618 51727274 [9] 51700094 51150786 Smallest eigenvalues: [1] 0.20815480 0.19527708 0.13001476 0.07394004 0.05268478 -0.02520543 [7] -0.03022643 -0.04639147 -0.18712336 -2.86933727 Largest eigenvalues: [1] 63362686 61063658 57705778 55877424 55340792 53945203 52744004 52432708 [9] 51874744 51619834 Smallest eigenvalues: [1] 0.320485037 0.308484457 0.294083995 0.287061731 0.236586395 [6] 0.161861584 0.032725122 -0.005492232 -0.144953778 -0.522917077 Largest eigenvalues: [1] 64171547 61147712 58395964 55891118 55767221 54364253 53237999 52349784 [9] 52116894 51922555 Smallest eigenvalues: [1] 0.4918629799 0.4834773366 0.4230672504 0.3498649743 0.3391757226 [6] 0.2622011103 0.2493391868 0.0006027109 -0.0047136550 -0.0656738895 Largest eigenvalues: [1] 61992275 60517246 57617107 55854646 54975045 54089904 52470477 52433817 [9] 51229294 51014200 Smallest eigenvalues: [1] 0.3364004 0.3289831 0.2962855 0.2262138 0.2071379 0.1997672 [7] 0.1718978 0.1221774 -0.3798499 -2.5629421 Largest eigenvalues: [1] 65213933 59900563 57366967 56070586 54801621 53236418 52165572 52027160 [9] 51510823 51178965 Smallest eigenvalues: [1] 0.43960886 0.40739004 0.38036940 0.29119135 0.28331892 0.15010614 [7] 0.04677086 -0.03605983 -0.10474583 -0.32354130 Largest eigenvalues: [1] 64395757 60692182 57313959 56079725 55705692 53907634 52786711 52051200 [9] 51774711 51464929 Smallest eigenvalues: [1] 0.2763762 0.2154392 0.1824499 0.1802923 0.1437914 0.1125075 [7] -0.2037908 -0.2308594 -0.3786692 -0.4594503 Largest eigenvalues: [1] 65043228 61026199 57678547 56174052 55510518 53897637 52985881 52156865 [9] 52064095 51786866 Smallest eigenvalues: [1] 0.35130208 0.32195043 0.25929832 0.21560677 0.19993165 -0.06684521 [7] -0.12772567 -0.30386030 -0.42230894 -0.56429931 Largest eigenvalues: [1] 64887832 59884269 56538136 56494640 54526093 52725113 52491518 52190857 [9] 51718398 51256374 Smallest eigenvalues: [1] 0.50100352 0.43554188 0.41233819 0.30676249 0.28168009 0.23034198 [7] 0.20108541 0.07812386 -0.00289683 -0.14461111 Largest eigenvalues: [1] 63905801 59824571 57232425 55822166 54696749 53191030 52245752 51787068 [9] 51659209 51048402 Smallest eigenvalues: [1] 0.38226613 0.36936228 0.36840363 0.34104063 0.22871764 0.22722070 [7] 0.21700001 0.13023772 0.07185889 -0.01500420 Largest eigenvalues: [1] 64551889 60467163 58052828 55668533 55378222 54135552 52760185 52159002 [9] 51911737 51745547 Smallest eigenvalues: [1] 0.44454890 0.39600696 0.35937368 0.33392174 0.20398786 0.06862949 [7] -0.43067560 -0.45885425 -1.07110227 -3.59165125 Largest eigenvalues: [1] 64721302 60074629 57264269 55818235 55237105 53021585 52213272 51976403 [9] 51734457 51260959 Smallest eigenvalues: [1] 0.36073040 0.32762768 0.32553822 0.28244905 0.27152783 0.17385777 [7] 0.12877348 0.02402656 -0.26864776 -1.67871407 Largest eigenvalues: [1] 63336801 59899788 57139555 55231761 54844198 53644892 52169184 52061273 [9] 51363479 51023299 Smallest eigenvalues: [1] 0.38919150 0.38198269 0.35993389 0.27814312 0.27361771 0.21880853 [7] 0.21064366 -0.04733215 -0.22615366 -1.18213899 Largest eigenvalues: [1] 64876586 59738225 57167871 56545952 54793387 53322920 52552913 52191143 [9] 51496041 50778932 Smallest eigenvalues: [1] 0.56599589 0.51522001 0.49716308 0.42173562 0.37622006 0.37414837 [7] 0.26249298 0.21907298 0.15529848 -0.01614275 Largest eigenvalues: [1] 65044260 59528686 56804412 55982911 54935764 53289992 52171507 51972175 [9] 51898375 51231592 Smallest eigenvalues: [1] 0.48076328 0.38622990 0.37523225 0.32448140 0.23316474 0.21960765 [7] 0.14829284 0.09201754 -0.09826087 -0.11605853 Largest eigenvalues: [1] 66301320 59326859 57246433 56655941 54051276 53267548 52561339 51334121 [9] 51137182 50525665 Smallest eigenvalues: [1] 0.5181210 0.5010810 0.4883916 0.4406659 0.4190410 0.3673086 [7] 0.2696495 0.1548473 -0.1228540 -0.2300485 Largest eigenvalues: [1] 63366952 60111230 56810156 55261569 55002375 53483030 52025304 51386874 [9] 50856721 50536505 Smallest eigenvalues: [1] 0.3934942 0.2690784 0.2653280 0.2518613 0.2162878 0.1790993 [7] 0.1593644 0.1175771 -0.1392969 -0.5375719 Largest eigenvalues: [1] 66530749 60558415 57877572 57276985 55065660 53399490 53207130 52953137 [9] 51671805 51516286 Smallest eigenvalues: [1] 0.47095992 0.41151151 0.39009730 0.23555497 0.22889025 0.12739543 [7] 0.11521296 0.08318608 0.06435559 -0.78822906 Largest eigenvalues: [1] 65784661 60536220 56993951 56779371 55145628 53496493 52748314 52261602 [9] 52051702 51288186 Smallest eigenvalues: [1] 0.49795664 0.49293705 0.46341960 0.39675058 0.34727816 0.27428560 [7] 0.16133323 0.02520763 -0.08061078 -0.67548394 Largest eigenvalues: [1] 63446078 59919192 57098632 55394866 54909682 53829454 52461465 51827299 [9] 51013573 50912857 Smallest eigenvalues: [1] 0.4059169 0.3553364 0.3515291 0.3078905 0.2967307 0.2566029 [7] 0.2360790 0.1652289 0.1104114 -0.0558672 Largest eigenvalues: [1] 64299467 61503460 58102473 56629090 55669088 54037930 52798274 52541105 [9] 52485403 51789855 Smallest eigenvalues: [1] 0.4460437 0.4370955 0.3816666 0.3473450 0.3281377 0.3055509 [7] 0.2611311 0.2450317 0.1088500 -0.1154320 Largest eigenvalues: [1] 64841249 61117481 58031276 56429263 56429118 54727577 53077512 52603011 [9] 52328076 51720325 Smallest eigenvalues: [1] 0.29172716 0.26705452 0.16475462 0.11652670 0.09431992 0.01559144 [7] -0.10874491 -0.10925043 -0.44551949 -1.44650426 Largest eigenvalues: [1] 64767110 60244226 57025007 55944094 54913161 53357316 52009406 51944806 [9] 51579422 50906645 Smallest eigenvalues: [1] 0.36347944 0.29839340 0.29050353 0.27232831 0.27195074 0.24277733 [7] 0.19766683 0.09278354 -0.46095206 -0.47329183 Largest eigenvalues: [1] 63926626 59805241 57282049 55213482 54470430 53013311 51953515 51381162 [9] 51152429 51105799 Smallest eigenvalues: [1] 0.33389114 0.28761147 0.25725293 0.24741809 0.23223098 0.21213310 [7] 0.20080965 0.08105087 -0.15044906 -0.24208737 Largest eigenvalues: [1] 65795003 60475623 57891783 56764538 55158152 53459724 53025740 52786711 [9] 52031389 51942040 Smallest eigenvalues: [1] 0.4327472 0.3712711 0.3592195 0.3255310 0.2916081 0.2505628 [7] 0.1975630 0.1294015 0.1226310 -1.0956320 Largest eigenvalues: [1] 65018324 59900371 57227164 56061496 55095751 53287288 52129538 52095714 [9] 51571133 51184690 Smallest eigenvalues: [1] 0.49976091 0.44936337 0.35862225 0.35276438 0.34221020 0.29944621 [7] 0.27312165 0.15231482 -0.06882362 -0.99085301 Largest eigenvalues: [1] 63552092 59153520 57013572 55547625 54473665 52932118 51610368 51507431 [9] 51463963 50580109 Smallest eigenvalues: [1] 0.44000755 0.39221958 0.32075230 0.31369847 0.26194793 0.21126722 [7] -0.04150861 -0.04166315 -0.04180957 -0.26528260 Largest eigenvalues: [1] 61138081 59059968 56149375 54859398 54134902 52952757 51834903 50853739 [9] 50135535 49964435 Smallest eigenvalues: [1] -0.2384820 -0.3236995 -0.3343005 -0.3601049 -0.4290560 -0.5295021 [7] -0.5546944 -0.9277185 -1.1302971 -1.2198926 Largest eigenvalues: [1] 64898588 61095112 58239056 55669635 55579062 54249523 52480127 52006758 [9] 51696025 51445370 Smallest eigenvalues: [1] 0.284032075 0.269374108 0.243847802 0.228442778 0.185862668 [6] 0.037836381 0.008364788 -0.257175665 -0.420003497 -0.881523873 Largest eigenvalues: [1] 64854170 61072067 57743302 56639843 55610572 54015814 52784207 52606800 [9] 52385667 51809985 Smallest eigenvalues: [1] 0.39745675 0.30378715 0.28698407 0.26038800 0.21561967 0.12034930 [7] 0.09870136 -0.08735814 -1.11663102 -1.26942154 Largest eigenvalues: [1] 64523575 60174634 56672842 56286533 55328894 53334607 52575618 52264961 [9] 52213394 51231045 Smallest eigenvalues: [1] 0.465164853 0.381467739 0.338419493 0.285814524 0.255618713 [6] 0.189508223 0.141939371 -0.007267245 -0.668396315 -1.002118380 Largest eigenvalues: [1] 64041823 58837004 56494584 55832043 54013667 52296979 51760999 51300462 [9] 51038577 49991980 Smallest eigenvalues: [1] 0.42135977 0.33064526 0.24581927 0.22783270 0.22315299 0.19639218 [7] 0.17289158 0.12267540 0.04686315 -5.31312804 Largest eigenvalues: [1] 61838534 59832243 56893230 55076043 54672635 53480740 52126963 51470915 [9] 50730290 50528299 Smallest eigenvalues: [1] 0.28167814 0.22157573 0.21288895 0.19779428 0.07514761 0.05132728 [7] -0.11726279 -0.18719471 -1.32155859 -2.87728671 Largest eigenvalues: [1] 66521296 60602632 57417818 56450468 55360607 53713243 52566459 52437993 [9] 51819287 51677782 Smallest eigenvalues: [1] 0.43084282 0.36104450 0.34359855 0.34209815 0.26088381 0.24825747 [7] 0.22729943 0.19323460 0.06281628 -0.05721952 Largest eigenvalues: [1] 64606593 60791818 58246345 55827890 55634400 54284458 52799172 52472818 [9] 51810122 51555398 Smallest eigenvalues: [1] 0.31737948 0.29517252 0.28227197 0.22005093 0.21848316 0.17054747 [7] 0.09857276 -0.16891386 -0.20307817 -2.19901137 Largest eigenvalues: [1] 65092502 60587247 57765907 55910841 55845101 54172541 52449565 52256703 [9] 52217606 51368550 Smallest eigenvalues: [1] 0.38163167 0.37451189 0.29926363 0.28470765 0.20351932 0.09792982 [7] 0.04525726 -0.12321008 -0.19859943 -1.45050876 Largest eigenvalues: [1] 63906345 59932378 57057508 55237595 55061015 53491821 52205040 51514534 [9] 51373076 51216214 Smallest eigenvalues: [1] 0.46659129 0.38597616 0.35789100 0.32751038 0.32706560 0.31221075 [7] 0.25349908 0.01068126 -0.01013948 -0.07940873 Largest eigenvalues: [1] 65265428 60401834 57500936 56436683 54876402 53095347 52565577 52149870 [9] 51327532 50910693 Smallest eigenvalues: [1] 0.37669338 0.36404481 0.34189170 0.26190141 0.24874713 0.20737541 [7] 0.05400449 -0.02976017 -0.09473307 -2.55934522 Largest eigenvalues: [1] 63181444 59833074 56975787 55162188 55000313 53385834 51720296 51676789 [9] 51154527 50900452 Smallest eigenvalues: [1] 0.49248639 0.40960297 0.38621108 0.36023736 0.25673056 0.21464356 [7] 0.19234884 0.12075105 0.04248594 -0.74549449 Largest eigenvalues: [1] 65248302 59959049 57181583 57138421 54533561 53101756 52865862 52025574 [9] 51921307 51080228 Smallest eigenvalues: [1] 0.39334122 0.33047064 0.32629501 0.19379635 0.16812416 0.13090414 [7] -0.05477706 -0.18408445 -0.58098414 -0.73843717 Largest eigenvalues: [1] 65099505 61015316 58085042 56802595 55375841 53431849 53031496 52679607 [9] 51855798 51724354 Smallest eigenvalues: [1] 0.30548339 0.24554368 0.23642478 0.15987535 0.12703925 0.09378831 [7] -0.01922214 -0.04353630 -0.76229442 -0.80612734 Largest eigenvalues: [1] 64876948 60619630 58099614 56431443 55108354 53540208 52736423 52490566 [9] 52120586 51811918 Smallest eigenvalues: [1] 0.32426554 0.28197256 0.27470200 0.22563615 0.14239162 0.02433923 [7] -0.10797768 -0.37291393 -0.37486837 -1.13147897 Largest eigenvalues: [1] 64183660 59619217 56887479 54899471 54800085 53098550 51321536 51264428 [9] 51136247 50515792 Smallest eigenvalues: [1] 0.40126316 0.25364061 0.22030842 0.21609708 0.17124851 -0.02436149 [7] -0.03301147 -0.03839447 -0.14124017 -1.71023636 Largest eigenvalues: [1] 63345061 59846669 56972690 55212679 54762249 53165915 51686538 51499515 [9] 51314190 50892958 Smallest eigenvalues: [1] 0.5420560 0.5337247 0.4513997 0.4431111 0.4387204 0.3984351 [7] 0.3288936 0.3042720 0.2969365 -0.1362922 Largest eigenvalues: [1] 64190092 60453721 57603505 55851775 55388324 53681934 51747159 51708031 [9] 51587499 50661375 Smallest eigenvalues: [1] 0.55073374 0.54297222 0.51082963 0.41523274 0.37805263 0.34798850 [7] 0.21287291 0.10695564 0.02502659 -0.30731463 Largest eigenvalues: [1] 62155485 59563751 56678418 55281099 54357100 53446897 51731277 51612997 [9] 50474959 50330190 Smallest eigenvalues: [1] 0.45152808 0.34221015 0.30429844 0.20070174 0.14375819 0.13941621 [7] 0.08835044 0.07877502 -0.05718764 -1.53016412 Largest eigenvalues: [1] 63522551 59582375 56789777 55303776 55069116 53402280 52399364 51864767 [9] 51457574 51231107 Smallest eigenvalues: [1] 0.5290067 0.5073476 0.4420684 0.3898846 0.3662684 0.3397274 [7] 0.3302179 0.2940417 0.2693324 -0.3899703 Largest eigenvalues: [1] 63840064 59665589 57254705 55531452 54728658 52972436 51716648 51544130 [9] 51094943 50413086 Smallest eigenvalues: [1] 0.38186404 0.31882138 0.28269268 0.26221908 0.20873195 0.15620325 [7] -0.02502617 -0.30825898 -0.31270897 -1.12140298 Largest eigenvalues: [1] 64256357 60086955 57105046 56034737 55098977 53576186 52434184 51980495 [9] 51940992 51457099 Smallest eigenvalues: [1] 0.39110953 0.34511263 0.31179453 0.27568164 0.22779465 0.19631693 [7] 0.19355203 0.04445829 -0.11891403 -0.22965545 Largest eigenvalues: [1] 64839947 61068909 58364751 56124469 55809464 54409762 52478759 52320824 [9] 52033838 51550025 Smallest eigenvalues: [1] 0.35694152 0.34963105 0.34781769 0.31988503 0.31902393 0.28779090 [7] 0.22480478 0.01865781 -0.21348169 -0.30714021 Largest eigenvalues: [1] 65504655 60510141 57714234 56596733 55246141 53717935 52512222 52195935 [9] 52006730 51271604 Smallest eigenvalues: [1] 0.4909675452 0.4701221131 0.4694390051 0.3028352919 0.2452801542 [6] 0.2434072671 0.2156807159 0.1587221503 0.1034061497 -0.0001388593 Largest eigenvalues: [1] 62734711 59648912 56895573 55276388 54848491 53646421 52111196 52070200 [9] 51026420 50847040 Smallest eigenvalues: [1] 0.48689541 0.48576490 0.42829449 0.42401995 0.34528136 0.34205796 [7] 0.28160503 0.25025727 0.22272704 -0.02304821 Largest eigenvalues: [1] 65413861 60757798 57982157 56637338 56053608 54461964 52624305 52393563 [9] 52307239 51374075 Smallest eigenvalues: [1] 0.3527634 0.3377088 0.2587051 0.2288362 0.2127325 0.1806885 [7] 0.1418255 -0.5672442 -0.7168194 -0.8473275 Largest eigenvalues: [1] 66350945 60730408 57995685 57153080 55114805 53539171 53286408 52343010 [9] 51910982 51533345 Smallest eigenvalues: [1] 0.339633151 0.310616532 0.291608181 0.277225532 0.252504765 [6] 0.169082446 0.162774847 0.001912881 -0.319071006 -0.434709805 Largest eigenvalues: [1] 63904353 60530472 57176519 55799468 55759682 54076998 52933246 52229310 [9] 51972024 51712235 Smallest eigenvalues: [1] 0.46803290 0.40007338 0.39735059 0.38421421 0.28975389 0.25730761 [7] 0.23455695 0.20195783 0.06326498 -0.10195046 Largest eigenvalues: [1] 64926444 59584366 57024175 56457057 54213155 52691044 52451666 51421785 [9] 51182888 50350749 Smallest eigenvalues: [1] 0.489624709 0.476595477 0.442252616 0.426693886 0.366338445 [6] 0.304354167 0.286983162 0.071696970 -0.009922337 -0.447757310 Largest eigenvalues: [1] 65282066 60214595 57649067 56349320 55503948 53486895 52614501 52116710 [9] 51764200 51074615 Smallest eigenvalues: [1] 0.26667410 0.26436845 0.22151618 0.19676606 0.16215809 0.03159199 [7] -0.14277823 -0.42581091 -0.60823173 -5.49263649 Largest eigenvalues: [1] 66280509 60867634 57250468 57233839 55635451 53794764 53255816 52423911 [9] 52234572 51477171 Smallest eigenvalues: [1] 0.28709078 0.20331330 0.20177601 0.12799313 0.07467996 -0.13078776 [7] -0.28376289 -0.37779122 -1.02675664 -1.90156009 Largest eigenvalues: [1] 64433506 60553778 57915879 56646316 55549939 53877112 52605303 52435448 [9] 52267266 51276730 Smallest eigenvalues: [1] 0.16609193 0.09717454 -0.02646772 -0.07053619 -0.20321858 -0.27499109 [7] -0.60901198 -1.23618886 -1.32677766 -1.47023854 Largest eigenvalues: [1] 66253058 60130437 57946127 55909172 54888313 53086936 52370053 51736024 [9] 51309271 50971911 Smallest eigenvalues: [1] 0.46975502 0.43519165 0.37942305 0.36708858 0.27975748 0.23585324 [7] 0.19380726 0.15939322 0.05698807 -0.11427379 Largest eigenvalues: [1] 65529438 61280097 58090169 56867114 55920524 54308978 53501979 52863928 [9] 52407450 52105472 Smallest eigenvalues: [1] 0.30493520 0.30361421 0.25118172 0.23662969 0.18855208 0.13848131 [7] 0.12401362 0.02835327 -0.79716026 -2.16432190 Largest eigenvalues: [1] 63520605 59810322 56988333 55559966 54828332 53227450 51975931 51770147 [9] 51535491 50967707 Smallest eigenvalues: [1] 0.30810328 0.29251766 0.28242599 0.25433050 0.24175884 0.21017416 [7] 0.13656731 0.09620963 -0.05430687 -4.88009646 Largest eigenvalues: [1] 63371756 60622385 57209715 55854883 54924041 53937623 51970148 51808118 [9] 51042825 50743218 Smallest eigenvalues: [1] 0.32692241 0.29829005 0.27990019 0.20355077 0.17774474 0.12937465 [7] 0.12499896 0.09147319 -0.02837267 -1.63256340 Largest eigenvalues: [1] 65896751 60994812 58298313 56665523 55690281 54023518 53070445 52622140 [9] 52504727 52218025 Smallest eigenvalues: [1] 0.29123360 0.25552098 0.24744107 0.18772308 0.14368051 0.13594990 [7] 0.08102463 -0.01648910 -1.26516585 -1.66643920 Largest eigenvalues: [1] 66363864 60452546 57785218 56830800 55104627 53950293 52662443 52521438 [9] 52403732 51841080 Smallest eigenvalues: [1] 0.3176570 0.2599552 0.2206302 0.1857760 0.1767845 0.1608564 [7] -0.1829376 -0.2739934 -0.3076590 -0.9759104 Largest eigenvalues: [1] 66225723 59997228 57408594 56895546 54695757 53083737 52883697 52487458 [9] 51680595 51629488 Smallest eigenvalues: [1] 0.28363349 0.21716033 0.17639894 0.14059422 0.08211850 -0.02726647 [7] -0.07456445 -0.45684450 -0.46106893 -0.66625631 Largest eigenvalues: [1] 63988847 60206749 57672892 55438938 54789217 53584650 51631636 51550552 [9] 51538830 50952331 Smallest eigenvalues: [1] 0.42425696 0.38013073 0.37781261 0.32415938 0.23073376 0.22262037 [7] 0.15176636 0.08159191 0.08022446 -0.18023148 Largest eigenvalues: [1] 64625430 60376646 57509574 56341473 55326289 53849102 52404494 52394558 [9] 52196673 51321110 Smallest eigenvalues: [1] 0.5191467 0.4686153 0.4516688 0.3730825 0.3441009 0.3229599 [7] 0.3111210 0.1283469 0.1048464 -0.1217506 Largest eigenvalues: [1] 64787356 59680482 57150602 55766186 54922128 53520921 51937823 51870435 [9] 51333616 50441071 Smallest eigenvalues: [1] 0.37900607 0.37579912 0.27173130 0.21796658 0.19640719 -0.01881112 [7] -0.02828844 -0.05670632 -0.06603805 -1.09931498 Largest eigenvalues: [1] 64317344 60501775 57312053 55711535 55517062 53842750 52919276 52012859 [9] 51925415 51669765 Smallest eigenvalues: [1] 0.50712127 0.48934228 0.45347655 0.41772840 0.31821041 0.31608375 [7] 0.25888299 0.21728037 0.21681046 -0.05002221 Largest eigenvalues: [1] 64251988 59601604 57278581 55460939 54652246 53099431 51707945 51415652 [9] 51329183 50664169 Smallest eigenvalues: [1] 0.3815020 0.3807990 0.3111092 0.2517962 0.2453625 0.2000132 [7] 0.1690091 -0.3948289 -0.6721841 -1.5067667 Largest eigenvalues: [1] 62652338 59239403 56794264 55101152 54862422 53183050 51910360 51763619 [9] 50959454 50629579 Smallest eigenvalues: [1] 0.60482897 0.59706653 0.55296030 0.44912071 0.40053895 0.35550987 [7] 0.28081158 0.22796525 0.13531928 -0.01172452 Largest eigenvalues: [1] 62827970 60198068 57100827 55800015 54823978 54143832 52473105 52220781 [9] 51084783 50859672 Smallest eigenvalues: [1] 0.28537640 0.27041960 0.25421609 0.25285332 0.21962138 0.14971529 [7] 0.04060564 -0.64100655 -0.89371618 -1.60482220 Largest eigenvalues: [1] 64845499 60310134 57853417 56182016 55183337 53355559 52475901 52174561 [9] 52123980 51625946 Smallest eigenvalues: [1] 0.4340012 0.3854872 0.3431338 0.3090682 0.2976295 0.1498647 [7] 0.1238922 0.1113390 -0.1564700 -1.0322496 Largest eigenvalues: [1] 65537564 60563339 57489206 56242934 55155758 53406753 52397355 52341330 [9] 51946283 51357532 Smallest eigenvalues: [1] 0.05972360 0.05200599 -0.04472271 -0.16168531 -0.16186883 -0.24938951 [7] -0.37060917 -0.50403192 -0.69908135 -1.45177859 Largest eigenvalues: [1] 63057342 59950075 57158487 55183252 54773629 53154759 52203185 51393303 [9] 51172907 50947017 Smallest eigenvalues: [1] 0.45780726 0.41737971 0.39189471 0.34565040 0.33201705 0.32925516 [7] 0.27582942 0.26857818 0.22532502 -0.02481878 Largest eigenvalues: [1] 61730421 59149979 56795635 54872641 54315883 53110801 51467664 51098763 [9] 50403432 50107821 Smallest eigenvalues: [1] 0.3833729 0.2971821 0.2509440 0.2385454 0.2273118 0.1989267 [7] 0.1780260 0.1460718 -0.1974149 -0.2472994 Largest eigenvalues: [1] 64559982 60233243 57646543 56378330 54917363 53389939 52527544 51636354 [9] 51499126 50476047 Smallest eigenvalues: [1] 0.3646963 0.3595078 0.3072282 0.2735260 0.2448138 0.2367198 [7] 0.1456193 0.1061710 -0.4978399 -0.7282223 Largest eigenvalues: [1] 65333194 60302100 58379970 55608168 55542254 54454931 52877525 52716338 [9] 51870592 51565797 Smallest eigenvalues: [1] 0.39905585 0.34746703 0.33720530 0.29311411 0.22012125 0.16280442 [7] 0.14794924 0.09903528 -0.24700643 -0.40767001 Largest eigenvalues: [1] 63695027 59342693 57346795 55885049 54196878 52875004 51793667 51721753 [9] 51423784 50701111 Smallest eigenvalues: [1] 0.434026699 0.420192491 0.371494212 0.358349883 0.347354950 [6] 0.346054388 0.288792083 0.260117823 -0.003616318 -5.376752724 Largest eigenvalues: [1] 64232300 60079341 57133128 55612150 55126506 53351497 52136211 51729628 [9] 51640725 50865858 Smallest eigenvalues: [1] 0.4585522 0.3856040 0.3708957 0.3625370 0.3149726 0.2731110 [7] 0.2052727 0.1783903 0.1507486 -0.1390350 Largest eigenvalues: [1] 64071662 59743549 57114570 55988912 54757544 53261189 52106801 51859210 [9] 51843735 50950023 Smallest eigenvalues: [1] 0.52550429 0.45846857 0.42359247 0.36130431 0.35432233 0.27856730 [7] 0.25876853 0.17755187 0.04585812 -0.02392554 Largest eigenvalues: [1] 61461227 59847398 56981738 56081301 54131884 53957016 52768555 51638564 [9] 50771560 50680765 Smallest eigenvalues: [1] 0.50990672 0.46278808 0.41709809 0.35218117 0.32965894 0.31780317 [7] 0.30296146 0.28301839 0.18501853 -0.00942292 Largest eigenvalues: [1] 63736727 60732480 57344755 55938129 55842612 54144641 52561228 52046197 [9] 51892779 51503323 Smallest eigenvalues: [1] 0.45191564 0.40166766 0.37066922 0.36635833 0.34610321 0.30301743 [7] 0.26437871 0.22812645 0.08560410 -0.04506491 Largest eigenvalues: [1] 61841680 60861022 57523438 55652906 55024490 53882842 52145718 52133906 [9] 51249343 50993076 Smallest eigenvalues: [1] 0.35778838 0.32313732 0.28070710 0.23478564 0.18571347 0.17820559 [7] 0.08602546 -0.09724300 -0.44512864 -0.61094981 Largest eigenvalues: [1] 64625903 61385440 58300290 56597975 55845160 54012351 53779061 52835131 [9] 52238935 52088055 Smallest eigenvalues: [1] 0.4258179 0.4123385 0.4066811 0.3173327 0.2935820 0.2873354 [7] 0.2741114 0.2036702 -0.1543384 -3.3223935 Largest eigenvalues: [1] 64939930 60522264 57799431 56325991 55224145 53740974 52412394 52134671 [9] 52080729 51217120 Smallest eigenvalues: [1] 0.270139743 0.258125051 0.203855010 0.077238656 -0.001353699 [6] -0.053471372 -0.118071092 -0.423497535 -0.585571198 -1.222890407 Largest eigenvalues: [1] 64910131 59792874 56955673 55471984 54675711 53020805 51973689 51656018 [9] 51318182 51136891 Smallest eigenvalues: [1] 0.39030630 0.36431513 0.36048649 0.33081098 0.32275195 0.30510288 [7] 0.30134017 0.19091043 0.13860613 -0.08821795 Largest eigenvalues: [1] 65305567 60809308 57448752 57138166 55260736 53667722 52883231 52679282 [9] 52342210 51421750 Smallest eigenvalues: [1] 0.4336938 0.3811972 0.3025028 0.2152404 0.2143854 0.2104441 [7] 0.1731974 -0.0584411 -0.5365725 -0.6975240 Largest eigenvalues: [1] 65336805 61045320 57411766 56236779 56023012 54133555 53072179 52554321 [9] 52224186 51677922 Smallest eigenvalues: [1] 0.5561153 0.4781759 0.4731293 0.4199611 0.3779361 0.3670875 [7] 0.3379363 0.3342902 0.2321161 -0.1889379 Largest eigenvalues: [1] 64128295 60229662 57354590 56035765 55393982 53533497 52070744 51986858 [9] 51783110 50818410 Smallest eigenvalues: [1] 0.31847471 0.27490608 0.23103712 0.22072614 0.18654000 0.15055378 [7] 0.13807697 0.05449083 0.04996715 -0.14503993 Largest eigenvalues: [1] 62145682 58953799 56457959 54823954 54766718 53069711 52032662 51514143 [9] 50725101 50484234 Smallest eigenvalues: [1] 0.54542371 0.54113868 0.48147653 0.43825609 0.40116155 0.39243073 [7] 0.36925263 0.22188467 0.13469984 -0.06763395 Largest eigenvalues: [1] 63989765 60064953 56688317 55432189 55317750 53611973 52250079 51468344 [9] 51428732 50599410 Smallest eigenvalues: [1] 0.357807286 0.349088475 0.306174172 0.277724705 0.261292687 [6] 0.173233031 0.162480802 0.025775202 0.003066232 -0.123847602 Largest eigenvalues: [1] 64934958 59195924 56706974 56383183 54608310 53050491 52425423 51637283 [9] 50773408 50214397 Smallest eigenvalues: [1] 0.38691058 0.37914400 0.33736700 0.31413882 0.29839175 0.22319961 [7] 0.03296122 -0.21851472 -0.23160158 -2.89636509 Largest eigenvalues: [1] 65486301 60407178 57524222 56061381 55528873 53988543 52680697 52180972 [9] 52000827 51801406 Smallest eigenvalues: [1] 0.191085559 0.065989762 0.008864738 -0.183355908 -0.232380493 [6] -0.334767617 -0.398897637 -0.657233726 -0.801103140 -4.031988330 Largest eigenvalues: [1] 62467877 59642617 56815956 55395970 54469087 53479396 52096444 51827825 [9] 51053428 50696642 Smallest eigenvalues: [1] 0.4398407 0.4306110 0.3948517 0.3484145 0.2794921 0.2648174 [7] 0.1589810 0.1463925 0.1036701 -1.7050408 Largest eigenvalues: [1] 63980535 60398989 57544343 55407189 55338956 53847128 52225912 52135617 [9] 51542032 51339157 Smallest eigenvalues: [1] 0.4169138 0.3747850 0.3499980 0.3279687 0.2570091 0.2533887 [7] 0.1829724 0.1039144 -0.3099311 -0.4348086 Largest eigenvalues: [1] 63146644 60498559 56882123 55837653 54962582 53275487 52182459 51720406 [9] 51549935 50745190 Smallest eigenvalues: [1] 0.3863383 0.3725693 0.3402612 0.3273823 0.2639087 0.2452811 [7] 0.2289172 0.1238991 -0.1618517 -1.8142402 Largest eigenvalues: [1] 61949083 59617663 56877805 54958154 54410347 53058589 51373009 51229911 [9] 50626749 50419702 Smallest eigenvalues: [1] 0.46990848 0.40559481 0.35611387 0.34376946 0.32571544 0.30474885 [7] 0.28793421 0.19319505 0.14470277 -0.02924618 Largest eigenvalues: [1] 64953733 59868091 57465829 56072246 54744131 53119010 52212536 51873610 [9] 51791675 51033031 Smallest eigenvalues: [1] 0.54957838 0.54463200 0.54083681 0.49891923 0.44485620 0.32740063 [7] 0.19661494 0.12678108 0.06429228 -0.11750755 Largest eigenvalues: [1] 63577287 60261787 57455345 55593772 55191894 53664021 52175088 51940753 [9] 51687081 51055238 Smallest eigenvalues: [1] 0.4709673 0.4291171 0.4028882 0.3893349 0.3609741 0.1549805 [7] 0.1294421 0.1147023 -0.2065128 -1.2897480 Largest eigenvalues: [1] 64544441 59253113 56768190 54881410 54868360 53166589 52188223 51313191 [9] 51236105 50625199 Smallest eigenvalues: [1] 0.45164240 0.44019667 0.40313259 0.37379501 0.29893470 0.17303321 [7] 0.15966312 0.10582758 0.04361385 -1.57612389 Largest eigenvalues: [1] 64465797 60173534 56910177 55991850 55341440 53346972 52389483 52067523 [9] 51626043 51233134 Smallest eigenvalues: [1] 0.27477744 0.19467440 0.15954488 0.13991501 0.04603371 0.03438404 [7] -0.14440284 -0.35007133 -0.71840349 -1.00148048 Largest eigenvalues: [1] 64265707 60898864 57567800 55670013 55293760 53592729 52122966 51866676 [9] 51558509 51228311 Smallest eigenvalues: [1] 0.4639443 0.3820820 0.3295740 0.3076395 0.2967086 0.2568272 [7] 0.2402834 0.2292922 -0.1798325 -1.5247088 Largest eigenvalues: [1] 63195149 60080687 57331128 55870705 54715203 53362558 52176900 51718922 [9] 51652835 51199680 Smallest eigenvalues: [1] 0.39226084 0.37562998 0.29721386 0.25695495 0.22287605 0.21889827 [7] 0.03522171 -0.01706078 -0.08423336 -4.77415802 Largest eigenvalues: [1] 63384454 59723997 56753544 55135280 55009229 52935019 51489509 51476458 [9] 51242597 50468580 Smallest eigenvalues: [1] 0.48214799 0.39204477 0.37424865 0.30111249 0.27718006 0.19968578 [7] 0.19933059 0.17981972 0.04870542 -0.95063877 Largest eigenvalues: [1] 64958122 59814991 57656939 55931689 54641361 53469264 52223894 51709642 [9] 51491801 50804445 Smallest eigenvalues: [1] 0.34432973 0.33329624 0.26655716 0.25276806 0.21523261 0.21465369 [7] 0.16558935 0.09561748 -0.20705440 -0.78292764 Largest eigenvalues: [1] 62475151 60265280 57299132 55650530 55076418 53513444 52320094 52193170 [9] 51463215 50825775 Smallest eigenvalues: [1] 0.22849935 0.18694592 0.18098389 0.16741839 0.07950545 0.06576836 [7] -0.09110808 -0.30732187 -1.42761057 -1.49394263 Largest eigenvalues: [1] 63628570 59499789 56996636 54843240 54713184 53246776 51625543 51142830 [9] 51003266 50462528 Smallest eigenvalues: [1] 0.35787283 0.35011015 0.24563930 0.20501641 0.17293359 0.10539791 [7] 0.02451984 -0.04600245 -0.27117584 -3.61089959 Largest eigenvalues: [1] 64993769 59728540 56948551 56312540 54900219 53180784 52474433 52270809 [9] 51783391 51276052 Smallest eigenvalues: [1] 0.31604271 0.19673866 0.15549241 0.13863547 -0.02487789 -0.06897950 [7] -0.08343397 -0.21110623 -1.12848267 -2.62019299 Largest eigenvalues: [1] 65900523 59804408 57078015 56628833 54590583 53078528 52673395 52198791 [9] 51430489 51405360 Smallest eigenvalues: [1] 0.45523176 0.35999222 0.22123303 0.19836564 0.16940852 0.15057724 [7] 0.12738629 -0.06692745 -0.36537776 -1.64320673 Largest eigenvalues: [1] 63838185 59446151 56371291 55103399 54663391 52965884 51742312 51303359 [9] 51148867 50390962 Smallest eigenvalues: [1] 0.39787487 0.35098284 0.25080461 0.21356840 0.06106247 0.02017161 [7] 0.00824589 -0.05994448 -0.06769519 -0.61758956 Largest eigenvalues: [1] 63377372 59462491 56783258 54808869 54550405 53042371 51706114 51281312 [9] 51090453 50666183 Smallest eigenvalues: [1] 0.48339463 0.40487813 0.39380319 0.37767780 0.31110870 0.29576419 [7] 0.28300147 -0.04288057 -0.04937407 -2.30489085 Largest eigenvalues: [1] 64330203 60638336 57010518 55710863 55589969 53647643 52214285 52008904 [9] 51837158 51149013 Smallest eigenvalues: [1] 0.255264366 0.254990769 0.217688954 0.035840286 0.004374647 [6] -0.135924345 -0.439217037 -0.712485014 -1.004096669 -1.462425588 Largest eigenvalues: [1] 65916877 59557708 56872477 56268542 54426004 53022054 52329167 51769053 [9] 51385268 50961594 Smallest eigenvalues: [1] 0.31873412 0.31250610 0.21958598 0.19047078 0.12456352 0.04217012 [7] -0.31752076 -0.84956313 -1.54931113 -1.85553762 Largest eigenvalues: [1] 66480855 60451398 58477588 56962582 55166767 53218412 52907259 52235169 [9] 51819266 51494708 Smallest eigenvalues: [1] 0.398368541 0.375293894 0.353760776 0.348714132 0.324237684 [6] 0.297573747 0.259491607 0.190384594 0.188742215 -0.007200348 Largest eigenvalues: [1] 64560412 60759659 58180807 55842189 55725554 54407633 52470706 52086613 [9] 51948297 51214153 Smallest eigenvalues: [1] 0.09924339 0.09212016 -0.07674742 -0.11192897 -0.11770956 -0.30974467 [7] -0.32442439 -0.41295500 -0.75624235 -1.25053246 Largest eigenvalues: [1] 66174916 60425722 58000364 57270357 54879815 53398413 53127546 52816238 [9] 51907206 51546062 Smallest eigenvalues: [1] 0.39169404 0.35807565 0.34137348 0.30946762 0.30397442 0.20935081 [7] 0.10948453 -0.08906589 -0.16411154 -1.18168583 Largest eigenvalues: [1] 63649704 60295657 57417707 56285869 55031440 53359681 52534598 52075870 [9] 51845050 51345187 Smallest eigenvalues: [1] 0.49899881 0.44947993 0.44740584 0.41504017 0.32800306 0.28183749 [7] 0.23949415 0.20376783 0.06009082 -0.05709857 Largest eigenvalues: [1] 66277567 60079407 57790439 57107823 54888753 53599572 53206689 51950193 [9] 51774331 51002716 Smallest eigenvalues: [1] 0.38366071 0.34406182 0.32912277 0.28789686 0.27037455 0.21597467 [7] 0.19302749 0.06957620 -0.01169218 -0.39114228 Largest eigenvalues: [1] 64975846 60161970 57064134 56596868 54936164 53341354 52572077 52522065 [9] 52017910 51569705 Smallest eigenvalues: [1] 0.20658819 0.20612932 0.16018438 0.13353185 -0.08180843 -0.25074857 [7] -0.49105292 -1.44979331 -1.64269705 -1.80304536 Largest eigenvalues: [1] 65304738 60312398 57707210 56519668 54775305 53442200 52649438 52170833 [9] 51628495 51359821 Smallest eigenvalues: [1] 0.5460028 0.5302948 0.5084107 0.4437580 0.3605250 0.3539121 [7] 0.1820593 0.1637137 0.1177607 -0.2146693 Largest eigenvalues: [1] 64230436 59313733 56643170 55582984 54401178 52349863 51640310 51166093 [9] 51136973 50298500 Smallest eigenvalues: [1] 0.54698461 0.50663764 0.44033516 0.41707953 0.35626267 0.29646196 [7] 0.26599981 0.04527109 -0.35341494 -4.01554427 Largest eigenvalues: [1] 65509740 59852530 56857360 56455643 54578768 52577185 52279191 51489216 [9] 51446201 50655796 Smallest eigenvalues: [1] 0.21512081 0.14906591 0.11011256 -0.02687004 -0.04432804 -0.11844368 [7] -0.12821064 -0.75861408 -1.07331104 -1.88364080 Largest eigenvalues: [1] 66346754 60430127 57394352 57201277 55015751 53289194 53142123 52837674 [9] 51867902 51817783 Smallest eigenvalues: [1] 0.3710866 0.3508347 0.3330107 0.2301228 0.1937342 0.1514765 [7] 0.1155636 -0.1839370 -0.3467024 -0.9801734 Largest eigenvalues: [1] 64161091 59907824 56932779 55163755 54732640 53146760 51799713 51708517 [9] 51315252 51075084 Smallest eigenvalues: [1] 0.40675491 0.39034868 0.37854384 0.31899379 0.24789933 0.21148566 [7] 0.18662655 0.06834084 0.04751032 -1.39155705 Largest eigenvalues: [1] 64636119 60346324 56880739 56056506 55420205 53660458 51922999 51808036 [9] 51730717 50887629 Smallest eigenvalues: [1] 0.37560935 0.32417452 0.28600191 0.17181566 0.16361341 0.10896189 [7] 0.07418611 0.04317457 0.01693225 -1.98185328 Largest eigenvalues: [1] 64017903 60209294 57307816 55527122 55100499 53941130 52052588 51609549 [9] 51137565 50816590 Smallest eigenvalues: [1] 0.23822468 0.15785225 0.07970109 0.03502709 -0.02867249 -0.03180909 [7] -0.04859561 -0.14190216 -0.35951790 -0.80680108 Largest eigenvalues: [1] 66185362 60797860 58203730 56379951 55293550 53795333 52608526 52301710 [9] 51941995 51468308 Smallest eigenvalues: [1] 0.45419461 0.44368857 0.43370536 0.34804360 0.27836663 0.25406331 [7] 0.05162261 0.03380550 -0.05274366 -2.24685353 Largest eigenvalues: [1] 65335127 60115805 57124621 56485791 55228878 53740399 52397571 52154837 [9] 51986445 51282511 Smallest eigenvalues: [1] 0.48826024 0.44528091 0.39528801 0.37821865 0.37242237 0.31592848 [7] 0.29375195 0.18116860 0.12910893 -0.07278919 Largest eigenvalues: [1] 64465138 59851261 56568612 55876383 54725508 53134958 51928974 51899398 [9] 51459432 50812873 Smallest eigenvalues: [1] 0.34388338 0.31470295 0.28232951 0.22163303 0.21047650 -0.05258964 [7] -0.09257466 -0.17995696 -0.55886801 -2.94081634 Largest eigenvalues: [1] 65528265 60800537 57441141 55909013 55398441 53481114 52024662 51925550 [9] 51660791 51175536 Smallest eigenvalues: [1] 0.42191337 0.40200855 0.38913334 0.34370348 0.31553045 0.31497820 [7] 0.27415048 0.25952143 0.22060993 -0.07022526 Largest eigenvalues: [1] 64195125 60152331 57304196 55463690 55434272 53799107 51926986 51583696 [9] 51343087 50445553 Smallest eigenvalues: [1] 0.4103166 0.3596281 0.3257396 0.2889494 0.2519206 0.1794170 [7] 0.1181834 -0.0274441 -0.1130602 -0.1458673 Largest eigenvalues: [1] 65764229 60379872 57456948 56463180 55395999 53968774 52502043 52023538 [9] 51853948 50636427 Smallest eigenvalues: [1] 0.30003658 0.27514071 0.17844680 0.15536466 0.12801314 0.11383686 [7] 0.03036235 -0.76134313 -1.02306789 -1.02501568 Largest eigenvalues: [1] 65345324 59863669 57682632 55964107 55052907 53777348 52565652 52048010 [9] 52036139 51682016 Smallest eigenvalues: [1] 0.47415951 0.37584902 0.36955926 0.36509014 0.34253408 0.28984457 [7] 0.26700710 0.23295508 0.17400323 -0.03047848 Largest eigenvalues: [1] 65451957 60215216 57924912 56724194 54828496 53211681 52742956 52001688 [9] 51813755 51223775 Smallest eigenvalues: [1] 0.142281911 0.101247008 0.058590347 -0.001330423 -0.018051874 [6] -0.165937088 -0.235156334 -0.324502851 -0.873190654 -1.518822952 Largest eigenvalues: [1] 63612917 60497610 57801040 55150393 54997608 53777524 51966738 51895853 [9] 51181740 50962162 Smallest eigenvalues: [1] 0.44430905 0.42370743 0.39945639 0.38466041 0.31193506 0.28184779 [7] 0.26945890 0.19909868 0.08485923 -0.02049831 Largest eigenvalues: [1] 65151204 60334609 58049947 55760301 55419529 53694643 52455348 52100206 [9] 51983032 51506661 Smallest eigenvalues: [1] 0.35826086 0.24687905 0.24497400 0.18758641 0.13949461 0.04921253 [7] 0.02583006 -0.04954255 -0.18359965 -0.53091826 Largest eigenvalues: [1] 66211298 60601066 57991016 56631218 55032931 53636523 52696588 52642256 [9] 51961725 51793681 Smallest eigenvalues: [1] 0.36911374 0.36687346 0.35853611 0.27108959 0.23069233 0.16791281 [7] 0.16721935 0.10432921 0.02927506 -0.42260927 Largest eigenvalues: [1] 66573956 61037979 57893578 57292566 56070603 54380361 53325296 53235505 [9] 52422433 52016380 Smallest eigenvalues: [1] 0.4190735 0.4070922 0.3405512 0.3072790 0.2964792 0.2503843 [7] 0.1807682 0.1407221 0.1123483 -0.6553671 Largest eigenvalues: [1] 65495821 59565246 57296642 56802713 54631670 53355384 52744751 51886134 [9] 51510542 51004241 Smallest eigenvalues: [1] 0.56463874 0.48159187 0.47784485 0.41365549 0.37551443 0.26991481 [7] 0.25479935 0.22357007 -0.07050388 -3.82438333 Largest eigenvalues: [1] 64843447 60121967 57418202 56099220 55146568 53460555 52210715 51970094 [9] 51943783 50976876 Smallest eigenvalues: [1] 0.45303443 0.44804797 0.41963693 0.39024844 0.34455935 0.25551341 [7] 0.24148828 0.09942670 0.06185218 -3.53302476 Largest eigenvalues: [1] 63805044 60644696 57912325 56030931 55706527 54414673 52713698 52670737 [9] 51886899 51591819 Smallest eigenvalues: [1] 0.4578711 0.3773066 0.3653459 0.3542151 0.3523558 0.3166131 [7] 0.2718408 0.2593948 0.1147047 -0.4169546 Largest eigenvalues: [1] 64253743 60372200 57746910 55665604 55563209 54205803 52588849 52325706 [9] 51650457 51142665 Smallest eigenvalues: [1] 0.44713283 0.42137137 0.38632405 0.29865266 0.20458295 0.18679541 [7] 0.09734140 0.05745541 0.01992097 -1.39667907 Largest eigenvalues: [1] 63035420 60100239 56982329 55403538 54676248 53660700 51811384 51729271 [9] 50947612 50846655 Smallest eigenvalues: [1] 0.51203841 0.46721205 0.43036363 0.38347410 0.36912243 0.35571560 [7] 0.34827207 0.14763799 0.10701455 -0.06605479 Largest eigenvalues: [1] 65203605 61313877 57696881 56611895 56318921 54595251 53459840 52595437 [9] 52313518 51842000 Smallest eigenvalues: [1] 0.44892974 0.42565504 0.38195828 0.37610479 0.33296835 0.28640749 [7] 0.26135775 -0.03768478 -0.18366181 -0.77853612 Largest eigenvalues: [1] 64156328 60460528 57654175 56136977 55415842 53872704 52373780 52179905 [9] 51819921 51193054 Smallest eigenvalues: [1] 0.31731585 0.21097395 0.20436093 0.18989051 0.12797501 [6] 0.08474374 0.02840311 -0.22049051 -0.29987531 -22.45608441 Largest eigenvalues: [1] 65886530 59829752 57773321 56119051 54976959 53811668 52505007 52310217 [9] 52004167 51444084 Smallest eigenvalues: [1] 0.4421756 0.4001940 0.3461679 0.2436915 0.2121544 0.1651616 [7] 0.1135466 -0.2049093 -0.2953542 -0.7346995 Largest eigenvalues: [1] 65775083 60449279 57675268 56924751 54877346 52924646 52865527 52450857 [9] 51750396 51548305 Smallest eigenvalues: [1] 0.5660133 0.5591972 0.4488088 0.4276763 0.3074990 0.2735265 [7] 0.2437631 0.2436161 -0.2092905 -0.2403396 Largest eigenvalues: [1] 65518084 60770237 57694984 56663045 55505105 53769933 52798593 52618856 [9] 51982966 51418190 Smallest eigenvalues: [1] 0.39201828 0.36607785 0.35204663 0.32680014 0.28956974 0.22437456 [7] 0.14268699 0.12509449 0.03413339 -2.99073803 Largest eigenvalues: [1] 63731433 59913220 57537649 55585139 54967054 53503923 51893813 51760078 [9] 51578795 50913673 Smallest eigenvalues: [1] 0.34244869 0.24713111 0.22917031 0.21855827 0.12267815 0.02799559 [7] -0.09435156 -0.25574024 -0.63660542 -1.31597273 Largest eigenvalues: [1] 65188942 60609757 57885515 56226885 55318100 53900123 52354358 52096839 [9] 51809490 51127977 Smallest eigenvalues: [1] 0.41227613 0.40870052 0.33616820 0.33362906 0.28079421 0.23104931 [7] 0.19895556 0.12086652 0.05272953 -0.39137290 Largest eigenvalues: [1] 65176525 60286508 57729669 56397156 55140153 53515113 53259637 52595000 [9] 51885942 51641438 Smallest eigenvalues: [1] 0.5008149 0.4216607 0.3996957 0.3841024 0.3261405 0.3150002 [7] 0.2412383 0.2055896 -0.1503619 -0.1628951 Largest eigenvalues: [1] 64503744 60436940 57293888 55935278 55144083 53420476 51923137 51838316 [9] 51810506 50910026 Smallest eigenvalues: [1] 0.6144951 0.5285018 0.5217817 0.5196151 0.4470148 0.3437827 [7] 0.2999062 0.2523786 0.2484838 -0.6737067 Largest eigenvalues: [1] 64546214 59863211 57068038 55710816 55048166 53609544 52170113 51846223 [9] 51643171 50809190 Smallest eigenvalues: [1] 0.37222354 0.37165058 0.31668573 0.28685235 0.27794986 0.18920346 [7] 0.18072816 0.17747899 0.13493871 -0.06034644 Largest eigenvalues: [1] 65832347 60698452 58366800 56387753 55512010 53945062 52598967 52453114 [9] 52357428 51818851 Smallest eigenvalues: [1] 0.35770525 0.33293579 0.32768492 0.30300358 0.25719724 0.20680826 [7] 0.19959926 0.09582846 -0.49196518 -3.15240362 Largest eigenvalues: [1] 65449561 59860469 57142189 56774543 54882509 52878486 52661818 52447356 [9] 51871090 51498949 Smallest eigenvalues: [1] 0.4517968 0.4144365 0.3300266 0.3087105 0.2581300 0.2437867 [7] 0.2334273 0.1675006 0.1075077 -0.5933252 Largest eigenvalues: [1] 61990273 59495261 56169635 54830368 54810776 53084656 51980907 51963983 [9] 50881904 50687090 Smallest eigenvalues: [1] 0.3506319230 0.2758619363 0.2657261017 0.2395028654 0.1649213441 [6] 0.0811668969 0.0003459881 -0.1449473441 -0.5231058413 -0.8660665085 Largest eigenvalues: [1] 65291053 61470136 58265204 57253097 55376675 53682057 53391601 52686558 [9] 52297482 51450792 Smallest eigenvalues: [1] 0.4793136 0.4583449 0.4146647 0.3706613 0.3250721 0.2587679 [7] 0.2264628 0.1974565 0.1659534 -0.5557488 Largest eigenvalues: [1] 62927075 59428130 56917992 54832712 54746405 53274805 51958205 51216053 [9] 50862840 50480673 Smallest eigenvalues: [1] 0.2412614 0.2390749 0.1992416 0.1908809 0.1331087 0.0116919 [7] -0.1018362 -0.2505629 -0.3093319 -1.0932292 Largest eigenvalues: [1] 64095374 59974165 57551797 55743796 54854443 53577597 51806523 51776650 [9] 51717979 50834386 Smallest eigenvalues: [1] 0.41544694 0.37910818 0.23492621 0.07291494 0.07267453 0.04956870 [7] -0.05042230 -0.06958034 -0.30108024 -2.05870162 Largest eigenvalues: [1] 63849817 60299918 57457323 55643758 55519229 53803956 52656806 51852855 [9] 51754879 51311383 Smallest eigenvalues: [1] 0.2246526516 0.1942011844 0.1937623025 0.1659102309 0.1623246554 [6] 0.1610865035 0.0879658289 -0.0009876474 -0.2353104174 -0.3403656520 Largest eigenvalues: [1] 63603903 59327103 56393229 55541008 54790499 53096645 51785774 51502903 [9] 50837448 50204772 Smallest eigenvalues: [1] 0.50770215 0.39444190 0.37925689 0.37911256 0.33363794 0.29753137 [7] 0.20674451 0.17236082 -0.08702109 -0.34161654 Largest eigenvalues: [1] 64556946 60777383 57801352 55956468 55380047 53784533 52804492 52188723 [9] 52119033 51895624 Smallest eigenvalues: [1] 0.3858945 0.3357381 0.3322148 0.2991350 0.2648856 0.2166075 [7] 0.2097733 0.1959674 -0.1248980 -1.5621686 Largest eigenvalues: [1] 64988000 60744097 58054952 55793758 55714057 54257483 52254240 52026348 [9] 51952737 51354732 Smallest eigenvalues: [1] 0.22561415 0.16207596 0.15719959 0.07536898 0.03632150 -0.06279389 [7] -0.35865122 -0.37470584 -1.38351044 -1.73710540 Largest eigenvalues: [1] 64611910 59590608 56910221 55998848 54675695 53070642 52256865 52004935 [9] 51630179 51039778 Smallest eigenvalues: [1] 0.44767823 0.40929841 0.31800547 0.29323309 0.24793446 0.23712671 [7] 0.17928678 0.16993373 -0.04305723 -1.19057602 Largest eigenvalues: [1] 64459967 60581001 57233205 56274291 55618530 53983003 52254222 52103640 [9] 51949071 51065380 Smallest eigenvalues: [1] 0.29175891 0.23391803 0.17408246 0.15674499 0.13489617 0.03069871 [7] -0.08542268 -0.29960155 -0.49240463 -1.15718716 Largest eigenvalues: [1] 65011155 60446753 57391949 56561354 54868283 53567535 52497609 52424645 [9] 51804319 51659271 Smallest eigenvalues: [1] 0.28625032 0.23514710 0.20044846 0.12233990 0.07800716 -0.17761160 [7] -0.25776908 -0.35657178 -0.52667098 -1.41482632 Largest eigenvalues: [1] 64139926 59265630 57053193 55480737 54299754 53206194 51861387 51672562 [9] 51475812 50955437 Smallest eigenvalues: [1] 0.22936969 0.21020719 0.17412006 0.16857077 0.14773110 -0.04124600 [7] -0.04524443 -0.13908801 -0.19386815 -1.60214300 Largest eigenvalues: [1] 64827179 60849185 57772424 56091366 55686590 54345296 52699600 52619501 [9] 52033152 51844209 Smallest eigenvalues: [1] 0.412687187 0.378728427 0.329309738 0.315846639 0.309482282 [6] 0.260399031 0.258287998 0.004449181 -0.127375454 -10.241339447 Largest eigenvalues: [1] 64424604 59948334 57293836 55663979 55086637 53523884 52232847 51767244 [9] 51558272 50970216 Smallest eigenvalues: [1] 0.36599217 0.35035789 0.33298055 0.24896675 0.20065789 0.16959265 [7] 0.13564926 0.13228616 0.07244268 -0.05980429 Largest eigenvalues: [1] 62703934 60077912 57137338 55468784 55142718 53363255 52450982 52300059 [9] 51319769 51097271 Smallest eigenvalues: [1] 0.3801999 0.3482936 0.2911245 0.2376649 0.2114886 0.2042119 [7] 0.1396087 -0.1238492 -0.3356010 -1.5960486 Largest eigenvalues: [1] 65509902 60152591 57115971 56687346 55225618 53671732 52595198 52389513 [9] 52049240 51614870 Smallest eigenvalues: [1] 0.40036700 0.34391822 0.33329054 0.27999331 0.18251816 0.15645880 [7] 0.04867742 -0.37491944 -0.43668209 -5.08273853 Largest eigenvalues: [1] 65539086 60222540 57388358 56269213 55131641 53232074 52490064 52041479 [9] 51631253 51249262 Smallest eigenvalues: [1] 0.1954337 0.1900241 0.1856947 -0.1009354 -0.1317049 -0.2657994 [7] -0.3685551 -0.3867340 -0.4988534 -1.0059088 Largest eigenvalues: [1] 65078229 61302853 57667033 56408164 56335387 54364814 53902332 52580335 [9] 52210065 51853661 Smallest eigenvalues: [1] 0.4477225 0.3848476 0.3436877 0.3162659 0.2796636 0.2688860 [7] 0.2687305 0.1863084 -0.1544271 -0.4701790 Largest eigenvalues: [1] 64188783 60775878 58101977 56181014 55269762 53746974 52018781 51951917 [9] 51867480 50942808 Smallest eigenvalues: [1] 0.29422165 0.19777063 0.10466091 0.09802734 0.08529111 -0.01484967 [7] -0.03153301 -0.07522498 -0.08202590 -2.15647362 Largest eigenvalues: [1] 65018490 59874004 57597808 56494080 55166656 53943434 52963395 52339654 [9] 52293857 51909023 Smallest eigenvalues: [1] 0.4571294 0.4331764 0.3556075 0.3295324 0.3015585 0.2531303 [7] 0.1890027 -0.0762550 -0.2423593 -2.0077737 Largest eigenvalues: [1] 65594600 59761014 56750503 56303172 54397133 52641892 52325120 51402736 [9] 51157988 50646589 Smallest eigenvalues: [1] 0.4646382 0.4500035 0.4326764 0.3553120 0.3421914 0.2759485 [7] 0.2269887 0.1665191 0.1383409 -0.3495080 Largest eigenvalues: [1] 64765642 59847766 57466185 55416579 55326091 53851506 51752952 51621365 [9] 51513030 50756216 Smallest eigenvalues: [1] 0.54077236 0.45580438 0.39245221 0.36618302 0.32701812 0.25522995 [7] 0.17374478 0.09220614 0.02697602 -0.18929149 Largest eigenvalues: [1] 64297809 60192559 57326812 55886898 55741257 54169291 52391068 52339491 [9] 51817913 51719604 Smallest eigenvalues: [1] 0.28795199 0.27277850 0.20074329 0.18314525 0.07810581 [6] 0.07390435 -0.14078310 -0.23773276 -0.81091645 -19.99259512 Largest eigenvalues: [1] 63386915 60157856 57630136 55396973 55059110 53740049 52612356 51764476 [9] 51217132 50971375 Smallest eigenvalues: [1] 0.44495994 0.43756862 0.40479803 0.36700433 0.29030394 0.28358212 [7] 0.20101780 0.16501665 0.06417002 -0.60855837 Largest eigenvalues: [1] 65777865 59744112 57271941 56758633 54656306 53142956 52658067 52156304 [9] 51650234 51153478 Smallest eigenvalues: [1] 0.5600320259 0.5197066362 0.4716906350 0.4274944451 0.3802579594 [6] 0.3145297440 0.1539205452 0.0993539107 0.0449715190 -0.0008183772 Largest eigenvalues: [1] 64622130 60260555 57568973 55499532 55270147 53859864 52528099 52187523 [9] 51608209 51386552 Smallest eigenvalues: [1] 0.38680342 0.38043602 0.29153600 0.24563297 0.23429306 0.18889191 [7] 0.01685479 -0.06894029 -0.25638247 -0.99896044 Largest eigenvalues: [1] 64469025 59751953 56836436 56087082 54973882 53396839 52174809 52118878 [9] 51635719 51052704 Smallest eigenvalues: [1] 0.46791424 0.42696534 0.40733922 0.29847974 0.27113267 0.26420213 [7] 0.22380461 0.19868696 0.03986304 -1.18350445 Largest eigenvalues: [1] 63467451 59614210 57326320 55294604 54774928 53569594 52225269 51868355 [9] 51462107 51049675 Smallest eigenvalues: [1] 0.43702356 0.42604157 0.39079303 0.34412615 0.33467068 0.30929347 [7] 0.21153955 0.05084477 -0.07964505 -0.36445304 Largest eigenvalues: [1] 62826830 59678675 57072272 55577700 54873055 53217787 51617413 51517158 [9] 51454822 50419893 Smallest eigenvalues: [1] 0.48176879 0.47590168 0.45135691 0.35256321 0.29979562 0.24374336 [7] 0.18477920 0.15047625 0.04436969 -0.31178165 Largest eigenvalues: [1] 64051732 60470592 57314570 55920693 55677193 53961064 52688454 52333781 [9] 52084407 51491467 Smallest eigenvalues: [1] 0.5016051 0.4968539 0.4371616 0.3619396 0.2849206 0.2823763 [7] 0.2764347 0.2168504 -0.4795734 -0.9207457 Largest eigenvalues: [1] 63668237 59487438 56679394 55383196 54760833 52965982 52505702 51419262 [9] 51258260 50827519 Smallest eigenvalues: [1] 0.41912095 0.41569188 0.38103989 0.35351037 0.32666803 0.15140703 [7] 0.10824039 0.04329408 0.01489731 -0.63925734 Largest eigenvalues: [1] 65886826 59762903 57373163 56081924 54784273 53253947 52266660 51992319 [9] 51872940 50786459 Smallest eigenvalues: [1] 0.43595765 0.39682051 0.39075055 0.33381001 0.29843423 0.27807291 [7] 0.08690499 0.06523444 -0.02987169 -0.15160563 Largest eigenvalues: [1] 64742431 59808026 57082245 55931053 55223080 53601270 51979427 51713581 [9] 51200746 50160068 Smallest eigenvalues: [1] 0.40488521 0.33661461 0.31488626 0.30953580 0.20523401 0.19087398 [7] 0.12114293 -0.04880466 -0.21783977 -1.20261650 Largest eigenvalues: [1] 63223035 60261246 57197895 55536047 54634545 53602041 51867519 51650129 [9] 51020678 50782355 Smallest eigenvalues: [1] 0.4849433275 0.4841665497 0.3777428439 0.3416971499 0.2464414420 [6] 0.1714379744 0.1662778665 0.1268239945 0.0005470483 -0.7292119221 Largest eigenvalues: [1] 62227487 59472121 56301950 54810892 54627139 52990412 51981668 51350084 [9] 50758495 50592550 Smallest eigenvalues: [1] 0.56944125 0.56092355 0.53088372 0.38999585 0.37768531 0.33125085 [7] 0.14577636 0.07204877 -0.01303944 -0.08134181 Largest eigenvalues: [1] 65509212 59707801 56930931 56801415 54693907 52846224 52825664 51613132 [9] 51241242 50563950 Smallest eigenvalues: [1] 0.45139495 0.33014890 0.32141809 0.24491037 0.20517283 0.06123890 [7] 0.05308619 -0.11056516 -0.41556868 -1.78319977 Largest eigenvalues: [1] 65090916 61286284 57576899 57017512 56036583 54061194 53642363 52598580 [9] 52562384 52037266 Smallest eigenvalues: [1] 0.37826796 0.26562021 0.22840776 0.21147742 0.10750055 0.08870933 [7] -0.07661383 -0.57303159 -0.72562523 -1.43752797 Largest eigenvalues: [1] 66099606 59632397 56959965 56639559 54271809 52790293 52774600 51948815 [9] 51194509 51138006 Smallest eigenvalues: [1] 0.49795328 0.48946833 0.37090172 0.34569614 0.34364666 0.24733095 [7] 0.23063347 0.03688379 -0.06018632 -0.07092340 Largest eigenvalues: [1] 64304716 59211940 56646151 55378824 54553727 52950678 51749212 51337080 [9] 51010538 50350073 Smallest eigenvalues: [1] 0.57828218 0.43946131 0.43929519 0.43191753 0.32229192 0.26328218 [7] 0.25870389 0.15465279 -0.01163865 -0.17573346 Largest eigenvalues: [1] 63856256 59434670 56599109 55565201 54294527 52741153 51592902 51416187 [9] 50854223 49980333 Smallest eigenvalues: [1] 0.32262618 0.28155888 0.26583075 0.25263305 0.18970866 0.18448297 [7] 0.14260862 0.06096392 0.02455327 -0.61564965 Largest eigenvalues: [1] 65520186 60717282 58313241 56814197 55276033 54077777 52758127 52422198 [9] 52209834 51323013 Smallest eigenvalues: [1] 0.26260530 0.21686847 0.19140481 0.18325633 0.15980163 0.06528655 [7] 0.03317500 -0.01989466 -0.02473640 -1.32647737 Largest eigenvalues: [1] 65137609 59739526 56861443 55352361 54609599 53063802 51844055 51464858 [9] 51354641 50984481 Smallest eigenvalues: [1] 0.49605156 0.47801544 0.38649387 0.32656970 0.29630198 0.29523228 [7] 0.27247007 0.23548578 -0.01054134 -4.59470119 Largest eigenvalues: [1] 65458625 60933445 58171282 56502806 55889848 54203623 52785493 52380574 [9] 52298581 51335343 Smallest eigenvalues: [1] 0.46684321 0.36387549 0.27705717 0.25738809 0.18158818 0.17546580 [7] 0.11212597 0.09262325 -0.04820603 -2.14074394 Largest eigenvalues: [1] 64472340 59723600 56643172 55327342 54632084 53111796 51594997 51417633 [9] 51103578 50351645 Smallest eigenvalues: [1] 0.12619207 0.11150809 -0.02642782 -0.11883213 -0.20232777 -0.26620876 [7] -0.29929589 -0.33377198 -0.40606544 -2.12884828 Largest eigenvalues: [1] 65215394 60451497 57823944 55590231 55242169 53697723 52268919 51749697 [9] 51616911 51551837 Smallest eigenvalues: [1] 0.5134272 0.4424175 0.4241758 0.4106739 0.2890797 0.2725983 [7] 0.2428147 0.1979289 0.1501808 -0.3316823 Largest eigenvalues: [1] 65618110 60382275 57637651 56388302 54993976 53577224 52547187 51891132 [9] 51701511 51075420 Smallest eigenvalues: [1] 0.59023219 0.58918366 0.47027725 0.45783010 0.32727309 0.31447231 [7] 0.26417584 0.23580021 0.09613169 -0.19109745 Largest eigenvalues: [1] 66106226 60462707 57873612 56510852 55256661 53910668 52629003 52425409 [9] 51906728 51459859 Smallest eigenvalues: [1] 0.45392489 0.37648662 0.36913566 0.34349880 0.27966157 0.22471334 [7] 0.19231751 0.15185063 -0.04310512 -0.54915024 Largest eigenvalues: [1] 65138793 60799831 58083511 56522591 55289786 54000798 52439949 52299768 [9] 52066025 51152576 Smallest eigenvalues: [1] 0.4809745 0.4590980 0.4387196 0.3687736 0.3483114 0.3247535 [7] 0.2592652 0.2098659 0.1649771 -0.2093161 Largest eigenvalues: [1] 64917145 59591691 56585076 56403815 54415806 52955504 52227002 51755799 [9] 51457858 50476682 Smallest eigenvalues: [1] 0.5524188 0.5253289 0.5077754 0.4161437 0.3520868 0.3513292 [7] 0.2103284 0.2087082 0.1859932 -0.1284037 Largest eigenvalues: [1] 63837922 60245945 57035962 55380949 55326319 53792924 52322533 52050087 [9] 51476482 51299291 Smallest eigenvalues: [1] 0.34254222 0.33927761 0.31655651 0.28933653 0.25041960 0.14760181 [7] 0.14038325 0.10272106 0.09726858 -0.04434161 Largest eigenvalues: [1] 62043686 60363468 57442009 55964839 55030812 54198462 52667039 52376837 [9] 51524088 51024495 Smallest eigenvalues: [1] 0.5968017 0.5715338 0.5118664 0.4725151 0.4217953 0.4008595 [7] 0.3050661 0.2051502 0.1252929 -0.6374712 Largest eigenvalues: [1] 64160435 60688682 57059963 55706722 55619054 54010276 52354304 52204999 [9] 51551473 51087770 Smallest eigenvalues: [1] 0.43921422 0.42016738 0.35638344 0.30966081 0.26502777 0.24474031 [7] 0.18751967 0.10361093 0.09089492 -0.24473658 Largest eigenvalues: [1] 65926783 60097564 57534009 57235572 54874892 53467654 53210909 52079431 [9] 52018865 51148221 Smallest eigenvalues: [1] 0.4080132 0.3844416 0.3041990 0.2304309 0.1596702 0.1284254 [7] 0.1103804 -0.1029656 -0.4918004 -6.7413261 Largest eigenvalues: [1] 65643124 60330007 57714685 56891546 55069589 53498821 52869298 52499837 [9] 52343252 51841262 Smallest eigenvalues: [1] 0.41389349 0.40761232 0.40226160 0.31894818 0.22299817 0.21388907 [7] 0.16096874 0.03526162 -0.25323135 -0.37868853 Largest eigenvalues: [1] 63486960 60336516 56992318 55336170 54965194 53270669 52033524 51574922 [9] 51378816 51136791
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.557765 | 0.6677545 | 15.21572 | 0.375 | 2.885361 | 1.556578 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + speed + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
speed = speed_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_speed_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 690 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.55555842 0.52728829 0.48163769 0.38049995 0.33141926 0.29894736 [7] 0.15965511 0.14236862 -0.04375265 -0.09781512 Largest eigenvalues: [1] 77852605 72468147 69543549 68101339 66340210 64604095 63247805 62692695 [9] 62497944 61172405 Smallest eigenvalues: [1] 0.5495996 0.5415181 0.4532786 0.4462895 0.4052362 0.3679991 [7] 0.3150882 0.2862877 0.2657705 -1.0512943 Largest eigenvalues: [1] 76791680 73355541 69298167 67145218 67094572 65290569 62731881 62659850 [9] 62210397 61176086 Smallest eigenvalues: [1] 0.5287191 0.4501140 0.4010844 0.3486700 0.3344508 0.2989247 [7] 0.2611175 0.1993226 0.1569827 -0.2345939 Largest eigenvalues: [1] 78487818 72662850 69727729 68466144 66817225 64840737 63957329 63618776 [9] 62883583 62484279 Smallest eigenvalues: [1] 0.37290417 0.33637153 0.33445878 0.30001438 0.26563984 0.21833416 [7] 0.14231247 0.03603118 -0.31116181 -2.34291591 Largest eigenvalues: [1] 77177249 73888194 69789260 67689470 67261042 65988562 63684124 63346254 [9] 62368724 62251599 Smallest eigenvalues: [1] 0.50705809 0.47539858 0.46162774 0.36896469 0.36028970 0.25692534 [7] 0.15870346 0.15055635 -0.09623954 -0.81247184 Largest eigenvalues: [1] 79298236 73628230 69295200 68914308 67151106 64899163 63840280 63447333 [9] 63160977 62179685 Smallest eigenvalues: [1] 0.39101450 0.32199371 0.28225693 0.16372635 0.14477794 0.11132128 [7] 0.04426752 -0.22348952 -0.26570912 -1.63083493 Largest eigenvalues: [1] 75485883 71611387 68181468 66444781 66052529 64357156 62739515 61672432 [9] 61300782 60822809 Smallest eigenvalues: [1] 0.5855252 0.5518508 0.4540662 0.4431510 0.4140982 0.3866626 [7] 0.3376545 0.2628605 0.2476326 -0.9894454 Largest eigenvalues: [1] 77293387 72188881 68415783 67610783 65719518 63658321 62638646 62461536 [9] 61816972 60770744 Smallest eigenvalues: [1] 0.5799460 0.5603298 0.5003988 0.4458324 0.4356506 0.4286793 [7] 0.4080188 0.3490708 0.1878189 -3.5536556 Largest eigenvalues: [1] 75988914 72913043 68994841 67156631 66138065 64785145 62214828 61963332 [9] 61562863 60875733 Smallest eigenvalues: [1] 0.69883501 0.61440128 0.59767830 0.49739299 0.49347247 0.36916433 [7] 0.30936676 0.28456154 0.08151468 -2.47153780 Largest eigenvalues: [1] 78015835 73849266 69612006 67790544 67127512 65036639 62908451 62852151 [9] 62704195 61519853 Smallest eigenvalues: [1] 0.5490136 0.5397547 0.4695575 0.4457312 0.3864518 0.3399353 [7] 0.3348434 0.2520170 0.1731115 -0.2825974 Largest eigenvalues: [1] 77069210 73391676 69401683 67693519 66707140 64851361 63589978 62831081 [9] 62616327 62192082 Smallest eigenvalues: [1] 0.5844980 0.5528689 0.5503917 0.4718512 0.4049323 0.3946117 [7] 0.2342542 0.1777444 -0.4862035 -0.7585808 Largest eigenvalues: [1] 78398351 73106463 69009886 68609684 66461426 64616292 63507885 63044836 [9] 62492222 61536088 Smallest eigenvalues: [1] 0.6194306 0.5779876 0.4874307 0.4630778 0.4264805 0.3411356 [7] 0.2928617 0.2079465 0.1335055 -0.4620508 Largest eigenvalues: [1] 77994146 72893271 69065832 68580585 65999183 64310120 63471605 62837147 [9] 62569495 61810980 Smallest eigenvalues: [1] 0.45788074 0.42309971 0.40090862 0.38221236 0.34828864 0.21213767 [7] 0.19372156 0.14505021 0.07888568 -0.80880130 Largest eigenvalues: [1] 78146310 72600696 69221140 67608841 66740406 64991234 62979454 62790393 [9] 62660626 61452409 Smallest eigenvalues: [1] 0.6168094 0.5572084 0.5374052 0.5251353 0.5249124 0.5046800 [7] 0.4569474 0.4548913 0.2314360 -0.6945941 Largest eigenvalues: [1] 76235526 72335723 68519846 66469621 66441775 64209451 62098185 61780148 [9] 61720044 60736950 Smallest eigenvalues: [1] 0.5314646 0.5099513 0.5099080 0.4973050 0.4577089 0.4410357 [7] 0.3009149 0.2989683 0.2120361 -0.0138035 Largest eigenvalues: [1] 79452910 73776748 70185105 68787719 67174984 65385856 63998128 63960675 [9] 63326930 62997863 Smallest eigenvalues: [1] 0.62493210 0.54725729 0.54327818 0.50156730 0.45121646 0.34538651 [7] 0.32638782 0.31876276 0.29815584 -0.04555588 Largest eigenvalues: [1] 76618357 72487579 69004664 67951299 66017218 64202249 62834942 62588284 [9] 62184932 61286842 Smallest eigenvalues: [1] 0.44078897 0.39139843 0.33659465 0.32896347 0.32197906 0.30968785 [7] 0.11162296 0.06384558 0.05809202 -1.05255301 Largest eigenvalues: [1] 77407628 71770446 68246119 67127652 66071967 64285362 62335156 62233380 [9] 61208716 60215649 Smallest eigenvalues: [1] 0.5263925 0.5188747 0.4577213 0.4524209 0.3546828 0.2752125 [7] 0.2539063 0.1666805 0.1617368 -0.2107332 Largest eigenvalues: [1] 76711786 72676320 69540517 67083898 66554204 64794139 62998451 62932216 [9] 62310847 61733304 Smallest eigenvalues: [1] 0.66481263 0.61482009 0.57523772 0.55175464 0.46494013 0.46226408 [7] 0.32666906 0.28826360 0.27784328 -0.06359557 Largest eigenvalues: [1] 76521100 72639045 68714086 67330102 66794859 64609065 63215306 62511510 [9] 62277628 61739928 Smallest eigenvalues: [1] 0.4986982 0.4279475 0.3961460 0.3905884 0.3350755 0.2597042 [7] 0.1955783 0.1518725 -0.3811265 -0.5243261 Largest eigenvalues: [1] 75980370 72551792 68500084 67136245 66173454 64407744 62346993 62125441 [9] 62114673 61126146 Smallest eigenvalues: [1] 0.5808036 0.5080080 0.3713764 0.3603891 0.3017764 0.2743892 [7] 0.2127487 0.1965267 0.1487910 -0.6944401 Largest eigenvalues: [1] 76897584 73355126 69750655 67473435 67302867 65417179 63246915 63028098 [9] 62431583 62004429 Smallest eigenvalues: [1] 0.3771406 0.3759812 0.3213990 0.2888245 0.2797256 0.2491324 [7] 0.1762963 0.1723401 0.1589532 -0.6173631 Largest eigenvalues: [1] 79046323 73295252 69607209 68381300 66840258 65095784 63559949 62856547 [9] 62628734 61455322 Smallest eigenvalues: [1] 0.53528264 0.53149011 0.48608870 0.43012781 0.41347810 0.31394941 [7] 0.21785592 0.20878756 0.06146585 -5.46813623 Largest eigenvalues: [1] 76290469 73070718 69381249 67298033 67046798 65215680 62928557 62867289 [9] 62205344 61657154 Smallest eigenvalues: [1] 0.66250390 0.61385810 0.55137979 0.54938417 0.50297337 0.45324812 [7] 0.37913765 0.33659068 -0.05761271 -0.12206886 Largest eigenvalues: [1] 75592215 72518838 68660255 66959070 66251459 64584417 62484978 61647906 [9] 61471263 60833785 Smallest eigenvalues: [1] 0.5849314 0.4373744 0.4091513 0.4010794 0.3815045 0.3560443 [7] 0.3373346 0.2877986 0.1450914 -1.4198170 Largest eigenvalues: [1] 77479604 73441696 69777301 68088435 66966636 65381673 63032728 62979445 [9] 62903511 61936537 Smallest eigenvalues: [1] 0.60557911 0.58484716 0.49393627 0.40280653 0.33287795 0.28972098 [7] 0.26601656 0.24841782 0.16388638 -0.05441307 Largest eigenvalues: [1] 77082156 73877017 69702471 68344600 67663697 66092828 63402700 63373197 [9] 62717161 61882140 Smallest eigenvalues: [1] 0.4889054 0.4871352 0.3191644 0.2962206 0.2906382 0.2786933 [7] 0.1662760 0.1265456 0.0657774 -0.3544348 Largest eigenvalues: [1] 78569694 73081345 69818041 68048219 66503846 64869983 63294435 63183628 [9] 62831383 62356103 Smallest eigenvalues: [1] 0.4756273 0.3934981 0.3874914 0.3440475 0.3134588 0.2927338 [7] 0.2740950 0.1973614 0.1959956 -0.3160029 Largest eigenvalues: [1] 77439127 73783931 69275346 68176072 67167841 65524213 63069362 62965066 [9] 62665077 61691586 Smallest eigenvalues: [1] 0.5063435 0.4917570 0.4443741 0.4362320 0.3029285 0.2605324 [7] 0.2520872 0.2459957 0.1044600 -0.1443511 Largest eigenvalues: [1] 76116027 72872160 68817488 66406472 66359732 64599828 62610965 61860263 [9] 61567110 61029715 Smallest eigenvalues: [1] 0.5290909 0.5083187 0.4665687 0.4234332 0.3736429 0.3054960 [7] 0.2335567 0.2270453 0.2116457 -0.1592977 Largest eigenvalues: [1] 77921759 72857949 69052171 68007068 66626653 64708125 63111426 63000426 [9] 62408304 61906800 Smallest eigenvalues: [1] 0.36661552 0.30929603 0.30742536 0.21494456 0.18134182 0.15057450 [7] 0.06002734 0.03195828 -0.06611011 -1.45526277 Largest eigenvalues: [1] 76614154 73331755 68923567 67435126 66884221 65180317 62888520 62602797 [9] 62060557 61622212 Smallest eigenvalues: [1] 0.4921167 0.3874164 0.3865490 0.2996914 0.2818525 0.2649377 [7] 0.1665864 0.1424315 0.0240136 -0.7258130 Largest eigenvalues: [1] 78149782 73620717 68703441 68392940 66734943 64560462 63457569 63002285 [9] 62769086 61616213 Smallest eigenvalues: [1] 0.54133226 0.47939196 0.47529224 0.44698848 0.43490710 0.40855642 [7] 0.28605858 0.28576910 0.21836058 -0.08238886 Largest eigenvalues: [1] 78220876 74062695 69384709 68038257 66855810 65067828 63037285 62984362 [9] 62490232 61693400 Smallest eigenvalues: [1] 0.5545459 0.5000074 0.4829989 0.3590129 0.3401603 0.3179716 [7] 0.2719059 0.2441626 0.2057473 -0.5421030 Largest eigenvalues: [1] 80489112 73477164 70392565 69607600 66787882 64862544 64811689 63843984 [9] 62815333 62305029 Smallest eigenvalues: [1] 0.65726321 0.63372687 0.62915262 0.47337714 0.36342521 0.34084810 [7] 0.28821564 0.23414021 0.20009144 -0.02142219 Largest eigenvalues: [1] 78984721 73516919 70004593 68436413 67120176 65214460 63637020 63605769 [9] 63086170 62326939 Smallest eigenvalues: [1] 0.6459865 0.6007240 0.5837996 0.5317114 0.4840707 0.3975918 [7] 0.3432262 0.2752723 0.2365726 -0.1149224 Largest eigenvalues: [1] 76186298 73137106 68662707 66929907 66904385 64778314 62789313 62429628 [9] 62029782 60954814 Smallest eigenvalues: [1] 0.41601355 0.40500918 0.39312189 0.34230354 0.33862652 0.29660024 [7] 0.27296627 0.19984604 0.03709052 -0.17789021 Largest eigenvalues: [1] 78788366 72220314 68704634 67920490 66241584 64367501 63094008 62782935 [9] 62401740 61739598 Smallest eigenvalues: [1] 0.4936840 0.4768644 0.4601447 0.4373802 0.4011646 0.3905537 [7] 0.3675231 0.2256587 -0.1364966 -1.2221878 Largest eigenvalues: [1] 78593286 72934108 69437870 68095433 66465923 64960650 63188327 62788460 [9] 62576967 61757346 Smallest eigenvalues: [1] 0.4427556 0.3518684 0.3170674 0.3041950 0.2530347 0.2177461 [7] 0.2037026 0.1886076 -0.1033008 -1.1603044 Largest eigenvalues: [1] 76391608 73948022 69751440 67659569 67414929 65901792 63651543 62837766 [9] 62616337 61748303 Smallest eigenvalues: [1] 0.51237604 0.49206066 0.42232257 0.39542546 0.35375987 0.33764933 [7] 0.31305289 0.21888474 0.15278400 -0.01144459 Largest eigenvalues: [1] 75144808 73235910 68655099 66743099 66149355 64965577 62722694 61580772 [9] 61120192 60692607 Smallest eigenvalues: [1] 0.4718915 0.4598640 0.4319729 0.3033941 0.2813592 0.2106465 [7] 0.2040379 0.1973647 -0.0501652 -1.6833649 Largest eigenvalues: [1] 79821936 74845410 70953182 69269966 67812576 66210710 64150178 64086565 [9] 63886077 62979316 Smallest eigenvalues: [1] 0.42923111 0.36939278 0.36411000 0.35084460 0.32337498 0.17725018 [7] 0.15312291 0.14547620 0.03321482 -0.07061571 Largest eigenvalues: [1] 76073107 73012740 69030440 66710402 66659338 65163082 62804458 62267529 [9] 61809913 61291701 Smallest eigenvalues: [1] 0.50733233 0.47407655 0.46170365 0.36481024 0.31770505 0.31603493 [7] 0.28670603 0.26559821 0.04709938 -0.60327226 Largest eigenvalues: [1] 77863969 72762349 69513834 67509929 66626572 65084528 62970628 62654396 [9] 62627947 61482228 Smallest eigenvalues: [1] 0.4665780 0.4438761 0.4409078 0.3138097 0.2494724 0.1996239 [7] -0.1891409 -0.2778360 -0.4473761 -1.9112227 Largest eigenvalues: [1] 77991741 72283868 68669492 68609516 65712985 63333096 63292635 62854444 [9] 62063437 61703054 Smallest eigenvalues: [1] 0.5457786 0.4659359 0.4465208 0.3980604 0.3579039 0.3550848 [7] 0.3425942 0.2554771 0.1533031 -0.5294102 Largest eigenvalues: [1] 77621762 73654559 70065271 67491687 66765709 65450796 63064068 62740847 [9] 62469800 61944286 Smallest eigenvalues: [1] 0.5093040 0.4525158 0.4406104 0.4210410 0.3436718 0.3380359 [7] 0.3199728 0.2061646 0.1537153 -0.9838352 Largest eigenvalues: [1] 77918892 72386125 69177196 68384773 66365883 64763653 63389419 62616996 [9] 62416252 61399950 Smallest eigenvalues: [1] 0.6005685 0.5557356 0.5551947 0.4810680 0.4710201 0.4104045 [7] 0.2809539 0.2286925 0.1828317 -0.4757996 Largest eigenvalues: [1] 76818195 72104379 68087691 67910726 65571185 63535607 62680589 62070470 [9] 62052357 60720316 Smallest eigenvalues: [1] 0.53121934 0.52352207 0.50841272 0.48808474 0.39277930 0.25357988 [7] 0.24704683 0.19446601 -0.06669131 -0.07913099 Largest eigenvalues: [1] 78199046 73507287 70170876 68808368 66975482 65333991 63562747 63415115 [9] 63378020 62075535 Smallest eigenvalues: [1] 0.54297918 0.41536686 0.37949719 0.36946249 0.34984323 0.33575353 [7] 0.31270920 0.28567660 0.06091615 -0.21260932 Largest eigenvalues: [1] 78163149 72798593 69570441 67243097 66506638 64878269 62498275 62481980 [9] 62355956 61550046 Smallest eigenvalues: [1] 0.37033329 0.35583734 0.26322290 0.25305384 0.21991260 0.11218478 [7] 0.09794139 0.06167154 -0.11005096 -0.45499641 Largest eigenvalues: [1] 76903246 72382656 68527707 67514262 66378832 64507244 62786897 62743626 [9] 62458906 61739738 Smallest eigenvalues: [1] 0.58800815 0.47419440 0.45919063 0.44037277 0.43657684 0.39258567 [7] 0.32954546 0.03262054 -0.06081041 -1.76203112 Largest eigenvalues: [1] 76347601 72048439 68477843 66633519 66301830 64619976 62367438 62082282 [9] 61436158 61023055 Smallest eigenvalues: [1] 0.462468722 0.458260595 0.384875201 0.367824485 0.344428880 [6] 0.218181970 0.191450396 0.093459614 0.007381912 -1.490534726 Largest eigenvalues: [1] 75119060 71992941 68606489 66176769 65742500 64684789 62752958 61602556 [9] 60868476 60653622 Smallest eigenvalues: [1] 0.56185265 0.54210568 0.47569234 0.45346800 0.42957012 0.38267164 [7] 0.38170993 0.25325944 0.15563271 -0.08828515 Largest eigenvalues: [1] 76114204 72236477 68468808 66977473 66021288 64188532 62534459 62054612 [9] 61942949 61138690 Smallest eigenvalues: [1] 0.4558232 0.4175097 0.3537204 0.3339841 0.2475841 0.2404107 [7] 0.1705162 0.1629028 0.1259151 -0.7633733 Largest eigenvalues: [1] 76522352 73175556 68715340 67398000 66647724 64854902 62531633 62498188 [9] 62254823 61309372 Smallest eigenvalues: [1] 0.5586266 0.5526287 0.4921719 0.4743769 0.4549045 0.4038731 [7] 0.3984109 0.3567929 0.3081261 -0.3016955 Largest eigenvalues: [1] 77164127 72405142 68644424 67247483 66323766 64512420 62576539 62342721 [9] 62162601 61153769 Smallest eigenvalues: [1] 0.48716308 0.41673406 0.38688070 0.30490397 0.26953392 0.23240527 [7] 0.17863313 0.02669953 -0.19969091 -0.25657171 Largest eigenvalues: [1] 78615891 74070376 70083665 68633058 67030476 65372267 63610619 63436103 [9] 63127338 62295644 Smallest eigenvalues: [1] 0.4873156 0.4634307 0.3578956 0.3331954 0.3233987 0.3123022 [7] 0.3022186 0.2715007 0.2501837 -0.4576190 Largest eigenvalues: [1] 78233313 72792404 68725412 67666840 66373338 64675584 62862872 62745200 [9] 62559873 61790179 Smallest eigenvalues: [1] 0.4564734 0.4240905 0.3443727 0.3325794 0.3324423 0.2588955 [7] 0.0984446 -0.1178044 -0.3719748 -0.7488622 Largest eigenvalues: [1] 81008761 73593516 69947139 69236475 66765745 64773360 64346571 63198531 [9] 63100040 62325457 Smallest eigenvalues: [1] 0.61259029 0.60732951 0.53437352 0.51495381 0.49212834 0.48904099 [7] 0.42842757 0.28460105 0.06857686 -2.04336368 Largest eigenvalues: [1] 77174875 73176116 69039870 67324842 66791462 65322684 63019009 62601322 [9] 62116748 61384826 Smallest eigenvalues: [1] 0.54933576 0.51380417 0.47782596 0.45551969 0.34510490 0.27095388 [7] 0.26813065 0.16104296 0.04072443 -0.75864868 Largest eigenvalues: [1] 77302252 73788277 69019137 67819871 66950020 65033327 62818595 62788717 [9] 62748066 61632728 Smallest eigenvalues: [1] 0.53138711 0.48911246 0.43675105 0.31482460 0.31072777 0.27613402 [7] 0.21496107 0.20197270 0.04715298 -0.19892965 Largest eigenvalues: [1] 76923241 73568837 70223084 67712402 67443893 65699500 63085515 63008554 [9] 62587232 61668685 Smallest eigenvalues: [1] 0.450209051 0.387324373 0.345866689 0.312662494 0.262500846 [6] 0.189234073 0.114228042 0.107244635 0.004308756 -0.934283239 Largest eigenvalues: [1] 75335410 72822865 69056538 66751085 66411379 64903946 62926640 62650423 [9] 61798905 61295707 Smallest eigenvalues: [1] 0.46065008 0.38197056 0.37204965 0.24824824 0.19054875 0.16490394 [7] 0.13560523 0.06256524 -0.17225380 -0.38723394 Largest eigenvalues: [1] 78127038 73373341 69659402 68820583 66779986 64749362 63513055 63201667 [9] 63020051 61932825 Smallest eigenvalues: [1] 0.65055514 0.63948990 0.57695358 0.49846813 0.48689460 0.43348191 [7] 0.34916637 0.27806090 0.12219865 -0.06065522 Largest eigenvalues: [1] 77695685 73248927 69300254 67073388 67026651 65088235 63092794 62394679 [9] 62168719 61799383 Smallest eigenvalues: [1] 0.38924135 0.35406052 0.33624003 0.32778739 0.27307669 0.24953740 [7] 0.23083767 0.22453287 0.07673283 -0.16541260 Largest eigenvalues: [1] 77224373 72860050 69358852 67554650 66666579 64991839 62571459 62549027 [9] 62267392 61051816 Smallest eigenvalues: [1] 0.5454172 0.5121232 0.4688329 0.4488098 0.4352464 0.2476439 [7] 0.2161434 0.1609220 0.1474564 -0.3959362 Largest eigenvalues: [1] 76253037 73535358 68774299 67382563 67093461 65178198 63037789 63018777 [9] 62401626 61727434 Smallest eigenvalues: [1] 0.4822018 0.4638746 0.4171191 0.4152838 0.3777053 0.3422812 [7] 0.3157871 0.2568775 0.1127558 -1.3095284 Largest eigenvalues: [1] 78660348 73972129 70082224 67926583 67558139 65751680 63261163 63114731 [9] 63047887 61828539 Smallest eigenvalues: [1] 0.5431078 0.5156256 0.4900267 0.4309330 0.4055578 0.3429571 [7] 0.3182595 0.2991290 0.2025225 -0.4265298 Largest eigenvalues: [1] 76025408 72781770 68831800 67443401 65972578 64210560 62760126 62355615 [9] 62085119 61523239 Smallest eigenvalues: [1] 0.5879611 0.5474388 0.5452024 0.5173931 0.4511520 0.4371621 [7] 0.4250925 0.2970864 0.2721661 -2.2219751 Largest eigenvalues: [1] 77440981 72354695 68579039 67242930 66414268 64664791 62489303 62339734 [9] 61902910 60960867 Smallest eigenvalues: [1] 0.5374780 0.5261551 0.3962173 0.3884212 0.3457020 0.3373046 [7] 0.2938120 0.2765028 -1.4034296 -3.9998523 Largest eigenvalues: [1] 77243963 72379382 68674264 67351456 66002575 64129342 62524157 62336532 [9] 61957453 60907053 Smallest eigenvalues: [1] 0.4390944 0.4101958 0.3236849 0.2805306 0.1679936 0.1191453 [7] -0.1844365 -0.2358975 -0.2858668 -2.4409963 Largest eigenvalues: [1] 77448658 73478825 69033967 67546738 67346516 65247356 63085100 62761462 [9] 62559450 61619587 Smallest eigenvalues: [1] 0.4362494 0.4227834 0.3921364 0.3919615 0.3392415 0.1479311 [7] 0.1215385 0.1061132 -0.4301498 -5.0122493 Largest eigenvalues: [1] 78144621 72430461 68805071 68331448 65668179 63833683 63402547 61758693 [9] 61686819 60522687 Smallest eigenvalues: [1] 0.47435807 0.43846313 0.39823452 0.26458360 0.18921173 0.15851571 [7] 0.07700463 0.07628123 -0.14747611 -2.66543543 Largest eigenvalues: [1] 75479584 73126834 68691725 66839234 66805937 64583628 62558375 62239965 [9] 61889835 61087434 Smallest eigenvalues: [1] 0.5690132 0.5624336 0.5174906 0.5023219 0.4833315 0.4825813 [7] 0.4018707 0.2944678 0.0840317 -1.0725444 Largest eigenvalues: [1] 77949808 72900188 68808576 67696128 65872921 63978078 62735646 62327947 [9] 62174550 61268892 Smallest eigenvalues: [1] 0.49092776 0.39831489 0.30697338 0.26844569 0.26257969 0.25445088 [7] 0.21259636 0.18645773 0.09680648 -0.71640440 Largest eigenvalues: [1] 77321785 72972348 69500644 67470128 66421233 64928512 62835540 62529297 [9] 62341889 61261093 Smallest eigenvalues: [1] 0.5267426 0.5003280 0.4498634 0.4147667 0.3943344 0.3842105 [7] 0.3654035 0.2999557 0.2691700 -0.2470747 Largest eigenvalues: [1] 79295243 73286238 70155096 69250248 66176346 64283158 64258978 62788191 [9] 62710673 61507240 Smallest eigenvalues: [1] 0.5714748 0.5659922 0.5297997 0.4990577 0.4879146 0.3859968 [7] 0.3858936 0.3337741 0.3037146 -4.8679987 Largest eigenvalues: [1] 77808567 72678402 69451539 67947524 66507960 64482159 62953675 62912890 [9] 62818298 61745998 Smallest eigenvalues: [1] 0.5550625 0.5030966 0.4304122 0.3967658 0.3591304 0.3140145 [7] 0.2905319 0.2775589 0.1135046 -0.1202976 Largest eigenvalues: [1] 78779761 74022729 69580835 69042604 67136333 65101346 63906262 63286988 [9] 63137985 61966041 Smallest eigenvalues: [1] 0.45590828 0.42587567 0.42064033 0.32102977 0.28763047 0.28511791 [7] 0.18366720 0.08301284 -0.82424471 -1.39875366 Largest eigenvalues: [1] 78076541 72600351 68699186 67927442 66485792 64685170 63015024 62906673 [9] 62802724 61774215 Smallest eigenvalues: [1] 0.57223432 0.56155580 0.51187072 0.48836899 0.42566460 0.41770339 [7] 0.33753361 0.32969244 0.29033880 -0.04521633 Largest eigenvalues: [1] 77440525 73164670 69008119 67662592 66730965 64652948 62851513 62608601 [9] 62484465 61137116 Smallest eigenvalues: [1] 0.4309983 0.3854496 0.3101752 0.3016417 0.2868240 0.2749075 [7] 0.2681891 0.2323112 0.2019840 -4.6883570 Largest eigenvalues: [1] 78817525 72809567 69050273 68324764 66434975 64699277 63248340 62352098 [9] 61906500 61117218 Smallest eigenvalues: [1] 0.57014534 0.56999401 0.46839676 0.40722292 0.39586910 0.34939015 [7] 0.30774642 0.21335055 0.11245027 -0.04889715 Largest eigenvalues: [1] 76793785 72756876 69335326 67556719 67181668 65432748 63075676 62771717 [9] 62538730 61376045 Smallest eigenvalues: [1] 0.56157162 0.55345822 0.39768083 0.30109046 0.28117137 0.21573065 [7] 0.08772619 -0.08414587 -0.44556665 -3.96076640 Largest eigenvalues: [1] 75835747 72712896 68345040 66641860 66488997 64505396 62372843 62033571 [9] 61728032 60693284 Smallest eigenvalues: [1] 0.51231421 0.43720980 0.41390860 0.32884426 0.32457900 0.24896340 [7] 0.14033167 0.12409762 0.08540747 -0.01180093 Largest eigenvalues: [1] 77021970 73526232 69489148 67561252 67202321 65203589 63151274 62893230 [9] 62714357 61717386 Smallest eigenvalues: [1] 0.44114998 0.39718736 0.39457352 0.29246040 0.29168453 0.21714202 [7] 0.20910741 0.18015633 0.05915063 -0.82093623 Largest eigenvalues: [1] 78186596 72843502 69382182 68021337 66719572 65068334 63170432 63159926 [9] 62847720 61873077 Smallest eigenvalues: [1] 0.620839191 0.609358141 0.607164033 0.588918505 0.561933872 [6] 0.484724508 0.362748018 0.274671470 0.007115184 -0.108696136 Largest eigenvalues: [1] 77792054 72563708 68348978 67599089 66002906 64110999 62583913 62133295 [9] 62014294 60891324 Smallest eigenvalues: [1] 0.48207010 0.43605004 0.42390392 0.34608546 0.34431323 0.32367444 [7] 0.22749647 0.12896035 0.06031848 -0.06142068 Largest eigenvalues: [1] 77103566 73421072 69908512 67154513 66874728 65139712 63125258 62911216 [9] 62496111 62135966 Smallest eigenvalues: [1] 0.56386231 0.49010969 0.44567713 0.36613244 0.31024201 0.29172466 [7] 0.28609594 0.14938307 0.06674204 -0.16239646 Largest eigenvalues: [1] 75172499 71938678 67873050 66378199 65807369 63930545 62517447 61344883 [9] 61195648 60245701 Smallest eigenvalues: [1] 0.6140533 0.5663002 0.5339815 0.5015216 0.4524964 0.2906862 [7] 0.2614498 0.2572475 0.1151126 -2.0149106 Largest eigenvalues: [1] 78809648 72643690 68381502 67823691 66154676 64001727 62972114 62144268 [9] 62064217 61088426 Smallest eigenvalues: [1] 0.61249014 0.51066459 0.44075614 0.43326336 0.40590562 0.30874055 [7] 0.28790049 0.11973603 0.02216328 -0.22931091 Largest eigenvalues: [1] 77452523 71865557 68878623 66840429 65892875 64237251 62771468 62383656 [9] 62068803 61294485 Smallest eigenvalues: [1] 0.53417849 0.49160453 0.47306168 0.35434021 0.32456402 0.28922058 [7] 0.26048013 0.17016350 0.03051261 -0.98324248 Largest eigenvalues: [1] 77559002 73639210 69907307 67938769 67396403 65684523 63149606 63083866 [9] 62812306 61992695 Smallest eigenvalues: [1] 0.6061415 0.5926390 0.5775080 0.5340179 0.4602865 0.4169953 [7] 0.4052033 0.3995662 0.1617461 -0.2125210 Largest eigenvalues: [1] 76293856 73042794 68773258 66743819 66442307 64856334 62206908 61778175 [9] 61432513 60396119 Smallest eigenvalues: [1] 0.4412863 0.4109118 0.3166150 0.3163672 0.2989847 0.2871846 [7] 0.1941897 0.1632140 -0.1467563 -1.1975323 Largest eigenvalues: [1] 76301322 72263329 68914488 66271035 66204766 64565208 62556004 61860869 [9] 61533455 60983386 Smallest eigenvalues: [1] 0.5691553 0.5157491 0.4919878 0.4840066 0.4179316 0.3777640 [7] 0.3773019 0.2771862 0.1276372 -1.1243563 Largest eigenvalues: [1] 80597930 73528841 69650624 69636491 66638645 64806593 64697809 63075705 [9] 62379982 61813164 Smallest eigenvalues: [1] 0.3956271 0.3690453 0.3683855 0.3504359 0.3434293 0.3321634 [7] 0.3289036 0.2912993 -0.0645717 -0.6684154 Largest eigenvalues: [1] 77761812 71864490 68418187 67854988 65558741 63911767 62896895 61859479 [9] 61831803 60807047 Smallest eigenvalues: [1] 0.25561160 0.19199105 0.05578501 -0.08400762 -0.09385599 -0.12955829 [7] -0.29443055 -0.78802726 -1.91587164 -2.27110083 Largest eigenvalues: [1] 77492520 72721206 68496216 66744056 66548065 64535940 62174270 62124799 [9] 61546188 60512047 Smallest eigenvalues: [1] 0.43005554 0.39099119 0.38472014 0.35721923 0.28251602 0.26128319 [7] 0.23158714 0.15949365 0.04091214 -1.06838284 Largest eigenvalues: [1] 78993951 73776301 69931542 69342701 66824665 64944804 64072174 63018735 [9] 62869296 61392187 Smallest eigenvalues: [1] 0.5123177 0.4892354 0.4675663 0.4553410 0.4515061 0.3900092 [7] 0.3750508 0.2300491 0.2153575 -0.1058415 Largest eigenvalues: [1] 79328226 73148351 69121125 67887313 66369976 64589793 63074643 62594801 [9] 62135293 61435334 Smallest eigenvalues: [1] 0.58377311 0.38880435 0.36742986 0.30941403 0.28914541 0.28003175 [7] 0.25621181 0.24570699 -0.03180994 -0.18301966 Largest eigenvalues: [1] 77918841 72771832 69590585 67556425 66601890 64898021 62636918 62618194 [9] 62510925 61672163 Smallest eigenvalues: [1] 0.42900861 0.41469112 0.36415341 0.32716474 0.32262251 0.25962546 [7] 0.23365289 0.18822705 -0.02816767 -0.10050295 Largest eigenvalues: [1] 77681408 73233545 69715983 67977900 66451537 64966095 63143309 62705037 [9] 62645625 61631037 Smallest eigenvalues: [1] 0.5353399 0.4847759 0.4563426 0.4389034 0.3921929 0.3666990 [7] 0.3492315 0.3293210 0.3112218 -0.1497576 Largest eigenvalues: [1] 77656398 74593542 69539397 68245956 67827554 65755209 63671387 63299228 [9] 62911144 61929572 Smallest eigenvalues: [1] 0.46591329 0.43152608 0.39676502 0.35592323 0.19940832 0.19915334 [7] 0.18260512 0.07678048 -0.07790773 -1.20175538 Largest eigenvalues: [1] 76778804 73631691 69947261 67762294 67189780 65675074 63292927 63210912 [9] 62622005 62205858 Smallest eigenvalues: [1] 0.62480026 0.60513308 0.55196867 0.53033567 0.48448632 0.43275462 [7] 0.32394105 0.12982561 -0.01749487 -0.10350376 Largest eigenvalues: [1] 76458170 73398599 68889334 67505637 67191310 65104501 63101995 62816218 [9] 62405583 61609613 Smallest eigenvalues: [1] 0.64714521 0.59426285 0.55144251 0.52421489 0.42198160 0.41509051 [7] 0.35198326 0.32684698 0.24387414 -0.03852206 Largest eigenvalues: [1] 78804107 73246741 69777659 67845249 66649360 64846591 63201730 62847511 [9] 62768347 62043968 Smallest eigenvalues: [1] 0.6139472 0.5714996 0.5651013 0.4774128 0.4559986 0.3474347 [7] 0.2926480 0.2675503 0.2584136 -1.0274554 Largest eigenvalues: [1] 76168656 73420530 69713342 67851847 66319162 65812841 63075959 62831442 [9] 61634652 61419471 Smallest eigenvalues: [1] 0.6487596 0.5662867 0.5124077 0.4836117 0.4665970 0.4044605 [7] 0.3796887 0.3588218 0.3033458 -0.5544879 Largest eigenvalues: [1] 77312991 73239310 69420686 67655170 66787426 65175534 62739503 62679570 [9] 62570031 61223341 Smallest eigenvalues: [1] 0.44763154 0.32006305 0.24821560 0.21930577 0.20857028 0.20600399 [7] 0.19452043 0.17926576 0.02588723 -3.48592062 Largest eigenvalues: [1] 78174492 74274802 69600866 67979355 67953685 65708247 64033944 63255929 [9] 63017997 62323954 Smallest eigenvalues: [1] 0.4522870 0.3420022 0.3294172 0.2924992 0.2899649 0.2431163 [7] 0.2184490 0.1938031 -0.1118705 -0.1505184 Largest eigenvalues: [1] 75995136 73619866 69245030 67162482 67128298 65416174 62996981 62702071 [9] 62020699 61417516 Smallest eigenvalues: [1] 0.4408793 0.4143093 0.3867732 0.3717432 0.3544544 0.3113710 [7] 0.2538062 0.2304832 0.2299398 -1.7512971 Largest eigenvalues: [1] 76309447 72625093 69211336 66864117 66168676 64811638 62639840 62124724 [9] 61916578 60905823 Smallest eigenvalues: [1] 0.3871649 0.3866981 0.2845997 0.2751389 0.2691283 0.2541871 [7] 0.2244560 0.1785875 0.1504328 -0.8205520 Largest eigenvalues: [1] 75933364 72749454 69251078 67307196 66130146 65128035 62726089 62139898 [9] 61383913 61238680 Smallest eigenvalues: [1] 0.66379908 0.56369598 0.55378139 0.48895366 0.44513755 0.39976995 [7] 0.39401013 0.30423142 0.01102191 -0.16057403 Largest eigenvalues: [1] 77209301 72661909 68743964 66701442 66581966 64746424 62445223 62410813 [9] 61817813 61367621 Smallest eigenvalues: [1] 0.53969104 0.52514344 0.51888726 0.44975055 0.35731474 0.35333462 [7] 0.31962477 0.05674661 0.05330030 -0.13488868 Largest eigenvalues: [1] 79304943 72511743 69152577 68879948 65864215 64047427 63980852 62444056 [9] 62083382 61223406 Smallest eigenvalues: [1] 0.5625119 0.5618533 0.4480813 0.3491762 0.2960418 0.2802478 [7] 0.2369759 0.1761882 -0.2342997 -2.7985405 Largest eigenvalues: [1] 77018686 73195081 69356420 67683581 67524846 65419626 63259482 63092624 [9] 62677446 61770599 Smallest eigenvalues: [1] 0.4758027 0.4690746 0.4596764 0.3278722 0.3099201 0.2564229 [7] 0.2147827 0.2002084 0.1903071 -0.1661220 Largest eigenvalues: [1] 76840837 73043205 68954570 66946938 66933981 64942480 63382208 62375250 [9] 62208448 62046150 Smallest eigenvalues: [1] 0.56857179 0.55762304 0.51816198 0.51441940 0.42126750 0.36025253 [7] 0.26044192 0.10327385 0.03049733 -0.41771515 Largest eigenvalues: [1] 76763513 72526017 68341178 66483962 66172828 64342221 62516390 61872525 [9] 61567251 60740125 Smallest eigenvalues: [1] 0.60619468 0.56912519 0.44207088 0.43665430 0.35488570 0.34680123 [7] 0.34395596 0.20934721 0.17916758 -0.06712159 Largest eigenvalues: [1] 79543828 72995115 70252688 67915245 66822344 64938175 63381227 63144347 [9] 62896144 62026618 Smallest eigenvalues: [1] 0.391872059 0.346943438 0.306831079 0.248936693 0.176147351 [6] 0.161945936 0.085446831 -0.005224048 -1.591494846 -3.523358608 Largest eigenvalues: [1] 77625987 73672519 69140991 67660221 67141197 65272522 62836106 62733643 [9] 62695319 61134305 Smallest eigenvalues: [1] 0.58624856 0.50319283 0.48965830 0.40719522 0.34626416 0.32198924 [7] 0.32066355 0.21456688 0.02324773 -0.26126780 Largest eigenvalues: [1] 77337773 72985829 68621789 67919231 66891503 64615683 63153088 63016640 [9] 62968181 62061069 Smallest eigenvalues: [1] 0.5447100 0.5074686 0.4980952 0.3507184 0.3380460 0.2235333 [7] 0.2037923 0.1955483 0.1145680 -3.2715633 Largest eigenvalues: [1] 77884762 73205619 69738142 67788459 66784096 65134140 63353127 63016470 [9] 62859270 61902937 Smallest eigenvalues: [1] 0.38224516 0.36813648 0.32757812 0.31609990 0.18094652 0.16525861 [7] 0.15823609 0.09153871 -0.16031953 -1.23990224 Largest eigenvalues: [1] 75380603 71409378 67972803 66186916 65819326 64408106 62746070 61316252 [9] 61010876 60530086 Smallest eigenvalues: [1] 0.3963042 0.3815812 0.3780751 0.3532953 0.2955249 0.2723363 [7] 0.1993975 0.1231163 -0.5349240 -0.9470528 Largest eigenvalues: [1] 77158413 72603113 68939281 67123321 66831222 65085062 62864075 62152174 [9] 62114098 61352429 Smallest eigenvalues: [1] 0.64840843 0.59417961 0.58796697 0.56846007 0.50040726 0.41780735 [7] 0.40888457 0.33034943 0.26697137 -0.04809979 Largest eigenvalues: [1] 78925455 73510460 69608373 68583636 66873501 64779746 63648296 63520116 [9] 62519769 61751418 Smallest eigenvalues: [1] 0.5885231 0.5196572 0.4871509 0.4705961 0.4378345 0.4221957 [7] 0.3939678 0.3106384 0.1959882 -0.1588607 Largest eigenvalues: [1] 78174678 73318784 69139051 68464811 66786672 64694341 63423405 62688505 [9] 62566194 61378212 Smallest eigenvalues: [1] 0.54363480 0.48619311 0.39394658 0.37988594 0.36749875 0.29077311 [7] 0.24297921 0.23166426 0.09832125 -0.10056106 Largest eigenvalues: [1] 76164835 72574722 68869727 66488981 66470566 64856372 62480109 62240834 [9] 61771553 61025355 Smallest eigenvalues: [1] 0.6595562 0.4778347 0.4777201 0.4560887 0.4447419 0.4439584 [7] 0.2804740 0.2065923 0.1723538 -0.6803653 Largest eigenvalues: [1] 79125120 73674378 69844261 68694087 66991856 65199841 63827488 63224284 [9] 62768620 62118346 Smallest eigenvalues: [1] 0.45792189 0.39662118 0.37191523 0.31746304 0.30048376 0.24817395 [7] 0.20698871 0.18659572 -0.03312312 -0.40503549 Largest eigenvalues: [1] 75502679 72296464 68629433 66273809 66140496 64531817 62432670 61908921 [9] 61048234 60777864 Smallest eigenvalues: [1] 0.60609753 0.48724689 0.40113697 0.37713882 0.31929558 0.21679750 [7] 0.17819190 0.17586278 0.04652941 -0.89972217 Largest eigenvalues: [1] 77471304 73210388 69640486 67522013 67144886 65328302 63524970 63316019 [9] 62551649 62313623 Smallest eigenvalues: [1] 0.70633069 0.63494042 0.52931937 0.51913596 0.49005110 0.45592691 [7] 0.37259819 0.35509308 0.08805054 -0.02293542 Largest eigenvalues: [1] 77107759 72542812 68583888 67506772 66221056 64252207 62571772 62395162 [9] 61905672 60723747 Smallest eigenvalues: [1] 0.5510777 0.4770974 0.4336779 0.3571755 0.3092820 0.2673447 [7] 0.2257909 0.2223011 0.1467407 -0.4736243 Largest eigenvalues: [1] 77738677 73772435 70099453 67686081 67537435 66248158 63742037 63251858 [9] 62687434 62193013 Smallest eigenvalues: [1] 0.38149718 0.31375098 0.23357183 0.15160711 0.13841068 0.12866970 [7] 0.09644159 0.04793429 -0.09238711 -0.20647185 Largest eigenvalues: [1] 74847175 72082885 68694949 67467830 65418051 65253126 63481225 61944673 [9] 61192914 61107086 Smallest eigenvalues: [1] 0.6245867 0.5796973 0.5190614 0.4325398 0.4214267 0.3978798 [7] 0.2926305 0.2460852 0.2409765 -1.5287758 Largest eigenvalues: [1] 77003044 73049864 69670203 67423669 67115769 65230995 63104300 63092017 [9] 62549201 61780050 Smallest eigenvalues: [1] 0.56079886 0.48858244 0.42706765 0.40608031 0.33983060 0.32964365 [7] 0.15826571 0.09026625 -0.04051922 -3.60849557 Largest eigenvalues: [1] 78911742 74229416 69819436 68577694 67418238 65310360 63962879 63688099 [9] 62900065 62365426 Smallest eigenvalues: [1] 0.60761826 0.52532968 0.46784554 0.46684787 0.40514918 0.33644806 [7] 0.33215359 0.20057026 0.14943476 -0.08340087 Largest eigenvalues: [1] 77093939 73605575 70064884 67337139 67070127 65444729 63420411 63169131 [9] 62631460 62158947 Smallest eigenvalues: [1] 0.4913825 0.4056712 0.3876215 0.3656003 0.3397728 0.3386400 [7] 0.3006801 0.2402215 0.2224611 -0.5915374 Largest eigenvalues: [1] 78278016 73185278 69577023 68349020 66386509 65043649 63286249 62704394 [9] 62380101 61438272 Smallest eigenvalues: [1] 0.48108982 0.47874154 0.42974418 0.41663263 0.33642249 0.31500940 [7] 0.17850291 0.14395950 0.03105633 -0.80111875 Largest eigenvalues: [1] 77657957 73440724 69543981 67937165 67240138 65511561 63648292 63193387 [9] 62725763 62100080 Smallest eigenvalues: [1] 0.6018141 0.5747620 0.5360249 0.4699175 0.4574797 0.4204036 [7] 0.4152570 0.2483100 0.1915887 -0.2923571 Largest eigenvalues: [1] 78065294 73277054 69399943 68059630 67245411 65088224 63412982 63222595 [9] 62829993 62127024 Smallest eigenvalues: [1] 0.63657869 0.58091123 0.47309795 0.46059524 0.41269535 0.34760522 [7] 0.34146028 0.19837766 0.06876946 -0.13168017 Largest eigenvalues: [1] 77899343 73614501 69444555 68110459 66799056 64969615 62970056 62770045 [9] 62610825 61501361 Smallest eigenvalues: [1] 0.4357575 0.3732435 0.3645624 0.3592569 0.3552020 0.3080500 [7] 0.2362022 0.1493750 -0.2002752 -2.0315635 Largest eigenvalues: [1] 78748565 73643944 69582593 68016762 66860298 65045573 63099151 62925793 [9] 62360766 61736742 Smallest eigenvalues: [1] 0.42481389 0.37432981 0.32187572 0.27197142 0.26573855 0.16092107 [7] 0.15336440 0.09317395 -0.06051743 -0.37033048 Largest eigenvalues: [1] 75711576 73474133 69615062 68381703 66238846 66083098 63634738 62843787 [9] 61661142 61360370 Smallest eigenvalues: [1] 0.5150574 0.4418686 0.4315439 0.4065888 0.3936410 0.3628619 [7] 0.2642223 0.2554318 0.2273828 -0.3865907 Largest eigenvalues: [1] 77167953 72562780 69275995 67936711 66358637 64458365 62923506 62647748 [9] 62509635 61541565 Smallest eigenvalues: [1] 0.4858002 0.4430913 0.4427014 0.4333576 0.3698012 0.3160379 [7] 0.2470549 0.2347776 -0.0347408 -0.3396567 Largest eigenvalues: [1] 75647342 72808046 68767115 67600272 66327972 65565166 63383275 61923155 [9] 61357546 61174884 Smallest eigenvalues: [1] 0.5665954 0.5388154 0.5199074 0.4277300 0.3997629 0.3427671 [7] 0.3306028 0.3027589 0.2764340 -0.7217431 Largest eigenvalues: [1] 76314903 73244073 68898219 66633340 66204347 64881948 62449174 62287504 [9] 61460890 61023903 Smallest eigenvalues: [1] 0.45718424 0.43970941 0.42923825 0.41499432 0.35557182 0.30087818 [7] 0.24246061 0.16345236 0.15193504 -0.07529902 Largest eigenvalues: [1] 76839816 73110856 69137821 66836645 66808408 64900844 63181676 62580347 [9] 62121421 61954764 Smallest eigenvalues: [1] 0.55903247 0.43355265 0.41496691 0.35873062 0.25666566 0.22644578 [7] 0.21554201 -0.05872214 -0.14301698 -0.39092403 Largest eigenvalues: [1] 78257825 73878317 70068444 67692061 67422703 65379324 63828005 63364274 [9] 63001168 62536479 Smallest eigenvalues: [1] 0.5408855 0.5147532 0.4866786 0.4243199 0.3457209 0.2782114 [7] 0.2743892 0.2210687 -0.3567955 -0.4170453 Largest eigenvalues: [1] 74828492 72106498 68418413 66507689 65996805 64265131 62600164 62327676 [9] 61253172 61178835 Smallest eigenvalues: [1] 0.673295193 0.574687077 0.540907735 0.502479163 0.367132647 [6] 0.223768030 0.201976435 0.159635409 -0.002899571 -0.266462213 Largest eigenvalues: [1] 75424260 73488624 69225364 67815960 66402582 65761639 63391798 63155673 [9] 61803281 61568243 Smallest eigenvalues: [1] 0.62746579 0.47622804 0.46088100 0.45061645 0.41257205 0.35507743 [7] 0.35081756 0.27222403 0.24943780 -0.04448669 Largest eigenvalues: [1] 76409113 73661609 68976906 67297743 67129175 65208875 62911705 62640918 [9] 62185613 61584288 Smallest eigenvalues: [1] 0.428332447 0.424640594 0.412452830 0.334091949 0.238696832 [6] 0.169365802 0.057118720 -0.006385144 -1.970289263 -5.042083032 Largest eigenvalues: [1] 76401266 72126884 68019348 66106222 66082281 64278609 62268223 62086039 [9] 61249800 61123150 Smallest eigenvalues: [1] 0.512802957 0.506701441 0.370299085 0.366171296 0.270104741 [6] 0.264633710 0.224598365 0.133455707 -0.007253256 -0.182442936 Largest eigenvalues: [1] 74425306 72344030 68952509 66328090 66220749 64493755 62491971 62362428 [9] 61336897 61166965 Smallest eigenvalues: [1] 0.6417037 0.6305799 0.6238270 0.5460037 0.5280871 0.4901620 [7] 0.4179043 0.2256567 0.2035596 -0.1511069 Largest eigenvalues: [1] 75421311 72218935 68140691 66546956 66349631 64256356 62324059 62228651 [9] 61355438 60817106 Smallest eigenvalues: [1] 0.51198871 0.47889834 0.47494702 0.41150978 0.33735183 0.26968989 [7] 0.24466367 0.14355934 0.04110170 -0.08871892 Largest eigenvalues: [1] 76328620 73072469 68721748 67797823 66733804 64602034 62725627 62635597 [9] 62572768 61185235 Smallest eigenvalues: [1] 0.39879439 0.34658969 0.34227974 0.29372074 0.29067076 0.24536202 [7] 0.24052590 0.22984693 0.21242451 -0.05608962 Largest eigenvalues: [1] 78351475 72087716 68999413 67775322 66103863 64381376 62813393 62356925 [9] 62213554 61434482 Smallest eigenvalues: [1] 0.46634621 0.44696700 0.44444587 0.38904494 0.30970307 0.27971186 [7] 0.15933218 0.15497750 -0.02103619 -1.02261753 Largest eigenvalues: [1] 77825658 72707307 68657619 68070980 66507194 64221102 63347452 62681138 [9] 62603727 61501486 Smallest eigenvalues: [1] 0.5808877 0.5248201 0.5037546 0.4978299 0.4760031 0.3534811 [7] 0.3283899 0.2494806 0.1460201 -1.3094150 Largest eigenvalues: [1] 76850523 72020378 68443319 66873665 65855099 63966071 62201628 61971705 [9] 61210962 60434400 Smallest eigenvalues: [1] 0.56257182 0.51946762 0.50874171 0.39533392 0.34884421 0.33854308 [7] 0.32399011 0.30889323 0.07327141 -0.27709396 Largest eigenvalues: [1] 76723834 72791755 68701360 67196088 66191959 64499532 62444383 62039791 [9] 61560440 60507109 Smallest eigenvalues: [1] 0.588199818 0.490744505 0.456928410 0.425199350 0.413628178 [6] 0.369664623 0.314389492 0.256124619 0.228927080 -0.007538688 Largest eigenvalues: [1] 75643366 72063305 68483211 66468486 66354008 64606047 62554869 61887994 [9] 61546499 60935552 Smallest eigenvalues: [1] 0.46849108 0.42356648 0.37590507 0.36593631 0.25564229 0.24939259 [7] 0.16839968 0.13375163 0.08418436 -0.11394377 Largest eigenvalues: [1] 76837552 72672298 69674492 67392149 66894653 65198267 62927638 62688409 [9] 62404220 61564771 Smallest eigenvalues: [1] 0.56497103 0.53176070 0.47957386 0.45403140 0.43282968 0.38617789 [7] 0.35841508 0.25000242 -0.03736873 -0.10142668 Largest eigenvalues: [1] 79351341 72323046 69527511 68291631 66037286 63999196 63523577 62733240 [9] 61993228 61609933 Smallest eigenvalues: [1] 0.51974607 0.43813118 0.43121073 0.42081449 0.40181562 0.39122910 [7] 0.38306838 0.36081799 0.04807745 -2.20500574 Largest eigenvalues: [1] 79087459 72503441 69042285 68596155 65871573 64124110 63635253 62357322 [9] 61819075 60996272 Smallest eigenvalues: [1] 0.4245323 0.3806241 0.3748610 0.3684958 0.3266432 0.3014496 [7] 0.2646318 0.2438948 0.1678264 -1.0569654 Largest eigenvalues: [1] 79572725 72975042 69620750 69016935 66196187 64353807 64147227 62667807 [9] 62143927 61363221 Smallest eigenvalues: [1] 0.4426613 0.4094225 0.4049305 0.2814929 0.2750891 0.2488869 [7] 0.2239836 0.2073271 0.1362423 -0.2924667 Largest eigenvalues: [1] 77209847 72740169 69203205 67525192 66938318 64938904 63581358 62826770 [9] 62612410 62055161 Smallest eigenvalues: [1] 0.6562435 0.6373410 0.6362037 0.5686744 0.5194375 0.4414786 [7] 0.3920645 0.1718008 0.1294767 -0.3612747 Largest eigenvalues: [1] 77070194 72691548 68987407 66853577 66768598 64972372 62721593 62625422 [9] 62037027 61295413 Smallest eigenvalues: [1] 0.46404765 0.44783901 0.38939080 0.37791612 0.37378334 0.30898780 [7] 0.29122926 0.24283605 0.08790804 -1.09750502 Largest eigenvalues: [1] 78933546 73662319 69730375 68607359 67013221 65389412 63597764 62980343 [9] 62687451 61658317 Smallest eigenvalues: [1] 0.6324682 0.4785468 0.4406933 0.4400356 0.4249065 0.2862495 [7] 0.2250434 0.2067813 -0.9708542 -1.2065334 Largest eigenvalues: [1] 79736456 74064485 70517850 69253040 67075627 64952314 64270829 64139666 [9] 62944313 62675861 Smallest eigenvalues: [1] 0.51036924 0.46187513 0.38731481 0.34378767 0.31484983 0.23360361 [7] 0.17180636 0.13030223 0.08488275 -0.32584227 Largest eigenvalues: [1] 78078315 73645533 70133156 67557203 67232525 65775582 63653387 63050005 [9] 62909694 62098980
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.246352 | 0.8509766 | 16.16517 | 0 | 2.054911 | 4.448354 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + steps + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
steps = steps_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_steps_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 670 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.582138894 0.534270824 0.513420139 0.471838431 0.454178749 [6] 0.452357755 0.393288732 0.113200758 -0.006292351 -0.133889058 Largest eigenvalues: [1] 65148070 60331692 57513833 56575966 54963080 53273464 52536849 51999059 [9] 51763132 50909537 Smallest eigenvalues: [1] 0.46398058 0.39857378 0.39331619 0.37421683 0.36338730 0.32369954 [7] 0.32296612 0.15405775 -0.01615417 -0.18726688 Largest eigenvalues: [1] 65365443 59982211 57005455 56300591 54952863 53026541 52524947 52464909 [9] 51458872 51418732 Smallest eigenvalues: [1] 0.61684261 0.56821037 0.47210371 0.44629476 0.41884613 0.40352989 [7] 0.35217761 0.25119561 -0.01777933 -0.02260171 Largest eigenvalues: [1] 64122964 60205133 57641181 55742245 55138462 53481183 52205342 51782133 [9] 51754441 51215694 Smallest eigenvalues: [1] 0.51802920 0.44278317 0.41322929 0.39435893 0.27396285 0.24895037 [7] 0.15988356 0.12814283 -0.02027725 -1.02468671 Largest eigenvalues: [1] 63430096 61116951 57769770 55940737 55403638 54005666 52794869 52490549 [9] 51932366 51680794 Smallest eigenvalues: [1] 0.504300412 0.459567766 0.375101290 0.285114588 0.271590294 [6] 0.249079905 0.190424226 0.004701724 -4.305062954 -21.397355310 Largest eigenvalues: [1] 63439869 59701325 56726978 55426873 54994492 53721540 52006049 51663306 [9] 51107182 50744442 Smallest eigenvalues: [1] 0.35979152 0.23292737 0.16802264 0.10782127 0.08170898 -0.35660917 [7] -0.85496108 -0.95355993 -4.62522331 -9.86603748 Largest eigenvalues: [1] 65283344 59961148 57436028 56133285 54867695 53301782 52223246 52091618 [9] 51563510 51245435 Smallest eigenvalues: [1] 0.44183621 0.40462111 0.35524045 0.30993226 0.24503424 0.22476122 [7] 0.12210689 0.09114042 0.05777706 -1.96546590 Largest eigenvalues: [1] 64463560 60747596 57381735 56142060 55769820 53970691 52847121 52108864 [9] 51826902 51528514 Smallest eigenvalues: [1] 0.49726825 0.40720772 0.35411498 0.33787783 0.32780184 0.32227653 [7] 0.22797604 0.01210434 -0.40294898 -1.17102763 Largest eigenvalues: [1] 65366604 60578524 58145310 56790936 55198690 53971974 52688634 52494451 [9] 52266766 51859224 Smallest eigenvalues: [1] 0.4920397 0.4383502 0.4284378 0.3534792 0.3144894 0.2845287 [7] 0.2798502 0.2204291 0.2004139 -1.9568552 Largest eigenvalues: [1] 65244776 60233986 57325326 56361126 55401399 53859713 52441787 52411283 [9] 52280202 51408821 Smallest eigenvalues: [1] 0.40962955 0.37548295 0.30511974 0.29634871 0.25324465 0.19755470 [7] -0.07159127 -1.07562920 -1.29689904 -2.51595934 Largest eigenvalues: [1] 64955628 59937525 56601139 56562623 54588278 52787426 52548497 52250312 [9] 51766836 51318097 Smallest eigenvalues: [1] 0.5026986 0.4713707 0.3848784 0.3323492 0.2938468 0.2310180 [7] 0.2201860 0.2159269 -0.2715102 -0.4560355 Largest eigenvalues: [1] 63971864 59877286 57293862 55884049 54757521 53247516 52297372 51843815 [9] 51716600 51110906 Smallest eigenvalues: [1] 0.45536481 0.32896107 0.29719832 0.24224524 0.22137155 0.21727199 [7] 0.09774093 0.08624682 -0.09241553 -3.87359645 Largest eigenvalues: [1] 64619204 60527206 58122772 55730758 55443362 54197920 52821484 52213299 [9] 51976204 51801919 Smallest eigenvalues: [1] 0.55306088 0.53278941 0.51247437 0.46124527 0.40592721 0.29763718 [7] 0.29088174 0.21484414 -0.02570754 -0.07793213 Largest eigenvalues: [1] 64785922 60126556 57323918 55879194 55294659 53081383 52272564 52030897 [9] 51784885 51323664 Smallest eigenvalues: [1] 0.45227127 0.36288271 0.34911706 0.34402992 0.31049747 [6] 0.28662176 0.19562599 -0.03826123 -0.62125560 -11.03690181 Largest eigenvalues: [1] 65111750 60515801 57931089 56540355 55908765 54419429 52607342 52323743 [9] 52209386 51424588 Smallest eigenvalues: [1] 0.47581333 0.43768791 0.37763536 0.31873869 0.31350395 0.30127597 [7] 0.21202479 0.16111747 0.07821737 -0.35123742 Largest eigenvalues: [1] 64325626 61342753 57571151 56351455 56291213 54409813 53980487 52392028 [9] 52174093 52034966 Smallest eigenvalues: [1] 0.5253661 0.4845086 0.3974313 0.3598291 0.2593125 0.2515001 [7] 0.2293299 0.1831083 0.1597757 -5.6348275 Largest eigenvalues: [1] 63402595 59957512 57202232 55295724 54905354 53704976 52228116 52111130 [9] 51426013 51080035 Smallest eigenvalues: [1] 0.4059256 0.4057105 0.3507398 0.2603932 0.2410954 0.2277764 [7] 0.1984418 0.1607915 -1.4570600 -6.1546804 Largest eigenvalues: [1] 64944363 59796905 57230546 56608424 54857074 53384537 52607956 52243509 [9] 51559732 50844034 Smallest eigenvalues: [1] 0.5190173 0.4664545 0.4273429 0.2802843 0.2520270 0.2505320 [7] 0.2303871 0.1175148 -0.6385760 -2.6030769 Largest eigenvalues: [1] 65109952 59585481 56872588 56043457 54997874 53350166 52230234 52026720 [9] 51945870 51294711 Smallest eigenvalues: [1] 0.2420610 0.2255808 0.1831371 0.1809581 -1.2235746 -1.3653772 [7] -3.1410483 -4.1044177 -4.2362828 -28.9074058 Largest eigenvalues: [1] 66371214 59388341 57310200 56728275 54116990 53324108 52626495 51397946 [9] 51190232 50592708 Smallest eigenvalues: [1] 0.5094121 0.4505063 0.4141838 0.3351829 0.1230920 0.0796625 [7] -0.2902778 -1.4702984 -1.6376954 -9.4512125 Largest eigenvalues: [1] 63433418 60169569 56874462 55324326 55065103 53543681 52073229 51447085 [9] 50909756 50599958 Smallest eigenvalues: [1] 0.303186030 0.292375825 0.004067745 -0.113120212 -0.137378876 [6] -0.323482728 -0.832901818 -0.988534255 -1.380347465 -2.243194540 Largest eigenvalues: [1] 66600855 60618822 57946490 57342227 55129390 53458960 53273553 53016655 [9] 51738112 51574550 Smallest eigenvalues: [1] 0.43203119 0.31957562 0.23781789 0.19365725 0.18396453 0.05542385 [7] 0.05058566 -0.01991147 -0.40707677 -3.08390338 Largest eigenvalues: [1] 65853369 60593154 57064085 56842854 55209617 53559969 52804240 52322603 [9] 52101278 51351213 Smallest eigenvalues: [1] 0.457397457 0.320457769 0.242980153 0.207149740 0.149612218 [6] 0.011288135 0.009577169 -2.026699135 -4.616648523 -6.649590643 Largest eigenvalues: [1] 63511584 59974555 57165485 55456214 54970351 53888720 52509155 51886746 [9] 51071567 50969646 Smallest eigenvalues: [1] 0.5108705 0.4763138 0.4498411 0.3954863 0.2899137 0.2800442 [7] 0.2375158 0.2154875 0.2004713 -0.6332202 Largest eigenvalues: [1] 64367888 61559209 58169235 56693481 55732368 54101490 52856923 52594194 [9] 52541862 51853392 Smallest eigenvalues: [1] 0.4384280 0.3981057 0.3757465 0.3625340 0.3061225 0.3012047 [7] 0.2125695 0.1989462 0.1115701 -0.7583390 Largest eigenvalues: [1] 64909383 61174234 58096617 56495606 56491848 54788326 53128603 52664620 [9] 52385494 51783872 Smallest eigenvalues: [1] 0.59479476 0.57035441 0.56250614 0.53616134 0.47446022 0.46023683 [7] 0.43611164 0.24748370 0.06581347 -0.16892236 Largest eigenvalues: [1] 65278986 60361879 57595282 56808569 55013132 53206151 52712570 51855195 [9] 51595625 50817231 Smallest eigenvalues: [1] 0.4270195 0.3747766 0.3380101 0.3298966 0.2549301 0.2512072 [7] 0.2473302 0.1969076 -0.6914395 -0.7782192 Largest eigenvalues: [1] 64836123 60299158 57089401 56008101 54977677 53420146 52058688 52002657 [9] 51640461 50969779 Smallest eigenvalues: [1] 0.3707116 0.3389766 0.3311187 0.2886437 0.1036859 -0.3543006 [7] -1.7384674 -3.2047003 -4.7830826 -24.1133702 Largest eigenvalues: [1] 63309190 60412405 57228517 55767639 54917999 53192534 51992913 51830170 [9] 51750055 50838745 Smallest eigenvalues: [1] 0.5417332 0.4896123 0.4644829 0.4233054 0.4160776 0.3555748 [7] 0.2914740 0.2241525 0.2123182 -0.8281746 Largest eigenvalues: [1] 63994471 59863448 57345239 55277102 54535078 53077700 52014300 51441019 [9] 51209151 51167725 Smallest eigenvalues: [1] 0.50725782 0.41934090 0.41383705 0.27729561 0.26473499 0.23669258 [7] 0.17127266 0.03307805 -0.57878346 -4.67633636 Largest eigenvalues: [1] 65209401 59456049 56827009 55725679 54816956 53240920 51939064 51701773 [9] 51507516 50728759 Smallest eigenvalues: [1] 0.3180695 0.2985033 0.2545072 0.2017825 0.1681180 0.1351658 [7] -3.8766700 -6.7190289 -14.7524683 -22.4548769 Largest eigenvalues: [1] 65861406 60532406 57961349 56826820 55219815 53522510 53087901 52841837 [9] 52092955 51999934 Smallest eigenvalues: [1] 0.38039276 0.34481875 0.25907228 0.25181584 0.24961091 0.20629351 [7] 0.03516675 -0.71212194 -0.98498885 -1.77684346 Largest eigenvalues: [1] 63291128 60576290 57848278 55876190 55127893 54513421 52852185 52534439 [9] 51507267 51205484 Smallest eigenvalues: [1] 0.2935939 0.2815964 0.2526242 0.2324772 0.1792697 -0.2801462 [7] -0.2824761 -0.6372673 -0.8530628 -1.3696133 Largest eigenvalues: [1] 65085877 59958688 57295578 56122876 55159137 53349778 52187254 52153897 [9] 51622367 51249778 Smallest eigenvalues: [1] 0.4636495 0.4241973 0.3813827 0.3650177 0.3357125 0.2721257 [7] 0.2604671 0.1814510 0.1254497 -0.6653157 Largest eigenvalues: [1] 63618500 59215353 57076645 55608960 54538361 52994120 51666115 51566125 [9] 51515881 50645429 Smallest eigenvalues: [1] 0.36652231 0.31603571 0.30783626 0.13851873 0.03389022 [6] -0.01334603 -0.19900935 -0.67484224 -37.53127421 -53.79307327 Largest eigenvalues: [1] 61202534 59118674 56207698 54922278 54195322 53011050 51880984 50910060 [9] 50188861 50018904 Smallest eigenvalues: [1] 0.37641638 0.28160544 0.27859626 0.23586849 0.13527819 0.01134310 [7] -0.04573632 -0.45534468 -2.69101621 -3.28285552 Largest eigenvalues: [1] 64969306 61160124 58300373 55738628 55645285 54314350 52544668 52063148 [9] 51756705 51512001 Smallest eigenvalues: [1] 0.45972451 0.44296116 0.39388481 0.30788031 0.29992387 0.24619009 [7] 0.04157764 -0.34971618 -0.42829049 -7.68965393 Largest eigenvalues: [1] 63054700 60658304 57455065 55580160 55501400 54207960 52569415 52142197 [9] 51433681 51039231 Smallest eigenvalues: [1] 0.39433129 0.36679916 0.31585773 0.21358950 0.21355444 0.20967491 [7] 0.18896538 0.16737422 0.15641722 -0.07897234 Largest eigenvalues: [1] 63117354 60446388 57348222 55529660 55310689 53699526 52854294 52041619 [9] 51677137 51450404 Smallest eigenvalues: [1] 0.53190929 0.52449781 0.50310948 0.42464075 0.35520278 0.33621567 [7] 0.31666149 0.25626923 0.22748197 -0.05643541 Largest eigenvalues: [1] 64921528 61126484 57810905 56702431 55673861 54077357 52841896 52665160 [9] 52439567 51872118 Smallest eigenvalues: [1] 0.44402409 0.42693470 0.29321791 0.26607362 0.25239042 0.14994960 [7] 0.04118788 -0.04611271 -0.39470826 -0.69863187 Largest eigenvalues: [1] 62465018 59542945 56247025 55450127 54488539 52757899 51905864 51575396 [9] 51059429 50281760 Smallest eigenvalues: [1] 0.4905395 0.4679585 0.4323883 0.3402013 0.3265913 0.3046923 [7] 0.2180993 0.1836426 0.1279358 -0.4123913 Largest eigenvalues: [1] 64685935 60047766 57665155 56052304 55401798 53968115 52258216 52202880 [9] 52009997 51523502 Smallest eigenvalues: [1] 0.5808287 0.5181906 0.4884345 0.3982290 0.3938184 0.3780191 [7] 0.3550720 0.3309355 0.3187282 -0.7128785 Largest eigenvalues: [1] 64606963 60711096 57811545 56277666 55802660 54242915 52451850 52276209 [9] 52250244 51371187 Smallest eigenvalues: [1] 0.29573646 0.28548900 0.13631423 0.09101294 0.04886930 0.03415961 [7] -0.02282863 -0.82249094 -1.11838746 -3.33712727 Largest eigenvalues: [1] 64589676 60226187 56738802 56347785 55388184 53393661 52622638 52322757 [9] 52267541 51292064 Smallest eigenvalues: [1] 0.384471971 0.291343405 0.262767255 0.225331121 0.177028896 [6] 0.155569637 0.111332297 -0.009455158 -1.238470055 -7.872201515 Largest eigenvalues: [1] 64109416 58895242 56559304 55894560 54075817 52357987 51815190 51352236 [9] 51100554 50050191 Smallest eigenvalues: [1] 0.4420265 0.4379181 0.4309511 0.4058506 0.3543849 0.3011116 [7] 0.2885254 0.2551085 0.2346812 -0.1523098 Largest eigenvalues: [1] 61903871 59891528 56951910 55140813 54734514 53539882 52175722 51527357 [9] 50791050 50585166 Smallest eigenvalues: [1] 0.4183948 0.4079354 0.3893765 0.3639861 0.2685296 0.2215397 [7] 0.1655500 0.1409848 -0.8635024 -3.6238826 Largest eigenvalues: [1] 66587928 60660483 57483247 56511083 55423761 53772725 52623248 52498535 [9] 51873341 51740835 Smallest eigenvalues: [1] 0.3822995 0.3349637 0.3140252 0.3121702 0.2596931 0.2378911 [7] 0.2081925 0.1764116 -0.5094574 -0.5130824 Largest eigenvalues: [1] 64674264 60844739 58311335 55890716 55696876 54346296 52850263 52536215 [9] 51867134 51617760 Smallest eigenvalues: [1] 0.63910144 0.61685112 0.58942740 0.55083323 0.49200432 0.42708875 [7] 0.37312576 0.25492659 0.07855744 -0.29657984 Largest eigenvalues: [1] 65336058 60461009 57568946 56502202 54941750 53162779 52625073 52213058 [9] 51384393 50977582 Smallest eigenvalues: [1] 0.4857895 0.4292037 0.3959083 0.3657526 0.3458585 0.3435992 [7] 0.3141451 0.1912363 0.1805988 -0.7261910 Largest eigenvalues: [1] 63247401 59893054 57035835 55228200 55061881 53445060 51770939 51733694 [9] 51211704 50961798 Smallest eigenvalues: [1] 0.4487396 0.3845477 0.3725236 0.3365801 0.2878332 0.2565840 [7] 0.2547981 0.1805501 -3.5341140 -6.1643446 Largest eigenvalues: [1] 65317504 60018953 57252415 57202693 54597809 53165302 52921615 52087658 [9] 51973519 51145378 Smallest eigenvalues: [1] 0.604535685 0.486314249 0.442001847 0.435220009 0.414558723 [6] 0.297290354 0.248239666 0.142352946 -0.003398047 -1.114340477 Largest eigenvalues: [1] 65167813 61071672 58152822 56867125 55438591 53496575 53089236 52736231 [9] 51911704 51789930 Smallest eigenvalues: [1] 0.545327466 0.519049578 0.504786705 0.451035254 0.393515566 [6] 0.358569237 0.329280561 0.279436969 0.277642076 -0.006866797 Largest eigenvalues: [1] 64319420 60700234 57722139 56156459 55835862 54557474 52950277 52138403 [9] 52020571 51475996 Smallest eigenvalues: [1] 0.45141749 0.38253218 0.37977975 0.29862668 0.25247099 0.13523288 [7] 0.06372699 -0.26592498 -0.62203637 -1.16139540 Largest eigenvalues: [1] 64946327 60677566 58167003 56495731 55173087 53604556 52799028 52550215 [9] 52175469 51877593 Smallest eigenvalues: [1] 0.5631793 0.5461064 0.4875077 0.4562461 0.3638974 0.3584800 [7] 0.3438786 0.2543562 0.1076786 -0.4530413 Largest eigenvalues: [1] 65311917 59906844 56985900 56476882 54854238 52887579 52450675 52138129 [9] 51639535 51208866 Smallest eigenvalues: [1] 0.5939966 0.5270798 0.5032330 0.4229257 0.3969222 0.3754482 [7] 0.3449907 0.3354566 0.2908666 -0.1194142 Largest eigenvalues: [1] 64259443 60517548 57668439 55916038 55456470 53745249 51805155 51766615 [9] 51643978 50728624 Smallest eigenvalues: [1] 0.4482323 0.4334117 0.3873700 0.3816662 0.3391291 0.2763107 [7] 0.2725865 0.1455238 -0.7910155 -1.2416415 Largest eigenvalues: [1] 62818285 60170130 57027997 55333910 55008869 53317013 52036779 52008368 [9] 51125093 51012129 Smallest eigenvalues: [1] 0.52338930 0.51916634 0.51802720 0.40898895 0.38106018 0.34818961 [7] 0.26314532 0.19972866 0.08942279 -0.12396346 Largest eigenvalues: [1] 62221759 59624694 56743772 55346164 54418424 53507238 51779605 51669336 [9] 50532283 50384938 Smallest eigenvalues: [1] 0.4802773 0.4500428 0.3651332 0.3532638 0.3364786 0.2986449 [7] 0.2825763 0.1524951 0.1286394 -1.6555082 Largest eigenvalues: [1] 63587639 59643610 56854613 55364657 55134545 53461920 52455268 51913882 [9] 51518403 51288009 Smallest eigenvalues: [1] 0.4750561 0.4666026 0.4491465 0.3618929 0.2969885 0.2441727 [7] 0.2265190 -0.0994749 -0.1879190 -3.8971143 Largest eigenvalues: [1] 65611200 60444404 57773103 56950411 54705607 53304939 53015738 52132293 [9] 51514878 51169591 Smallest eigenvalues: [1] 0.4990037 0.4419385 0.4303572 0.4170202 0.2810512 0.2518895 [7] 0.2435805 0.2267070 0.2183130 -0.9566458 Largest eigenvalues: [1] 64323691 60147743 57171880 56096714 55165625 53637034 52493195 52032670 [9] 51999230 51518835 Smallest eigenvalues: [1] 0.40554281 0.39307933 0.35224568 0.29881751 0.25156641 0.21184460 [7] 0.20582112 0.19764824 0.07209213 -5.25581622 Largest eigenvalues: [1] 64909369 61129126 58428614 56188950 55875786 54473679 52532312 52383440 [9] 52091219 51615600 Smallest eigenvalues: [1] 0.3922102 0.3620180 0.3268108 0.2611272 0.2529055 0.2058618 [7] 0.1975627 0.1959268 0.1217729 -2.1681830 Largest eigenvalues: [1] 65571747 60568455 57776239 56659420 55308631 53780616 52566828 52247656 [9] 52071813 51337332 Smallest eigenvalues: [1] 0.485370356 0.310864100 0.307989957 0.296572828 0.220046394 [6] 0.151461521 0.002218544 -0.895487191 -1.530775376 -1.939084785 Largest eigenvalues: [1] 62799527 59710533 56958342 55341016 54909034 53705196 52161778 52126877 [9] 51083987 50906260 Smallest eigenvalues: [1] 0.40943220 0.40923920 0.37720660 0.30750753 0.20546174 [6] 0.15602178 0.08009306 -0.03155124 -1.08163518 -17.64683617 Largest eigenvalues: [1] 65011877 59902886 56763757 56529187 55043132 53415437 52434734 51972918 [9] 51757720 51043243 Smallest eigenvalues: [1] 0.5696885 0.5200058 0.4349116 0.4035829 0.3020217 0.2704845 [7] 0.2684303 0.2512133 0.2419236 -1.4535085 Largest eigenvalues: [1] 65543313 60966032 58067480 56512064 55696669 54193156 52723471 52612508 [9] 52109418 51618272 Smallest eigenvalues: [1] 0.40096058 0.35083143 0.32859303 0.32601818 0.28127811 0.22925439 [7] 0.21195304 0.18646779 0.04865597 -2.01116212 Largest eigenvalues: [1] 65900101 59853999 57187752 56603485 54742607 53457136 52650043 52005321 [9] 51882321 51182385 Smallest eigenvalues: [1] 0.4649486 0.4568153 0.4341013 0.4080081 0.3421340 0.2834149 [7] 0.2537515 0.2349537 0.2327321 -0.3315201 Largest eigenvalues: [1] 65482613 60816554 58048249 56700024 56120910 54524195 52682598 52448386 [9] 52371316 51439683 Smallest eigenvalues: [1] 0.57068226 0.42211693 0.39747428 0.39689597 0.37707957 0.34723472 [7] 0.30803484 0.24994537 -0.01339311 -1.00383665 Largest eigenvalues: [1] 66420032 60787081 58063763 57216759 55177665 53603304 53344990 52405416 [9] 51966515 51598951 Smallest eigenvalues: [1] 0.35043920 0.31639147 0.29461594 0.26699996 0.23734749 [6] 0.14742534 0.10872102 0.08751024 -2.59212710 -12.27370009 Largest eigenvalues: [1] 63968624 60587267 57241963 55858968 55822691 54135264 52990040 52280121 [9] 52026469 51772628 Smallest eigenvalues: [1] 0.4420123 0.4357314 0.3516233 0.3426413 0.3073509 0.1924930 [7] 0.1805966 0.1346656 -0.2101050 -0.8369537 Largest eigenvalues: [1] 64995062 59643408 57089027 56521548 54277184 52755528 52508285 51475254 [9] 51245996 50417057 Smallest eigenvalues: [1] 0.51048804 0.45580278 0.39095756 0.33934288 0.33473126 0.27488713 [7] 0.27409689 -0.08764137 -0.30070317 -0.40846445 Largest eigenvalues: [1] 64662438 60857915 58215130 56351829 55531551 54074757 53011058 52349669 [9] 52283685 52163300 Smallest eigenvalues: [1] 0.52884928 0.50887246 0.44794902 0.38208101 0.36930356 0.36792831 [7] 0.33291083 0.25796138 0.01876542 -0.15594624 Largest eigenvalues: [1] 65348685 60272311 57711004 56410396 55565765 53548089 52669521 52176989 [9] 51818943 51138695 Smallest eigenvalues: [1] 0.5127975 0.4966310 0.4265970 0.4125918 0.3396251 0.2625984 [7] 0.1666105 0.1434122 0.1429262 -0.2603449 Largest eigenvalues: [1] 63718756 61355276 57782812 56375545 55305516 53859789 52852244 52287447 [9] 52261508 51912831 Smallest eigenvalues: [1] 0.4206898 0.3693107 0.3671705 0.3430170 0.3144401 0.3067283 [7] 0.1995124 0.1496485 -1.0483970 -4.6744849 Largest eigenvalues: [1] 66348277 60918782 57312876 57301833 55696792 53855646 53311968 52484686 [9] 52284560 51539900 Smallest eigenvalues: [1] 0.4335716 0.4292870 0.3543884 0.3436370 0.2887624 0.2803902 [7] -0.2580284 -1.5438717 -2.0344285 -3.4414541 Largest eigenvalues: [1] 64464386 59772236 56780844 56401755 54635512 52859047 52177665 52142265 [9] 51642181 51175340 Smallest eigenvalues: [1] 0.47922946 0.39915544 0.31475005 0.30556300 0.22686749 0.21518141 [7] 0.15850637 0.15257790 -0.06018905 -0.54311125 Largest eigenvalues: [1] 66320847 60187470 58003398 55972624 54950478 53151004 52429283 51802356 [9] 51365090 51037974 Smallest eigenvalues: [1] 0.51891681 0.49664889 0.44967162 0.37073948 0.26787808 0.20476697 [7] 0.18228656 0.17300728 0.04872697 -1.41871962 Largest eigenvalues: [1] 65598631 61340935 58159376 56931134 55986208 54373636 53563457 52922123 [9] 52463148 52169973 Smallest eigenvalues: [1] 0.365058229 0.323195797 0.300704524 0.107977260 0.091708186 [6] 0.024732365 -0.006456436 -0.066814925 -3.262360890 -24.195205360 Largest eigenvalues: [1] 63588423 59868185 57053870 55623161 54891888 53290107 52035527 51822195 [9] 51592733 51031827 Smallest eigenvalues: [1] 0.6128888 0.6005414 0.5084246 0.4647590 0.3576826 0.3320714 [7] 0.2924757 0.2352079 0.2192629 -0.0116011 Largest eigenvalues: [1] 63436488 60677069 57270421 55915963 54984756 53995230 52027421 51859383 [9] 51096587 50804366 Smallest eigenvalues: [1] 0.5429188 0.4624436 0.4484672 0.3660855 0.2859350 0.2802123 [7] -0.2252810 -3.2127511 -4.0366510 -5.3848628 Largest eigenvalues: [1] 65541444 60253537 57759824 56620516 54984595 53379433 52452385 52386620 [9] 52035835 51615543 Smallest eigenvalues: [1] 0.49384678 0.47034096 0.43110013 0.41232906 0.34579495 0.27326848 [7] 0.20258560 -0.06413743 -0.15323955 -0.42340140 Largest eigenvalues: [1] 65964400 61049404 58365404 56728603 55751973 54084782 53131516 52679136 [9] 52557385 52283067 Smallest eigenvalues: [1] 0.5178194 0.5068474 0.4966723 0.4001511 0.3682761 0.2510546 [7] 0.1937007 0.1569781 -0.8098995 -6.3224046 Largest eigenvalues: [1] 64696145 59715023 56604277 56306975 54524378 52795171 52360671 51600397 [9] 51158899 50489429 Smallest eigenvalues: [1] 0.4720272 0.4532888 0.4397408 0.3437993 0.2903784 0.2699869 [7] 0.2437427 0.2251591 0.1048481 -0.3145790 Largest eigenvalues: [1] 62874802 59644683 56751587 54942486 54725488 53265018 51928608 51313040 [9] 50887639 50504973 Smallest eigenvalues: [1] 0.201544408 0.177171397 0.144626455 0.091076722 0.004548103 [6] -0.148259185 -0.289884175 -1.575043898 -13.263955105 -79.579311945 Largest eigenvalues: [1] 66433540 60511774 57856772 56895086 55170876 54014777 52720474 52584682 [9] 52453225 51907112 Smallest eigenvalues: [1] 0.46984889 0.40535815 0.38373415 0.31445632 0.30424470 0.20821907 [7] 0.20479267 0.05942211 -0.19443799 -0.46006852 Largest eigenvalues: [1] 66295014 60055206 57477136 56958999 54760055 53148485 52942568 52550470 [9] 51745790 51682275 Smallest eigenvalues: [1] 0.4332651 0.4308242 0.3583716 0.2661786 0.2522003 0.2274065 [7] 0.2265533 0.1934069 -0.3544133 -0.7795985 Largest eigenvalues: [1] 64693328 60433656 57576991 56403901 55390048 53911610 52457037 52451694 [9] 52257789 51384720 Smallest eigenvalues: [1] 0.48280950 0.44458607 0.41297101 0.39655617 0.38245266 0.36329757 [7] 0.32586276 0.27999321 0.06975889 -6.56738212 Largest eigenvalues: [1] 64854384 59736790 57216159 55827698 54986718 53582752 51994993 51922870 [9] 51396962 50504492 Smallest eigenvalues: [1] 0.39820962 0.37804776 0.35628992 0.34829729 0.33528928 0.26461008 [7] 0.23280099 0.21468200 0.21248646 -0.09839829 Largest eigenvalues: [1] 64267814 60678050 57849347 56272576 55681003 54238859 52495499 52198944 [9] 52099877 51544577 Smallest eigenvalues: [1] 0.41887154 0.31343041 0.30939448 0.27154099 0.25444678 0.17239703 [7] 0.15336427 0.09724497 0.03846142 -4.62230843 Largest eigenvalues: [1] 64383814 60560185 57378585 55773472 55580811 53903495 52976999 52062940 [9] 51987916 51724972 Smallest eigenvalues: [1] 0.3321982 0.3099001 0.2951779 0.2923714 0.2593001 0.2387524 [7] 0.1839233 -0.4091854 -2.7724645 -32.5836795 Largest eigenvalues: [1] 62714617 60840721 57265914 55515224 55452445 53767227 52345127 52260058 [9] 51422482 51241427 Smallest eigenvalues: [1] 0.5511623 0.5137978 0.3973151 0.3698572 0.2714385 0.2601094 [7] 0.2599047 0.2129028 -0.6039468 -3.7364834 Largest eigenvalues: [1] 62892615 60256629 57165253 55863827 54884526 54202055 52521761 52276902 [9] 51146891 50914739 Smallest eigenvalues: [1] 0.4482666 0.4132002 0.4043009 0.3446677 0.3057986 0.2371929 [7] 0.2231859 0.1849645 -0.3806293 -1.2192000 Largest eigenvalues: [1] 64912913 60365249 57915971 56245247 55245503 53419182 52538053 52231428 [9] 52175101 51690647 Smallest eigenvalues: [1] 0.5429959 0.5029861 0.4617789 0.3660918 0.3307626 0.3030359 [7] 0.2941898 0.2423092 0.2093103 -1.4799506 Largest eigenvalues: [1] 65310285 61205449 58387605 56788205 56219393 54775783 53121119 52773489 [9] 52719250 52173340 Smallest eigenvalues: [1] 0.5757681 0.5170118 0.3817440 0.3695223 0.3446561 0.2849770 [7] 0.2656549 0.1959019 0.1725764 -0.2854450 Largest eigenvalues: [1] 65604887 60614573 57557609 56305090 55216214 53469352 52454467 52402152 [9] 51998177 51419384 Smallest eigenvalues: [1] 0.36186136 0.22478492 0.21982184 0.20091140 0.15866189 0.05321775 [7] -0.02753659 -0.18814786 -0.73649376 -1.83930125 Largest eigenvalues: [1] 63126554 60013297 57218445 55247689 54841283 53218257 52264101 51445755 [9] 51232175 51009566 Smallest eigenvalues: [1] 0.5889792 0.5325782 0.4799873 0.4081175 0.3822931 0.3360016 [7] 0.3165796 0.2596338 0.1156711 -0.2926909 Largest eigenvalues: [1] 65118790 60088139 57034713 56302051 54940701 53275640 52253927 51582079 [9] 51517645 50753394 Smallest eigenvalues: [1] 0.5462084979 0.4596289757 0.4425864504 0.4092067562 0.3946468524 [6] 0.3602657817 0.2447315615 0.1547394310 0.0193964287 -0.0004436288 Largest eigenvalues: [1] 61796298 59213323 56855892 54938033 54377620 53172281 51519650 51155755 [9] 50459207 50163983 Smallest eigenvalues: [1] 0.5161071 0.4864884 0.3918835 0.3876054 0.3870837 0.3559756 [7] 0.3370716 0.2599319 0.1657500 -0.3115592 Largest eigenvalues: [1] 63609026 59775759 57293552 55094734 55002818 53520016 51926489 51647070 [9] 51198665 51058964 Smallest eigenvalues: [1] 0.3844704 0.2869086 0.2678615 0.2414951 0.1662366 0.1649803 [7] -0.2931335 -1.8512067 -2.2663332 -2.6126528 Largest eigenvalues: [1] 65399203 60358455 58444718 55669337 55604086 54514489 52942546 52772772 [9] 51926528 51626828 Smallest eigenvalues: [1] 0.40034295 0.36388802 0.34484062 0.25063321 0.22174912 0.18652089 [7] 0.17892611 0.17140740 -0.07209435 -1.44236241 Largest eigenvalues: [1] 63763732 59405332 57413034 55948630 54263154 52938941 51853268 51781222 [9] 51477112 50766747 Smallest eigenvalues: [1] 0.4313798 0.4229571 0.3923769 0.3760412 0.3112095 0.3109464 [7] 0.2526391 -0.1554225 -0.8900478 -16.5592499 Largest eigenvalues: [1] 63152583 59993602 57085284 55419122 55064076 53533837 51865233 51627201 [9] 51350229 50770855 Smallest eigenvalues: [1] 0.41276988 0.40321953 0.40185311 0.23765414 0.22292144 0.19771954 [7] 0.16912023 0.08295498 -0.67170684 -1.12303792 Largest eigenvalues: [1] 64139585 59804873 57183976 56051727 54822511 53324425 52168035 51909804 [9] 51898737 51015452 Smallest eigenvalues: [1] 0.53276256 0.46594849 0.43924900 0.39697820 0.31945362 0.29167345 [7] 0.28980983 0.25929236 -0.01086218 -0.13285833 Largest eigenvalues: [1] 63273773 59720686 57231816 54882059 54713773 53247788 51957631 51438734 [9] 50977746 50627827 Smallest eigenvalues: [1] 0.46748942 0.34423002 0.31387525 0.24507436 0.24340465 0.15076138 [7] 0.09617273 -0.69562439 -1.18076695 -4.47359899 Largest eigenvalues: [1] 61526702 59905855 57046257 56146055 54189655 54017569 52814392 51694398 [9] 50826284 50742824 Smallest eigenvalues: [1] 0.4923785 0.3984089 0.3937567 0.3549236 0.3122952 0.3109052 [7] 0.2706105 0.2394305 -0.2794429 -0.9258592 Largest eigenvalues: [1] 62845171 59886485 57063124 55382063 54919764 53291971 51992605 51803111 [9] 51226728 50848565 Smallest eigenvalues: [1] 0.5459344 0.4891997 0.4786678 0.4104942 0.3288842 0.2848951 [7] 0.2847681 0.1815102 0.1424909 -0.3119798 Largest eigenvalues: [1] 65061303 60674413 57479748 55796434 55694628 53880747 52647245 52183251 [9] 52014319 51568813 Smallest eigenvalues: [1] 0.4503516 0.4380780 0.3798042 0.3404305 0.2878967 0.2793281 [7] 0.2346284 0.2103938 -0.1151525 -16.0634542 Largest eigenvalues: [1] 63801784 60786631 57408112 56000477 55902736 54203077 52619103 52096529 [9] 51947571 51564852 Smallest eigenvalues: [1] 0.53132581 0.47939255 0.44143427 0.41821041 0.40036708 0.39283256 [7] 0.26125258 0.25440452 0.04234018 -0.05788324 Largest eigenvalues: [1] 61908991 60921013 57583495 55719933 55087847 53944109 52199272 52187053 [9] 51311269 51051015 Smallest eigenvalues: [1] 0.55633858 0.55459905 0.51682411 0.45409873 0.36279853 0.28371626 [7] 0.27734235 0.24286158 0.16919659 -0.04879497 Largest eigenvalues: [1] 65870742 60146762 57478444 56195525 55011350 53145199 52490917 51801209 [9] 51725161 51007665 Smallest eigenvalues: [1] 0.29941142 0.28255724 0.26899353 0.26408874 0.24559457 0.18665779 [7] 0.03204212 -0.16302223 -0.62465421 -0.77217633 Largest eigenvalues: [1] 64692988 61448493 58366388 56660214 55912037 54073882 53831609 52892771 [9] 52302123 52147463 Smallest eigenvalues: [1] 0.4999409 0.4392076 0.3276502 0.3157298 0.2767293 0.2717452 [7] 0.2070822 -0.2590587 -0.8639667 -1.6282596 Largest eigenvalues: [1] 67366903 60256808 57940051 57564310 55064301 53967328 53436716 52456655 [9] 51710071 51405849 Smallest eigenvalues: [1] 0.5156335 0.4515649 0.3378194 0.3355335 0.3027039 0.2655431 [7] 0.1546276 -0.2241411 -0.6055852 -2.8591961 Largest eigenvalues: [1] 64976128 59853182 57012931 55533646 54739601 53080864 52033152 51713440 [9] 51370904 51200155 Smallest eigenvalues: [1] 0.45290694 0.44925560 0.40351757 0.30919014 0.25459596 0.17384010 [7] 0.17026083 0.11022259 -0.02776676 -0.31821990 Largest eigenvalues: [1] 61432810 59985832 57193901 54767519 54531619 53265460 51504147 51440013 [9] 50665853 50507831 Smallest eigenvalues: [1] 0.52622357 0.50680189 0.46369968 0.38817044 0.25210285 0.20384335 [7] 0.20338961 0.19141173 0.12685740 -0.07178254 Largest eigenvalues: [1] 66202026 60897045 58063314 57194555 55475013 53311879 53307392 52911864 [9] 52169260 52040648 Smallest eigenvalues: [1] 0.52234995 0.45402038 0.43663174 0.41554924 0.40579497 0.28840887 [7] 0.13245821 0.08557838 -0.75062913 -2.86560419 Largest eigenvalues: [1] 65374252 60863355 57518564 57202689 55322858 53729674 52938897 52731382 [9] 52403820 51485447 Smallest eigenvalues: [1] 0.39084695 0.36914184 0.30025457 0.26474489 0.24560916 0.13375087 [7] -0.05033575 -0.05521544 -1.65185785 -4.82023978 Largest eigenvalues: [1] 65400558 61101185 57473590 56295735 56083895 54190276 53128989 52606597 [9] 52276979 51737422 Smallest eigenvalues: [1] 0.5780271 0.5484737 0.4845899 0.4175106 0.3248807 0.3082034 [7] 0.2996564 0.2535816 0.1127043 -1.8725486 Largest eigenvalues: [1] 64195941 60285711 57416563 56098671 55456384 53595903 52126600 52038599 [9] 51843900 50875133 Smallest eigenvalues: [1] 0.4125340 0.3617126 0.3277186 0.3125530 0.2747283 0.2422840 [7] 0.2351366 -0.0112572 -0.1799453 -3.4878682 Largest eigenvalues: [1] 63717076 59716227 57283402 55579766 55459389 53816847 51984241 51458117 [9] 51418582 50617527 Smallest eigenvalues: [1] 0.158950216 0.138747110 0.095224104 -0.003804913 -0.234584077 [6] -0.376242437 -1.934583821 -2.615940916 -11.366270562 -42.885478214 Largest eigenvalues: [1] 62210639 59008470 56523613 54883978 54828048 53128814 52077971 51570901 [9] 50778089 50548099 Smallest eigenvalues: [1] 0.5606641 0.5178252 0.4550787 0.4136515 0.4128867 0.3802478 [7] 0.2519912 0.1598622 0.1547290 -0.8574677 Largest eigenvalues: [1] 64056664 60121490 56752301 55494222 55381324 53671925 52297441 51526186 [9] 51485984 50661714 Smallest eigenvalues: [1] 0.3618078 0.3443411 0.3132744 0.3096701 0.2477763 0.1948330 [7] 0.1731113 0.1549858 -0.1465254 -1.7413840 Largest eigenvalues: [1] 65003619 59255885 56773132 56444943 54675165 53113186 52481697 51687999 [9] 50838184 50270887 Smallest eigenvalues: [1] 0.54426953 0.48562884 0.44388094 0.42821535 0.34888349 0.26731143 [7] 0.23998793 0.12993691 -0.02737212 -0.44424968 Largest eigenvalues: [1] 65550998 60465719 57587850 56121483 55591168 54046566 52740053 52235743 [9] 52054542 51864556 Smallest eigenvalues: [1] 0.42169354 0.39682148 0.39261339 0.33989100 0.32935115 0.22938059 [7] 0.21809042 0.08154989 -0.51332259 -1.69754904 Largest eigenvalues: [1] 62982266 60428341 57530010 55442263 55109750 53755454 52044607 51863246 [9] 51237195 50876446 Smallest eigenvalues: [1] 0.52459098 0.51053602 0.35515245 0.33980637 0.30118029 0.21321678 [7] 0.18689065 0.12651958 -0.08038237 -0.27084950 Largest eigenvalues: [1] 62531812 59705008 56872443 55459454 54529444 53538600 52154088 51877923 [9] 51114746 50752980 Smallest eigenvalues: [1] 0.52171155 0.49562694 0.49447592 0.44617475 0.38149637 0.31870354 [7] 0.29634753 0.25018251 0.24601879 -0.05523009 Largest eigenvalues: [1] 64247196 60702959 57811455 56511277 55326045 53743379 52828963 52591858 [9] 51993151 51674647 Smallest eigenvalues: [1] 0.4856958 0.4851811 0.4698809 0.4536448 0.3643883 0.2650687 [7] -0.6305192 -2.6167447 -6.9863113 -8.5079493 Largest eigenvalues: [1] 65767631 60192997 57414536 56986437 55017791 53821130 52858098 52238089 [9] 52077024 51222271 Smallest eigenvalues: [1] 0.62210840 0.51544880 0.51387347 0.48528008 0.32260528 0.24645020 [7] 0.12895498 -0.07462728 -0.42245680 -1.01614870 Largest eigenvalues: [1] 65192444 60626017 57792212 56461719 55435968 53943961 52519697 52470748 [9] 52090557 51424514 Smallest eigenvalues: [1] 0.6123584 0.5180206 0.4697137 0.4490226 0.3160412 0.2512016 [7] 0.2429981 0.2276873 -0.3757075 -2.4693377 Largest eigenvalues: [1] 64512255 60939379 57510406 55856670 55830455 54158421 52430522 52328012 [9] 51957775 51395342 Smallest eigenvalues: [1] 0.50285305 0.42119011 0.33842476 0.32740418 0.32042739 0.23890470 [7] 0.19142499 0.08581807 -1.07829160 -1.57508291 Largest eigenvalues: [1] 63212056 60557886 56946985 55900077 55025855 53336499 52238259 51773561 [9] 51602547 50807734 Smallest eigenvalues: [1] 0.45464091 0.43894610 0.40747460 0.35503655 0.31265786 0.29094006 [7] 0.23802606 -0.01934277 -0.28903710 -4.57884983 Largest eigenvalues: [1] 65020984 59922993 57531605 56134514 54805829 53182111 52268454 51935433 [9] 51843598 51096607 Smallest eigenvalues: [1] 0.56759586 0.56189578 0.41514216 0.38441990 0.37557169 0.33648270 [7] 0.31638758 0.30483067 0.09840617 -0.14551585 Largest eigenvalues: [1] 63645797 60322326 57525748 55656889 55258278 53726751 52232143 51994825 [9] 51743852 51118727 Smallest eigenvalues: [1] 0.3709913079 0.3575170694 0.3507039142 0.1969533121 0.1864759946 [6] 0.1562555900 0.0005067288 -0.1428596895 -1.4036005271 -4.8821616389 Largest eigenvalues: [1] 64609448 59304612 56830482 54940485 54928090 53223922 52235880 51373447 [9] 51291503 50684140 Smallest eigenvalues: [1] 0.5378951 0.4152804 0.4125642 0.3603796 0.3574761 0.3439116 [7] 0.2817114 0.2490014 -1.1908588 -2.1304555 Largest eigenvalues: [1] 63262192 60140606 57396805 55933981 54780326 53424578 52233240 51771048 [9] 51709538 51262078 Smallest eigenvalues: [1] 0.4139446 0.4003821 0.3210964 0.2948652 0.2792177 0.2462764 [7] 0.1485048 -0.1665783 -0.2396231 -1.1166169 Largest eigenvalues: [1] 65025560 59874668 57719944 55994411 54705952 53532693 52281068 51764539 [9] 51555256 50870097 Smallest eigenvalues: [1] 0.27577537 0.27200639 0.22353516 0.19749033 0.18221636 0.17288771 [7] 0.14576046 0.06904516 0.04295397 -7.41265447 Largest eigenvalues: [1] 62544032 60326473 57361667 55714935 55141761 53576873 52373218 52255801 [9] 51519940 50889022 Smallest eigenvalues: [1] 0.34824419 0.32624775 0.32412938 0.30055734 0.28486927 0.24196818 [7] 0.18425453 0.12732401 0.06721902 -1.14091795 Largest eigenvalues: [1] 63695684 59558522 57054951 54907965 54775839 53308952 51675649 51204229 [9] 51060347 50525826 Smallest eigenvalues: [1] 0.4461087 0.4100242 0.3564076 0.3077360 0.2705415 0.2075168 [7] 0.1856098 -0.2798966 -1.4998011 -1.7307294 Largest eigenvalues: [1] 65060073 59788240 57010817 56374372 54962676 53241951 52533464 52326643 [9] 51834648 51339657 Smallest eigenvalues: [1] 0.4345425 0.3460610 0.3452705 0.3419106 0.2650077 0.1179957 [7] -0.0407012 -0.0478749 -0.6777024 -2.7087721 Largest eigenvalues: [1] 65968492 59864148 57144255 56690856 54655176 53140523 52731877 52259841 [9] 51488220 51465275 Smallest eigenvalues: [1] 0.5542803 0.5512591 0.5228604 0.4515252 0.4155063 0.3076948 [7] 0.2845276 0.2396812 0.1807905 -0.3428144 Largest eigenvalues: [1] 63905137 59502253 56433069 55165699 54726656 53026970 51790581 51360145 [9] 51208848 50453061 Smallest eigenvalues: [1] 0.464282566 0.429567178 0.415205333 0.378129428 0.336070306 [6] 0.259183622 0.216600995 0.033002374 0.006506839 -0.042244432 Largest eigenvalues: [1] 63444504 59522734 56847150 54871722 54615621 53105096 51765857 51333580 [9] 51148670 50729429 Smallest eigenvalues: [1] 0.2372722011 0.2225235054 0.2015075882 0.0929144775 -0.0006222235 [6] -0.2148215623 -0.2224678712 -0.4906172915 -3.0041167833 -3.3593404025 Largest eigenvalues: [1] 65984700 59620554 56934014 56331887 54491746 53085033 52386737 51831911 [9] 51436998 51028028 Smallest eigenvalues: [1] 0.42762804 0.41302478 0.40983814 0.40478580 0.35859747 [6] 0.29442122 0.24534593 -0.08207897 -0.22919430 -10.25323178 Largest eigenvalues: [1] 66549384 60508087 58540776 57026439 55228675 53282403 52964350 52299347 [9] 51874854 51561945 Smallest eigenvalues: [1] 0.43601688 0.43273579 0.35929767 0.23928188 0.20507564 0.17869410 [7] 0.16006524 0.15735591 0.06578892 -0.00884030 Largest eigenvalues: [1] 64630586 60822955 58244976 55906329 55794335 54472403 52524935 52152055 [9] 52006919 51281686 Smallest eigenvalues: [1] 0.40359710 0.29078424 0.28913387 0.24170298 0.13901900 0.09786114 [7] 0.05907958 -0.07789732 -0.62712754 -1.53270335 Largest eigenvalues: [1] 66245908 60488538 58068049 57335231 54946414 53464666 53188835 52880647 [9] 51973737 51603106 Smallest eigenvalues: [1] 0.5617142 0.5599401 0.5083362 0.4206503 0.4119482 0.3668112 [7] 0.3366286 0.2675939 0.0604494 -0.3029912 Largest eigenvalues: [1] 63735402 60132302 56906030 55650046 55220216 53401815 51648460 51633654 [9] 51566797 50685450 Smallest eigenvalues: [1] 0.40801604 0.40389371 0.33990475 0.31620434 0.31242965 [6] 0.29992452 0.19358977 0.05662348 -2.66980776 -16.78142650 Largest eigenvalues: [1] 63715977 60355191 57482558 56348171 55093563 53422203 52593371 52129938 [9] 51897846 51409226 Smallest eigenvalues: [1] 0.4359027 0.3340343 0.3214657 0.3154707 0.2913169 0.2623459 [7] 0.1672228 0.1357154 -0.1990377 -0.6847689 Largest eigenvalues: [1] 66348176 60141875 57861809 57171768 54956008 53665745 53265811 52015686 [9] 51831777 51070947 Smallest eigenvalues: [1] 0.35136998 0.30718827 0.30041682 0.27201388 0.15773403 0.15405150 [7] 0.09808916 -0.05159188 -0.41221943 -2.22285813 Largest eigenvalues: [1] 65043567 60219670 57130463 56659700 55000249 53405129 52629781 52582847 [9] 52067161 51633049 Smallest eigenvalues: [1] 0.51304442 0.50070467 0.46793052 0.27801358 0.24674705 0.23081110 [7] -0.02424976 -0.04756692 -0.45654980 -5.69860578 Largest eigenvalues: [1] 65920403 59915422 57226585 56292137 54626891 53049380 52511637 51598153 [9] 51550425 50591028 Smallest eigenvalues: [1] 0.42857068 0.42233951 0.33428665 0.28511286 0.27304769 0.06738081 [7] 0.06159214 -0.02269885 -0.04753362 -2.62666136 Largest eigenvalues: [1] 65373132 60371013 57772896 56582558 54839576 53505278 52709407 52231512 [9] 51683667 51424207 Smallest eigenvalues: [1] 0.5527861 0.5191890 0.5109496 0.4552053 0.3569596 0.3308421 [7] 0.1655400 -0.2481752 -0.2485755 -14.8087171 Largest eigenvalues: [1] 64298426 59365986 56712783 55646048 54461595 52413836 51695841 51218018 [9] 51195453 50362335 Smallest eigenvalues: [1] 0.5879522 0.5586164 0.4919110 0.4150249 0.3334988 0.3268393 [7] 0.1071417 -0.1503952 -0.3219681 -1.5340869 Largest eigenvalues: [1] 65576323 59905413 56922328 56518290 54638236 52638453 52332864 51549585 [9] 51496916 50719685 Smallest eigenvalues: [1] 0.4452586 0.4253285 0.3897178 0.2382964 0.2189670 0.1750966 [7] 0.1718941 -0.2858584 -0.8273859 -1.8439859 Largest eigenvalues: [1] 66414068 60487398 57456568 57264512 55076190 53346019 53204558 52899585 [9] 51922869 51881458 Smallest eigenvalues: [1] 0.579322470 0.495724326 0.475819493 0.457585349 0.357925325 [6] 0.281455716 0.260275895 -0.001111107 -0.025555299 -0.430857479 Largest eigenvalues: [1] 64228370 59963578 56998759 55226178 54795231 53208368 51859128 51758102 [9] 51371890 51137177 Smallest eigenvalues: [1] 0.5053258 0.4497076 0.3842383 0.2980560 0.2917675 0.1977349 [7] 0.1435539 -0.1076327 -0.1294795 -0.2666228 Largest eigenvalues: [1] 64171263 59863976 57283743 55783843 54713585 53345568 52096852 51865869 [9] 51747188 50845488 Smallest eigenvalues: [1] 0.4874405 0.4831283 0.4762235 0.4539044 0.4132227 0.2655075 [7] 0.2654035 0.1649278 -0.7497195 -3.6836471 Largest eigenvalues: [1] 64703810 60404872 56947943 56118265 55487160 53720828 51980623 51859404 [9] 51791012 50951196 Smallest eigenvalues: [1] 0.53090711 0.52857996 0.40532111 0.31788968 0.29253928 0.28888361 [7] 0.19107938 0.15011937 0.09222173 -0.41676164 Largest eigenvalues: [1] 66256197 60857400 58269889 56445434 55358595 53862156 52668530 52366326 [9] 51998104 51534903 Smallest eigenvalues: [1] 0.5632778 0.5368090 0.4897684 0.4513131 0.3952916 0.3864297 [7] 0.3376703 0.1976449 -0.6951041 -1.5668546 Largest eigenvalues: [1] 65400796 60174958 57188597 56547107 55292785 53800498 52453111 52216088 [9] 52037523 51347479 Smallest eigenvalues: [1] 0.4661901 0.4080849 0.3753071 0.3083683 0.2636065 0.2484938 [7] 0.2471375 0.2301789 0.1823539 -0.7611671 Largest eigenvalues: [1] 64533648 59908454 56634158 55939317 54790492 53195839 51984942 51947753 [9] 51519753 50875168 Smallest eigenvalues: [1] 0.55301142 0.53508523 0.48531364 0.46827562 0.28645905 0.26865378 [7] 0.02387740 0.00851412 -0.04974736 -2.88107699 Largest eigenvalues: [1] 65593782 60854360 57499461 55971282 55457354 53540754 52087735 51980213 [9] 51712925 51238089 Smallest eigenvalues: [1] 0.4606986 0.4150882 0.3895332 0.3698456 0.3016220 0.1967325 [7] -0.2412423 -0.4353416 -4.2177200 -12.4418833 Largest eigenvalues: [1] 66642222 60497163 58211313 57644600 54848392 53687334 53568098 52186766 [9] 51817447 51307454 Smallest eigenvalues: [1] 0.4444366 0.4443511 0.4334750 0.4235253 0.3942360 0.3622654 [7] 0.3180757 0.2967322 0.2288908 -26.3081421 Largest eigenvalues: [1] 64396580 59472323 56986246 56387089 54520198 52437651 52340066 52099638 [9] 51148609 50775198 Smallest eigenvalues: [1] 0.4832095 0.4816598 0.4099703 0.4003063 0.3778948 0.3354794 [7] 0.3217115 0.2173993 0.1108074 -1.8167742 Largest eigenvalues: [1] 64261862 60209997 57363944 55525902 55499370 53860182 51978820 51639716 [9] 51407576 50509109 Smallest eigenvalues: [1] 0.4159491 0.3887005 0.3636342 0.3339376 0.2719207 0.2071950 [7] -0.1554395 -0.1753642 -1.6493714 -3.1613924 Largest eigenvalues: [1] 65831936 60436230 57527128 56524973 55460560 54029766 52557061 52076846 [9] 51920156 50700276 Smallest eigenvalues: [1] 0.4991566 0.4450847 0.3848060 0.3752293 0.2972533 0.2585703 [7] 0.2508491 0.1809243 0.1793704 -0.4216766 Largest eigenvalues: [1] 64369103 60376898 57361903 56147636 55339820 53647877 52442006 52110402 [9] 51926524 51411287 Smallest eigenvalues: [1] 0.3919340 0.3685712 0.2556420 0.2305837 0.2224366 0.1234887 [7] -0.2761569 -0.3616016 -11.4560427 -16.1561883 Largest eigenvalues: [1] 65412366 59923422 57748249 56026030 55116757 53840008 52628318 52101955 [9] 52094337 51747853 Smallest eigenvalues: [1] 0.5405937 0.4704579 0.4415416 0.3790221 0.3078424 0.2719302 [7] 0.2296209 0.0186659 -0.0744638 -0.7226621 Largest eigenvalues: [1] 65520519 60275203 57988226 56788103 54892970 53276053 52799941 52066448 [9] 51868418 51291721 Smallest eigenvalues: [1] 0.57591289 0.53984830 0.44469187 0.40822789 0.35845191 0.26293753 [7] 0.16328850 0.07937359 -0.04800096 -6.00683329 Largest eigenvalues: [1] 64289485 59455696 56834512 55315299 54648085 53056009 51574283 51470745 [9] 51377222 50566365 Smallest eigenvalues: [1] 0.58586685 0.51402486 0.42743002 0.40341103 0.34743473 0.22118159 [7] 0.16053106 0.08174534 0.06713376 -0.40198544 Largest eigenvalues: [1] 63682699 60558805 57862601 55217118 55062996 53841954 52020460 51958573 [9] 51242398 51026267 Smallest eigenvalues: [1] 0.50906806 0.43992522 0.38269723 0.37411904 0.34578560 0.31168999 [7] 0.22278832 0.09681184 -0.08672713 -1.92598298 Largest eigenvalues: [1] 65216969 60390600 58111830 55821549 55480546 53756032 52516394 52155805 [9] 52037381 51570033 Smallest eigenvalues: [1] 0.37125346 0.33622651 0.29554754 0.28392163 0.25954336 0.18204743 [7] 0.10794663 0.07439459 -1.71415284 -1.76398125 Largest eigenvalues: [1] 66281357 60659706 58058772 56696467 55097852 53702741 52758194 52705716 [9] 52016429 51860011 Smallest eigenvalues: [1] 0.4915993 0.4851726 0.4418545 0.4320093 0.4096783 0.3744207 [7] 0.3444420 0.1834299 0.1197684 -0.1764419 Largest eigenvalues: [1] 61917877 59848034 56853819 54935056 54622197 53424167 51985452 51214462 [9] 50675931 50435386 Smallest eigenvalues: [1] 0.44518733 0.41460183 0.32436259 0.31668699 0.29987897 0.19623957 [7] 0.19542040 0.07259145 -2.80552716 -2.92745036 Largest eigenvalues: [1] 66640375 61095951 57961718 57353193 56134267 54440333 53381865 53295039 [9] 52478193 52079181 Smallest eigenvalues: [1] 0.4634656 0.3698625 0.3634382 0.3519396 0.3517787 0.3205757 [7] 0.3197558 0.2100936 0.1818245 -0.3952971 Largest eigenvalues: [1] 64753557 60999215 57910651 56065071 55968898 54252348 52532757 52183472 [9] 52080847 51572769 Smallest eigenvalues: [1] 0.3858889 0.3639822 0.3448909 0.3411816 0.2677283 0.2321544 [7] 0.1140600 -0.1581726 -0.7332295 -1.4332558 Largest eigenvalues: [1] 65565004 59630014 57366436 56865100 54699649 53420088 52803464 51950272 [9] 51565967 51071268 Smallest eigenvalues: [1] 0.4878207 0.4736053 0.4604077 0.4501137 0.4259043 0.2673243 [7] 0.2605347 0.2207386 0.1528024 -0.8640331 Largest eigenvalues: [1] 63872043 60705633 57978116 56097159 55768979 54475466 52770612 52723140 [9] 51950648 51649096 Smallest eigenvalues: [1] 0.4226829 0.4049011 0.3693947 0.3473756 0.2799854 0.2396624 [7] 0.1791423 0.1474199 -4.0729856 -19.3983485 Largest eigenvalues: [1] 64321911 60430367 57812735 55732140 55625407 54268799 52640600 52389440 [9] 51708865 51207869 Smallest eigenvalues: [1] 0.5553300 0.4967537 0.4364663 0.4144603 0.3296271 0.3032553 [7] 0.2884542 0.2636767 0.1265461 -18.7405014 Largest eigenvalues: [1] 63101342 60157442 57042025 55467023 54738047 53721113 51871042 51779396 [9] 51009249 50904160 Smallest eigenvalues: [1] 0.4966046 0.4709479 0.3776067 0.3097582 0.2638198 0.2393345 [7] 0.1111486 -0.1408088 -0.8568489 -1.4758753 Largest eigenvalues: [1] 65270513 61372036 57764697 56673041 56384759 54655131 53518208 52651284 [9] 52366803 51905607 Smallest eigenvalues: [1] 0.44346563 0.42564798 0.34981173 0.31166490 0.29445893 0.25320201 [7] 0.22600226 0.21321413 0.07203382 -1.65710364 Largest eigenvalues: [1] 63898644 59870162 57230832 55478703 54860298 53458313 51864385 51618377 [9] 51568458 50839329 Smallest eigenvalues: [1] 0.46244840 0.38948767 0.37215329 0.26736355 0.19798737 0.16938847 [7] 0.12489110 -0.01901132 -0.76193337 -3.55169477 Largest eigenvalues: [1] 65952490 59884255 57836859 56179865 55038290 53870873 52556097 52365838 [9] 52069754 51507352 Smallest eigenvalues: [1] 0.42999778 0.38555428 0.37323619 0.36471501 0.32681658 0.32183526 [7] 0.15807602 0.05987858 -6.59816174 -7.33697480 Largest eigenvalues: [1] 64034822 60439047 57778130 55756713 55345882 54104653 51944458 51895153 [9] 51443279 50903441 Smallest eigenvalues: [1] 0.6424924 0.6164485 0.5648250 0.4252163 0.3786334 0.3785901 [7] 0.3333032 0.2573348 -0.2328014 -0.3363637 Largest eigenvalues: [1] 65843703 60504600 57741779 56989262 54939473 52987954 52922512 52512440 [9] 51803876 51612969 Smallest eigenvalues: [1] 0.56231586 0.39004207 0.36305529 0.32163075 0.27072760 0.24938666 [7] 0.22502081 0.08064115 -0.35063075 -0.43664614 Largest eigenvalues: [1] 65587673 60830487 57764657 56726586 55570430 53833902 52855569 52680560 [9] 52038380 51483534 Smallest eigenvalues: [1] 0.4295399 0.3392148 0.3266543 0.3067237 0.2652543 0.2038584 [7] 0.1140841 -0.1150886 -0.2993984 -1.2668640 Largest eigenvalues: [1] 65242863 60345619 57795897 56458293 55203857 53578015 53318279 52652814 [9] 51949893 51697251 Smallest eigenvalues: [1] 0.430067710 0.422533650 0.298756962 0.277670314 0.149106526 [6] 0.004114766 -0.151584554 -1.716368655 -14.456496183 -15.246523300 Largest eigenvalues: [1] 64570556 60491679 57362371 55997647 55204651 53481933 51974861 51894203 [9] 51866692 50972864 Smallest eigenvalues: [1] 0.4367080 0.3518828 0.3323773 0.3312061 0.3238202 0.3020763 [7] 0.2846286 0.2665455 -0.1121726 -1.1884098 Largest eigenvalues: [1] 65735735 60835951 58215531 56787345 55486000 54009957 52739215 52403891 [9] 52355074 51511373 Smallest eigenvalues: [1] 0.34953304 0.34263765 0.33106232 0.28835138 0.28621615 0.27790996 [7] 0.24896089 0.20303937 0.08655229 -2.27140333 Largest eigenvalues: [1] 65095325 60085501 57590523 56051404 54770889 53440447 52167452 51943210 [9] 51656173 51275428 Smallest eigenvalues: [1] 0.6592048 0.6404003 0.5166595 0.4033482 0.4028323 0.3708722 [7] 0.3462916 0.2698337 0.2648815 -0.7286708 Largest eigenvalues: [1] 64613077 59920510 57132441 55773065 55111497 53670501 52220693 51902478 [9] 51703973 50873263 Smallest eigenvalues: [1] 0.37891647 0.31123961 0.30510601 0.19230167 0.17716224 0.03259586 [7] -0.17742905 -0.64515518 -2.02278639 -2.28797808 Largest eigenvalues: [1] 65900707 60756964 58434230 56451026 55575079 54007667 52663257 52506551 [9] 52413928 51885792 Smallest eigenvalues: [1] 0.45556575 0.36751171 0.35966646 0.26996310 0.26295304 0.19468767 [7] 0.18823328 -0.03956099 -0.15294538 -0.34344492 Largest eigenvalues: [1] 63440266 61070682 56983675 55922306 55303250 54043908 52022979 51873568 [9] 51411685 50654573 Smallest eigenvalues: [1] 0.4905209 0.4643631 0.4284030 0.4142746 0.2207196 0.1673253 [7] -0.5509606 -1.6271276 -7.1104395 -9.8297614 Largest eigenvalues: [1] 65516259 59914351 57209289 56836790 54941499 52939629 52716622 52506521 [9] 51921697 51562362 Smallest eigenvalues: [1] 0.4106379 0.3301665 0.2167164 0.2040239 0.1352433 0.1261937 [7] -0.1479056 -1.4012180 -1.9481681 -4.5814904 Largest eigenvalues: [1] 62053635 59553829 56229488 54892512 54870917 53141701 52027549 52017605 [9] 50939490 50742460 Smallest eigenvalues: [1] 0.23339206 0.19264821 0.14566220 0.09516121 0.01871251 -0.10373377 [7] -0.28396276 -0.87932007 -1.53954870 -2.86300275 Largest eigenvalues: [1] 65363760 61528790 58337241 57320176 55442653 53749587 53451881 52751825 [9] 52355324 51516724 Smallest eigenvalues: [1] 0.46900975 0.45756721 0.45639449 0.42779764 0.38861220 0.27796359 [7] 0.24700575 0.20415410 0.16402602 -0.02413903 Largest eigenvalues: [1] 62994291 59486543 56982678 54894778 54810845 53335460 52007252 51275553 [9] 50918118 50544221 Smallest eigenvalues: [1] 0.56332150 0.56235172 0.53824983 0.53555934 0.46745360 0.45266697 [7] 0.38544392 0.23974666 0.09397433 -0.07977456 Largest eigenvalues: [1] 63506834 60585083 57685873 55448152 55411504 53919463 52154542 51873020 [9] 51453738 50900873 Smallest eigenvalues: [1] 0.45586335 0.44886781 0.38949076 0.37173644 0.36319228 0.27477958 [7] 0.04376298 0.04111338 -0.18370843 -9.00470598 Largest eigenvalues: [1] 65263619 60764933 57655387 57042414 55057333 53274063 53081235 52058941 [9] 51956356 51192634 Smallest eigenvalues: [1] 0.42942178 0.42424857 0.39652557 0.38896025 0.33227749 0.31281139 [7] 0.26494138 -0.09445423 -0.51650472 -1.42408393 Largest eigenvalues: [1] 64162879 60036713 57612890 55807625 54920771 53641231 51860806 51835422 [9] 51778135 50900906 Smallest eigenvalues: [1] 0.5132643 0.5029630 0.4351605 0.4099295 0.3557336 0.2691699 [7] 0.2262361 0.1695444 0.1412563 -1.3564060 Largest eigenvalues: [1] 63726205 60267131 57125561 55734594 55459744 53931121 52284879 51836487 [9] 51321733 50949508 Smallest eigenvalues: [1] 0.6947738 0.5524289 0.5163589 0.3769426 0.3621315 0.3343969 [7] 0.3005910 0.2647608 0.1340909 -0.1257241 Largest eigenvalues: [1] 63915112 60359994 57515484 55705835 55580355 53864952 52717574 51906035 [9] 51811247 51374724 Smallest eigenvalues: [1] 0.17399293 0.14668297 0.13014329 0.10154982 0.05478427 [6] -0.07858091 -0.08885453 -0.38554795 -2.55661303 -10.46824644 Largest eigenvalues: [1] 63671141 59391123 56451760 55603415 54857795 53157005 51835080 51557921 [9] 50900544 50269519 Smallest eigenvalues: [1] 0.5565602876 0.4412926206 0.3703934677 0.3242838418 0.2929735410 [6] 0.2866446591 0.2326488857 0.0004668943 -0.4870154074 -0.5942967261 Largest eigenvalues: [1] 64621816 60829664 57869410 56017177 55439920 53843014 52863578 52242244 [9] 52173231 51954614 Smallest eigenvalues: [1] 0.4294170 0.2906370 0.2838302 0.2368419 0.2036671 0.1859544 [7] 0.1632616 0.1387046 -1.4531621 -15.6338062 Largest eigenvalues: [1] 64679069 59651279 56971323 56061394 54739390 53132849 52317677 52062137 [9] 51683223 51105237 Smallest eigenvalues: [1] 0.4768358 0.4633440 0.4134908 0.3899816 0.3311158 0.3232596 [7] 0.2825004 -0.6337067 -6.9747085 -26.9398822 Largest eigenvalues: [1] 64526309 60636211 57295159 56336653 55681572 54043629 52302861 52158735 [9] 52010805 51129006 Smallest eigenvalues: [1] 0.44937738 0.41200232 0.38136894 0.26573141 0.22418340 0.18096288 [7] 0.15753976 0.12372860 0.01736977 -0.90399644 Largest eigenvalues: [1] 65485371 61207567 58668150 56571645 55672649 54252856 52769983 52643571 [9] 52480537 51858158 Smallest eigenvalues: [1] 0.4927097 0.3541109 0.3403424 0.3067935 0.3039201 0.2957033 [7] 0.2955304 0.2553524 0.1724951 -0.6452331 Largest eigenvalues: [1] 64363823 59914191 56930183 55718190 54838230 53186891 51957963 51857211 [9] 51396822 51066086 Smallest eigenvalues: [1] 0.4445254 0.4325453 0.4180866 0.3392527 0.3293453 0.2918831 [7] 0.2819983 0.2135124 0.1794837 -0.9750292 Largest eigenvalues: [1] 65079999 60507571 57459036 56624897 54934481 53631010 52558210 52483901 [9] 51857988 51722368 Smallest eigenvalues: [1] 0.35238406 0.30235391 0.28126035 0.23503907 0.23020427 0.01862637 [7] -0.54217517 -0.62257215 -1.66134727 -6.06466464 Largest eigenvalues: [1] 64206520 59327298 57117161 55543154 54364857 53267864 51922715 51723964 [9] 51532529 51021170 Smallest eigenvalues: [1] 0.3727948 0.3474193 0.3254185 0.3116484 0.2841517 0.2740666 [7] 0.2120624 0.1155873 -0.4931777 -3.9524265 Largest eigenvalues: [1] 62045232 59317993 56434316 54636107 54404068 53041601 51763938 51297251 [9] 50613816 50489818 Smallest eigenvalues: [1] 0.3933471 0.3471600 0.3320841 0.3306430 0.2960491 0.2025489 [7] 0.1797307 0.1717850 0.1313368 -3.8661918 Largest eigenvalues: [1] 64896235 60908382 57840302 56154951 55754018 54406921 52751216 52680298 [9] 52092783 51906524 Smallest eigenvalues: [1] 0.58382175 0.46840075 0.43570285 0.39391324 0.38179398 0.33526374 [7] 0.33285675 0.15951703 -0.05347295 -9.23003284 Largest eigenvalues: [1] 64021201 60112179 57377663 55482512 55476044 54003150 52367237 52205834 [9] 51580870 51232105 Smallest eigenvalues: [1] 0.5679771 0.5136341 0.4454096 0.4098713 0.3246302 0.2852869 [7] 0.2810462 0.2742600 0.1594525 -0.9096981 Largest eigenvalues: [1] 62402250 59945731 56876040 55088529 54775174 53395944 51771857 51663222 [9] 50733360 50563583 Smallest eigenvalues: [1] 0.5208800 0.5131013 0.4176284 0.3495412 0.3087863 0.2598037 [7] 0.2594486 0.1430163 0.1112036 -0.1455603 Largest eigenvalues: [1] 64730411 60918235 58019251 56041332 55812023 54316581 52664103 52328449 [9] 52179450 51424259 Smallest eigenvalues: [1] 0.51429120 0.49676158 0.44222096 0.39439018 0.34219113 0.31474323 [7] 0.11792681 0.05927812 -0.03319816 -7.07977194 Largest eigenvalues: [1] 63952055 59936772 57256508 55541418 55167004 53683301 52276794 51994404 [9] 51563416 51075028 Smallest eigenvalues: [1] 0.31044308 0.25629393 0.16914060 0.13848943 0.12932323 0.04998798 [7] -0.53621952 -0.99503219 -1.38720389 -3.18335418 Largest eigenvalues: [1] 62771592 60134043 57204467 55531513 55205386 53424257 52509237 52349368 [9] 51375022 51158186 Smallest eigenvalues: [1] 0.3435085 0.3334230 0.2694998 0.2170939 0.1734174 0.1204316 [7] 0.1135274 -0.7253679 -5.1454549 -29.7942473 Largest eigenvalues: [1] 65575891 60206493 57181444 56748017 55287651 53731993 52651717 52450969 [9] 52098622 51678461 Smallest eigenvalues: [1] 0.54896002 0.53930877 0.52887691 0.32190308 0.27647123 0.23428633 [7] 0.22939166 0.06935047 -0.02291231 -0.05160940 Largest eigenvalues: [1] 63033814 60881869 57725918 56353474 54964041 54488758 52888474 52591832 [9] 51648111 51144277 Smallest eigenvalues: [1] 0.53688674 0.50979492 0.35955751 0.34266514 0.33681509 0.22482783 [7] 0.18510949 0.10494858 0.04029477 -1.21583142 Largest eigenvalues: [1] 63082588 61122435 57922257 56548851 55201858 54717729 52950649 52864058 [9] 51948054 51283083 Smallest eigenvalues: [1] 0.37055333 0.24397796 0.22535539 0.22064736 0.20276503 0.20001838 [7] 0.16633918 0.05716543 -1.93005306 -6.40058671 Largest eigenvalues: [1] 65278890 59918567 57430993 56262550 54734647 53438270 52354384 52071414 [9] 51797266 51290060 Smallest eigenvalues: [1] 0.457640508 0.434488032 0.415186189 0.378885804 0.370192720 [6] 0.294331408 0.156670212 0.151513969 0.002483472 -0.068920470 Largest eigenvalues: [1] 64260653 60839144 58165575 56247786 55338077 53814764 52079468 52014303 [9] 51922844 51010359 Smallest eigenvalues: [1] 0.34855723 0.32653035 0.21678353 0.20444853 0.03070099 [6] -1.47484974 -2.61706685 -9.63598610 -10.65152405 -11.81698325 Largest eigenvalues: [1] 65085852 59936137 57667199 56556491 55233158 54006823 53023309 52398653 [9] 52347806 51973266 Smallest eigenvalues: [1] 0.3381866 0.3227711 0.3098073 0.2812932 0.2717524 0.2368776 [7] 0.1772994 -1.2831674 -2.5541371 -15.3659377 Largest eigenvalues: [1] 64668112 60361693 57195391 56379975 54830152 53255052 52520586 52363800 [9] 51869621 51710322 Smallest eigenvalues: [1] 0.6008290 0.5774503 0.5152635 0.4450602 0.4363860 0.4048657 [7] 0.2738052 0.2437140 0.1016007 -0.2659326 Largest eigenvalues: [1] 65662001 59818585 56814940 56366223 54458983 52704285 52380267 51463555 [9] 51209721 50711322 Smallest eigenvalues: [1] 0.36773786 0.34527390 0.31587361 0.28753809 0.24899620 0.07115531 [7] 0.07013047 0.02301751 -0.29917983 -0.55715220 Largest eigenvalues: [1] 64833014 59910569 57528814 55484897 55387991 53913139 51807501 51686018 [9] 51570911 50822061 Smallest eigenvalues: [1] 0.42114651 0.41012319 0.27469020 0.21575691 0.20137663 0.09823638 [7] 0.03508838 -0.45886452 -0.91304983 -2.30407978 Largest eigenvalues: [1] 64361593 60247304 57389767 55946292 55801165 54225426 52448197 52389107 [9] 51873376 51778606 Smallest eigenvalues: [1] 0.5239711 0.4660117 0.4390764 0.4384642 0.2931430 0.2334313 [7] 0.2302813 0.1873801 0.1763725 -11.2653385 Largest eigenvalues: [1] 63453016 60212635 57687679 55459311 55121073 53799618 52661547 51824672 [9] 51279725 51028949 Smallest eigenvalues: [1] 0.4941352 0.3978747 0.3490921 0.2902397 0.2815614 0.2734541 [7] 0.2595843 0.2544340 -1.5936816 -4.4238888 Largest eigenvalues: [1] 65845680 59805365 57340790 56821329 54719602 53206672 52712707 52219037 [9] 51702344 51220631 Smallest eigenvalues: [1] 0.51356322 0.49695658 0.49159728 0.43954030 0.34125666 [6] 0.23246579 0.20326497 0.14610412 0.02726586 -15.33415248 Largest eigenvalues: [1] 64413183 60109496 56859240 56060069 55029419 53201102 52047343 52006692 [9] 51767086 50956372 Smallest eigenvalues: [1] 0.5355418 0.4460271 0.4436493 0.3404052 0.2988852 0.2740152 [7] 0.2665325 0.2030855 -0.1478093 -0.3066490 Largest eigenvalues: [1] 64688108 60314315 57637293 55560905 55330792 53920476 52587938 52238865 [9] 51664518 51446987 Smallest eigenvalues: [1] 0.50025753 0.44788931 0.37637313 0.34216412 0.28581862 0.27678297 [7] 0.09094782 -0.01622387 -1.34507222 -6.79008198 Largest eigenvalues: [1] 64534920 59809700 56904018 56148298 55038247 53457244 52232116 52175519 [9] 51688107 51115216 Smallest eigenvalues: [1] 0.48890093 0.38292492 0.36992951 0.35624224 0.23811757 0.23788674 [7] 0.18817711 -0.05535112 -0.38692746 -1.37068085 Largest eigenvalues: [1] 63534652 59675338 57395507 55357123 54840424 53632265 52284759 51921644 [9] 51519247 51114186 Smallest eigenvalues: [1] 0.50408815 0.43963425 0.41289794 0.38187241 0.35225835 0.34647649 [7] 0.34299125 0.32091325 0.31336602 -0.02669146 Largest eigenvalues: [1] 62895176 59742572 57136264 55640866 54940740 53281578 51674828 51576426 [9] 51509171 50484428 Smallest eigenvalues: [1] 0.5317972 0.4111299 0.3156682 0.2807998 0.2799069 0.2146495 [7] 0.1659147 0.1238339 -0.6588994 -0.7753490 Largest eigenvalues: [1] 64118211 60527814 57381779 55982082 55740875 54021148 52745121 52385741 [9] 52140453 51552308 Smallest eigenvalues: [1] 0.50709128 0.49099777 0.40388220 0.37044460 0.35276207 [6] 0.05156476 0.03688797 -2.64826461 -3.19911244 -10.65902213 Largest eigenvalues: [1] 63856036 60138867 56921212 55829284 55189170 53515160 51835841 51665493 [9] 51643967 50642379 Smallest eigenvalues: [1] 0.513142749 0.395678723 0.356456868 0.339783740 0.223403441 [6] 0.200601311 0.005595955 -0.353177970 -0.424262348 -1.266350097 Largest eigenvalues: [1] 63734011 59548656 56744384 55444984 54823432 53028764 52564218 51473893 [9] 51308682 50890905 Smallest eigenvalues: [1] 0.41250445 0.36135583 0.23407873 0.12024406 0.02703175 [6] -0.59760540 -1.05935942 -1.15977714 -14.21677087 -25.84205488 Largest eigenvalues: [1] 65953425 59815186 57442187 56142899 54845114 53314603 52321618 52044911 [9] 51935666 50849781 Smallest eigenvalues: [1] 0.36615439 0.31326129 0.28495931 0.21551577 0.19159089 0.13238991 [7] 0.02555591 -1.91107869 -6.16149963 -8.45163422 Largest eigenvalues: [1] 64811459 59869089 57150571 55992868 55291305 53664492 52036887 51766814 [9] 51265665 50214149 Smallest eigenvalues: [1] 0.45007466 0.43451046 0.41871822 0.34876442 0.27131051 0.25260930 [7] 0.17996303 0.13108908 -0.04422398 -3.82919130 Largest eigenvalues: [1] 62928653 59214590 56752903 54675098 54613992 53038678 51411295 51156372 [9] 50814684 50462889 Smallest eigenvalues: [1] 0.49268166 0.48263594 0.41107868 0.40034653 0.37068409 0.26057429 [7] 0.14597205 0.07235150 0.03807847 -2.53513236 Largest eigenvalues: [1] 62292103 59532020 56365181 54874367 54688050 53050250 52035823 51398565 [9] 50818688 50648019 Smallest eigenvalues: [1] 0.5278855 0.4758727 0.4338333 0.4282913 0.4171706 0.3689617 [7] 0.2936994 0.2033135 -0.1243822 -1.4423889 Largest eigenvalues: [1] 65577663 59767918 56997841 56864343 54757559 52901387 52889416 51675037 [9] 51295138 50629651 Smallest eigenvalues: [1] 0.5204820 0.4225804 0.4155447 0.3779917 0.3631986 0.2949551 [7] 0.2277822 -0.1807936 -1.1845013 -1.5216757 Largest eigenvalues: [1] 65648655 60112696 57563338 56832083 54708105 52908926 52670447 52074726 [9] 51670763 51203976 Smallest eigenvalues: [1] 0.39859094 0.34904025 0.31045039 0.26102341 0.12235162 0.09026301 [7] 0.02238457 0.02061492 -4.92707840 -5.92397543 Largest eigenvalues: [1] 65156532 61344783 57639545 57079460 56097183 54121380 53700622 52650893 [9] 52612872 52099386 Smallest eigenvalues: [1] 0.37820033 0.35014782 0.33763113 0.33480218 0.28982951 0.26945971 [7] 0.20797659 0.19721865 0.08415929 -0.95241435 Largest eigenvalues: [1] 66168494 59692238 57024740 56703378 54335689 52848992 52839439 52011249 [9] 51248214 51202882 Smallest eigenvalues: [1] 0.4334646 0.3884285 0.3570164 0.3296284 0.2183761 0.2167296 [7] 0.1806627 0.1454605 -0.8857873 -2.3714396 Largest eigenvalues: [1] 64370625 59268930 56707960 55440157 54615398 53011247 51796337 51390240 [9] 51073100 50413122 Smallest eigenvalues: [1] 0.58426383 0.58321723 0.53197649 0.44854330 0.40623896 0.39575861 [7] 0.36774993 0.17371816 -0.04097231 -0.25655805 Largest eigenvalues: [1] 63924784 59492838 56665637 55629089 54358797 52804916 51649014 51467250 [9] 50915770 50044818 Smallest eigenvalues: [1] 0.3318537 0.2901188 0.2727990 0.2651640 0.2297298 0.1693474 [7] -0.1287857 -0.1425885 -3.0594349 -21.9744984 Largest eigenvalues: [1] 65592052 60782668 58385805 56880154 55344360 54145498 52816661 52488715 [9] 52267393 51392132 Smallest eigenvalues: [1] 0.45676739 0.44932882 0.36923430 0.34882823 0.30920800 0.27799927 [7] 0.12146820 0.07497249 -0.27544281 -1.73156160 Largest eigenvalues: [1] 62977568 60268357 57461357 55734827 55323960 54132613 52305680 52225240 [9] 51333933 51131169 Smallest eigenvalues: [1] 0.37591592 0.34939391 0.28394355 0.22288594 0.02183537 [6] -0.13688291 -0.89638787 -1.87339689 -4.26093626 -33.15763459 Largest eigenvalues: [1] 65204940 59795188 56925205 55414986 54673291 53127366 51908386 51523503 [9] 51404041 51047409 Smallest eigenvalues: [1] 0.4117747 0.4005399 0.3992011 0.3304966 0.3046413 0.2551265 [7] 0.1850499 0.1543968 0.1345448 -0.5482180 Largest eigenvalues: [1] 63981840 59956176 57294991 55683757 55268825 53483755 52624990 51617780 [9] 51583966 51339124 Smallest eigenvalues: [1] 0.54588648 0.54438498 0.46984053 0.43218464 0.41920238 0.28237188 [7] 0.27370193 0.26754378 -0.04608023 -0.24557334 Largest eigenvalues: [1] 64539581 59781570 56704900 55390191 54696216 53173699 51644082 51473733 [9] 51166525 50415484 Smallest eigenvalues: [1] 0.3113205 0.2909393 0.2809136 0.2588262 0.1333198 -1.0004547 [7] -1.4927454 -2.0314479 -2.2647917 -2.7687152 Largest eigenvalues: [1] 65283855 60509423 57883477 55654332 55307358 53762030 52333977 51810699 [9] 51671180 51616296 Smallest eigenvalues: [1] 0.4837935 0.4553574 0.4505911 0.4154184 0.4053612 0.4034359 [7] 0.3928558 0.2583591 0.2003834 -0.3563524 Largest eigenvalues: [1] 64274093 60120534 57524312 55883456 55363625 53796518 52096232 51948413 [9] 51746521 50995978 Smallest eigenvalues: [1] 0.48284963 0.37793857 0.36901334 0.33060318 0.26928105 0.26230950 [7] 0.22734393 0.18096328 0.03577805 -0.62467375 Largest eigenvalues: [1] 63420055 60508344 57049049 55589578 55244582 53565600 52629417 51657562 [9] 51581482 51412647 Smallest eigenvalues: [1] 0.4399150 0.4208253 0.2980640 0.2855796 0.2076432 0.1894704 [7] 0.1833774 0.1710420 -1.2419875 -2.0152343 Largest eigenvalues: [1] 63836011 60169673 57052417 55458551 55344531 53806757 52367084 52214421 [9] 51573106 51281117 Smallest eigenvalues: [1] 0.53875488 0.47593114 0.38327921 0.38137554 0.36900828 0.35832974 [7] 0.31410037 0.28686666 0.01598865 -0.63067804 Largest eigenvalues: [1] 65686353 60443186 57702067 56451625 55058677 53640595 52604128 51954061 [9] 51756421 51141710 Smallest eigenvalues: [1] 0.6032834 0.4546018 0.4216246 0.3932967 0.3325949 0.2875735 [7] 0.2786494 0.2449993 0.2355360 -1.2404562 Largest eigenvalues: [1] 66173796 60524674 57939570 56573687 55321825 53972627 52685442 52488056 [9] 51963098 51526695 Smallest eigenvalues: [1] 0.47471732 0.41001096 0.37543119 0.35652599 0.18515664 0.15704361 [7] 0.06375342 -0.08862345 -1.52155284 -1.85649957 Largest eigenvalues: [1] 65208262 60859311 58154447 56587520 55354355 54065181 52496298 52355682 [9] 52128816 51219621 Smallest eigenvalues: [1] 0.39010591 0.38772164 0.34102365 0.29848154 0.08962970 [6] 0.06336244 -0.79794362 -1.84033589 -2.13556826 -15.01566994 Largest eigenvalues: [1] 64984035 59649025 56652940 56467108 54477533 53017444 52281300 51805761 [9] 51518878 50541685 Smallest eigenvalues: [1] 0.565502102 0.481928124 0.450176821 0.444762778 0.254680255 [6] 0.185377803 0.168778671 0.006248232 -0.791545041 -1.916082975 Largest eigenvalues: [1] 63903269 60301926 57102455 55441762 55389464 53852520 52380464 52100368 [9] 51532276 51361169 Smallest eigenvalues: [1] 0.34335350 0.32955884 0.31210499 0.28523221 0.20733693 0.17953085 [7] 0.15290637 0.09511059 -0.35694884 -8.53844157 Largest eigenvalues: [1] 62109519 60423723 57509442 56030908 55091527 54258754 52722879 52428320 [9] 51586847 51080760 Smallest eigenvalues: [1] 0.54457663 0.50456799 0.42099679 0.39756795 0.25794836 0.21988428 [7] 0.09436892 0.03252724 -1.21052870 -2.42474555 Largest eigenvalues: [1] 64225085 60746350 57121270 55768021 55680021 54068193 52412244 52254165 [9] 51603579 51149800 Smallest eigenvalues: [1] 0.4249970 0.4218964 0.3080185 0.2841112 0.2789110 0.2096348 [7] 0.2081632 0.1909149 -0.8827535 -1.0276920 Largest eigenvalues: [1] 65997044 60156927 57604506 57299503 54940742 53533320 53270265 52143358 [9] 52073714 51213849 Smallest eigenvalues: [1] 0.56352954 0.54750293 0.50053218 0.44036317 0.39531692 0.37396949 [7] 0.28074698 0.20713717 -0.05200555 -0.50019092 Largest eigenvalues: [1] 63554401 60391406 57058316 55398723 55028791 53332468 52090579 51626648 [9] 51437210 51198436 Smallest eigenvalues: [1] 0.5216278 0.4307288 0.4200359 0.4128112 0.3793602 0.3494066 [7] 0.3266821 0.2936509 0.2189408 -0.5980169 Largest eigenvalues: [1] 65356849 60605480 58034169 56449423 55321652 53935545 52534872 52302176 [9] 52238990 51552313 Smallest eigenvalues: [1] 0.5670216 0.4868008 0.4643145 0.3776589 0.3357970 0.1967524 [7] -0.2041937 -0.2798641 -0.3427553 -1.2985528 Largest eigenvalues: [1] 64857935 60050708 57421086 56157476 54776540 53297154 52221990 52155247 [9] 51937533 51432883 Smallest eigenvalues: [1] 0.5204519 0.4595059 0.3175062 0.3045108 0.2837890 0.2703324 [7] 0.2699931 0.2489191 0.1548238 -0.3876310 Largest eigenvalues: [1] 63658788 59593115 57205743 55884840 54326103 52897787 51868289 51569947 [9] 51179189 50504370 Smallest eigenvalues: [1] 0.60215041 0.52312027 0.43963147 0.40742445 0.36040984 0.32678984 [7] 0.23726243 0.15771312 0.08797395 -1.64710534 Largest eigenvalues: [1] 63729224 59870168 57103599 55552808 54842836 53335001 51700393 51589148 [9] 51532808 50732599 Smallest eigenvalues: [1] 0.51699535 0.50554701 0.46953293 0.36119902 0.33526766 0.24925559 [7] 0.20661811 0.01767268 -0.20654133 -2.27933558 Largest eigenvalues: [1] 65474350 59576281 57216172 56437852 54575757 52772914 52502288 51935481 [9] 51389338 51061769 Smallest eigenvalues: [1] 0.5694480 0.5523880 0.5045152 0.5028494 0.4763201 0.4132950 [7] 0.2830584 0.2491897 0.2015181 -1.2580334 Largest eigenvalues: [1] 64449168 60170429 57194726 56224052 54591774 53132886 52092576 51819879 [9] 51444546 50890557 Smallest eigenvalues: [1] 0.56190068 0.46452296 0.44329888 0.34392623 0.29880342 0.29704275 [7] 0.23897772 0.22827357 0.10759848 -0.02860955 Largest eigenvalues: [1] 63464266 60584499 57340173 55646098 55046927 53508497 52082130 52056645 [9] 51779392 51375070 Smallest eigenvalues: [1] 0.26208087 0.24585301 0.21944902 0.16933434 0.04943113 [6] -0.13696131 -0.21953305 -0.49880907 -7.20362046 -30.09318837 Largest eigenvalues: [1] 64549792 59673595 57439029 57057742 54531930 53038942 52667570 52626709 [9] 51898041 51161085 Smallest eigenvalues: [1] 0.4085359 0.3940913 0.3764065 0.2795715 0.2534743 0.2310830 [7] 0.2050530 -0.1491286 -0.6555420 -0.7526958 Largest eigenvalues: [1] 66595143 61672174 58871135 57767475 55776318 54171919 53697429 53028618 [9] 52612064 52299067 Smallest eigenvalues: [1] 0.41985536 0.34744602 0.33963154 0.31382586 0.30230572 0.26991030 [7] 0.07564455 -0.06564710 -0.21107038 -1.26331436 Largest eigenvalues: [1] 64905909 60196206 57572316 56064966 54472796 53404938 52155079 51985153 [9] 51755697 51473477 Smallest eigenvalues: [1] 0.56665657 0.53420415 0.45797345 0.40978592 0.40664044 0.32174511 [7] 0.31384912 0.25903760 0.21983098 -0.03078901 Largest eigenvalues: [1] 62874763 59657330 56979933 55310913 55017296 53414808 51892802 51589644 [9] 51130094 50719204 Smallest eigenvalues: [1] 0.4523856 0.4283625 0.3907697 0.3051477 0.3035231 0.2303833 [7] 0.2218429 -0.2850989 -1.8029084 -3.7914718 Largest eigenvalues: [1] 65377809 60305610 57946480 56234647 55036341 53466446 52154180 52099074 [9] 51646246 51298890 Smallest eigenvalues: [1] 0.5122451 0.4252697 0.3474607 0.2704993 0.2536186 0.2107707 [7] -0.1067480 -0.7252001 -1.4469827 -2.4991351 Largest eigenvalues: [1] 66019221 60793026 58029059 56541345 55605992 54053986 52853602 52756445 [9] 52535871 51894446 Smallest eigenvalues: [1] 0.5480063 0.5343391 0.4154038 0.3745385 0.3115282 0.3097118 [7] 0.2899511 0.2644871 0.2550387 -1.1419339 Largest eigenvalues: [1] 65957063 60428386 57695892 56899556 55281366 53945526 52960656 52205228 [9] 52171616 51310725 Smallest eigenvalues: [1] 0.42313923 0.40991807 0.35546893 0.26965487 0.25743431 0.21984232 [7] 0.17762344 0.03473504 -0.20072486 -0.35606531 Largest eigenvalues: [1] 62806641 59341796 57064658 54891543 54129130 53333256 51664474 51193060 [9] 50610187 50399707 Smallest eigenvalues: [1] 0.40742609 0.38145632 0.33882274 0.29279607 0.24472277 0.24151625 [7] -0.03001365 -0.16345436 -0.65571891 -1.35975963 Largest eigenvalues: [1] 65031702 60393149 57758210 55406343 54893085 53524044 52187803 51585040 [9] 51402406 51309189 Smallest eigenvalues: [1] 0.5486390 0.5156129 0.4195664 0.3918329 0.3564056 0.3364130 [7] 0.3078334 0.2899076 0.1423248 -0.4230701 Largest eigenvalues: [1] 65568706 59932364 57300922 56389533 54783745 53382263 52496445 51913007 [9] 51894024 51087781 Smallest eigenvalues: [1] 0.5202029 0.5140320 0.5114391 0.4569729 0.3193646 0.2008783 [7] 0.1655013 -0.1041523 -0.1415162 -1.9817074 Largest eigenvalues: [1] 62284853 59429629 56001815 54760569 54235189 52787325 51521834 50790275 [9] 50296574 49994857 Smallest eigenvalues: [1] 0.458718532 0.438775672 0.346712783 0.292639995 -0.002781101 [6] -0.488893223 -0.595328606 -0.631138311 -0.997272931 -8.262999017 Largest eigenvalues: [1] 64068459 59915218 57262574 55742748 55510255 53935162 52591694 52047434 [9] 51691952 51551054 Smallest eigenvalues: [1] 0.48634602 0.47936263 0.46160011 0.40297858 0.29135504 0.25391103 [7] 0.15862343 -0.07041424 -0.27646361 -2.43797582 Largest eigenvalues: [1] 64332644 59897209 56470920 55183410 54838770 52954550 51578078 51243264 [9] 51196083 50683648 Smallest eigenvalues: [1] 0.082846267 -0.005581226 -0.030466258 -0.197740171 -0.296137775 [6] -1.473451796 -3.707591644 -15.051128134 -16.126222283 -22.053085868 Largest eigenvalues: [1] 63027655 59188696 56172161 54910120 54447753 52918552 52066746 51512786 [9] 50886452 50576636 Smallest eigenvalues: [1] 0.61443220 0.58391278 0.52931697 0.46519635 0.38714309 0.31769963 [7] 0.31209848 0.28466427 -0.02873817 -0.26177468 Largest eigenvalues: [1] 64458968 60497059 57228017 56402655 55114734 53271518 52691697 52401047 [9] 51809570 51546118 Smallest eigenvalues: [1] 0.47498698 0.43907139 0.38818481 0.36293211 0.33091355 0.29491259 [7] 0.09201517 -0.10576516 -0.35183403 -1.04367754 Largest eigenvalues: [1] 63381666 60251291 57431491 55902782 55061044 53274016 52041578 51976478 [9] 51865078 50966852 Smallest eigenvalues: [1] 0.48231828 0.47064359 0.45700345 0.40907645 0.40052300 [6] 0.22379677 0.20123232 0.12988660 0.04069322 -10.46087346 Largest eigenvalues: [1] 62951268 60869894 57175218 55863040 55280518 53985731 52289225 51903576 [9] 51316391 51023437 Smallest eigenvalues: [1] 0.4530239 0.4006749 0.3989586 0.3836229 0.3066514 0.2944299 [7] 0.2567527 0.2222983 -0.8898274 -1.8020845 Largest eigenvalues: [1] 65057921 60038553 57735901 56732147 54912000 53663192 52542060 52343902 [9] 51908462 51562676 Smallest eigenvalues: [1] 0.36550792 0.35813549 0.35230397 0.34406144 0.26305876 [6] 0.24066573 0.23861919 -0.09986753 -1.20440284 -38.91301801 Largest eigenvalues: [1] 64280823 60552879 57440472 56068947 55365706 53849815 52481967 52422169 [9] 52004825 51428756 Smallest eigenvalues: [1] 0.30389990 0.18237623 0.13047252 0.06924863 0.04933696 -0.46901345 [7] -0.90598384 -2.05739524 -3.17678867 -4.88804782 Largest eigenvalues: [1] 65814289 59346236 56544729 56045852 54180737 52715817 52117799 51668468 [9] 51386058 50818227 Smallest eigenvalues: [1] 0.4704790 0.4511027 0.4456544 0.3703976 0.3397021 0.3101340 [7] 0.2253259 0.1486695 -0.6726460 -7.8476789 Largest eigenvalues: [1] 64782270 60821047 57882959 55958174 55825667 54258539 53097850 52174524 [9] 52009772 51779557 Smallest eigenvalues: [1] 0.45904995 0.42647196 0.37888662 0.34251901 0.29816932 0.25406977 [7] 0.18202582 0.14217355 -0.02940969 -0.37898229 Largest eigenvalues: [1] 65024544 60817490 58143012 56262786 55649739 53885789 52846642 52231988 [9] 52155433 51763212 Smallest eigenvalues: [1] 0.5455218 0.5303258 0.5080793 0.3732920 0.3393157 0.2854801 [7] 0.2603636 0.2111399 0.1835342 -0.2537073 Largest eigenvalues: [1] 61683626 59828641 57000643 55188322 54322432 53347141 52305285 51362369 [9] 50994008 50451246 Smallest eigenvalues: [1] 0.23649434 0.19348165 0.19312155 0.15397270 0.13096985 [6] 0.10018482 -0.03443138 -1.16534576 -3.06160539 -16.53599980 Largest eigenvalues: [1] 66341359 60227728 57649906 57445546 55089442 53828172 53084267 52272703 [9] 52117761 51550276 Smallest eigenvalues: [1] 0.5319380 0.4680688 0.4220319 0.3854596 0.3137564 0.2823258 [7] 0.2642564 0.1643395 0.1085846 -0.7460929 Largest eigenvalues: [1] 64284462 61047810 57952905 56361682 56287940 54565769 52995151 52526545 [9] 52332539 51733625 Smallest eigenvalues: [1] 0.3872983 0.3718288 0.2864391 0.2854666 0.2345735 0.1857269 [7] 0.1423190 0.1057419 -1.5526508 -20.2690897 Largest eigenvalues: [1] 64179396 59689006 56898099 55128441 54901988 53398530 51759432 51524378 [9] 51175761 50990164 Smallest eigenvalues: [1] 0.56961296 0.50211579 0.44720842 0.42223273 0.28130779 0.27534215 [7] 0.25147123 0.21537915 0.13279976 -0.02095331 Largest eigenvalues: [1] 64184582 60436894 57899031 55767740 54944131 54249461 52922033 51960906 [9] 51704696 51225030 Smallest eigenvalues: [1] 0.53460627 0.48513699 0.45841813 0.41870000 0.35149039 0.26360364 [7] 0.18542450 0.18530241 0.06283988 -0.02437856 Largest eigenvalues: [1] 65182962 60004574 57855558 55896936 54950303 53383366 52172631 52169501 [9] 51908222 51320099 Smallest eigenvalues: [1] 0.51792872 0.47212651 0.39845731 0.36518041 0.30676181 0.17766244 [7] 0.16946911 0.02711115 -0.19072387 -1.27581554 Largest eigenvalues: [1] 63289504 60655951 57091378 55756244 55607503 53517099 52384267 51853917 [9] 51375768 50877973 Smallest eigenvalues: [1] 0.35428402 0.31058178 0.24239380 0.22800816 0.14366385 [6] 0.12448140 0.03062687 -0.47869851 -5.06478606 -23.70376459 Largest eigenvalues: [1] 64145724 59963504 57210943 55354251 55349428 53391942 52545954 51901404 [9] 51661341 51559959 Smallest eigenvalues: [1] 0.51276329 0.49977214 0.45915053 0.43379300 0.30729224 0.21820161 [7] 0.21343604 0.07972120 0.07041202 -0.47744528 Largest eigenvalues: [1] 64650803 60190840 56983154 55833077 55120328 53489655 52413247 51909332 [9] 51714069 51121776 Smallest eigenvalues: [1] 0.5025642 0.4721828 0.3668636 0.3230614 0.3146502 0.2637488 [7] 0.2031941 -0.1467369 -1.4206695 -2.1226795 Largest eigenvalues: [1] 63715589 60111156 57618041 56047231 55312315 54392889 52805750 52044473 [9] 51444691 51115785 Smallest eigenvalues: [1] 0.57618936 0.50437109 0.44253556 0.40162290 0.38143383 0.37137165 [7] 0.34330487 0.30554625 0.29375354 -0.01864911 Largest eigenvalues: [1] 64837960 60267482 57162178 56120568 55417987 53476621 52603059 52252707 [9] 51659271 51478283 Smallest eigenvalues: [1] 0.58747222 0.46247493 0.40615564 0.37252154 0.30938274 0.28769590 [7] 0.27621797 0.21745839 -0.09714347 -0.32569202 Largest eigenvalues: [1] 62227312 59514272 57100534 55172135 54543366 53429789 51792465 51402797 [9] 50634725 50505127 Smallest eigenvalues: [1] 0.46147735 0.38056247 0.29618611 0.29002196 0.25084440 0.23936072 [7] 0.16339231 0.08561973 -0.22944040 -0.86014343 Largest eigenvalues: [1] 64639040 60353994 57656192 55508975 55380277 53875566 52403306 52172145 [9] 51728105 51354625 Smallest eigenvalues: [1] 0.57988811 0.51784458 0.51381191 0.45793024 0.37170030 0.25735942 [7] -0.06295068 -0.13836125 -0.52675154 -1.11966227 Largest eigenvalues: [1] 63573915 59632503 56521656 55296162 54347553 52699011 51471821 51310638 [9] 51268506 50448895 Smallest eigenvalues: [1] 0.5214007 0.4768875 0.4298152 0.4212942 0.3716958 0.3493964 [7] 0.3239597 0.2362379 0.0699308 -0.1126082 Largest eigenvalues: [1] 62602423 59104969 56230342 54975342 54357951 52666610 51535995 51278994 [9] 50949311 50449507 Smallest eigenvalues: [1] 0.4619851 0.4373467 0.2804770 0.2619680 0.2446529 0.1830913 [7] 0.1278125 -1.0903324 -10.9656909 -15.0244509 Largest eigenvalues: [1] 62694405 60767248 56922074 55840588 55311746 54200471 52499931 52427577 [9] 51266031 51192816 Smallest eigenvalues: [1] 0.4691136 0.4675890 0.4521460 0.4215578 0.3961748 0.3735821 [7] 0.3233972 0.3086474 0.2560002 -2.5796506 Largest eigenvalues: [1] 64598599 59810243 57125325 56740307 54552084 53168614 52570067 51720052 [9] 51627871 50864959 Smallest eigenvalues: [1] 0.4950739 0.4182841 0.3632045 0.3131121 0.2895653 0.2741059 [7] 0.2276522 0.1932157 -2.8474786 -4.3829595 Largest eigenvalues: [1] 65116606 60196932 57591854 55723036 55332585 53907481 52410544 51780837 [9] 51767593 51596822 Smallest eigenvalues: [1] 0.42881371 0.42843055 0.41330292 0.34826939 0.27471201 0.25118000 [7] 0.22749707 0.05175862 -0.14980698 -0.62629763 Largest eigenvalues: [1] 65562037 60096164 57572794 56167306 55241240 53826638 52312279 52252265 [9] 52149083 51267152 Smallest eigenvalues: [1] 0.4398722 0.3542322 0.3352858 0.3278937 0.2830944 0.2761435 [7] 0.2545866 0.2401905 0.2218608 -2.2757988 Largest eigenvalues: [1] 64910548 60538846 57331118 56481801 55065655 53573763 52537394 52188850 [9] 51958811 51082411 Smallest eigenvalues: [1] 0.5825820 0.5214181 0.4655219 0.3664353 0.2955329 0.2874229 [7] 0.2437339 0.1509109 0.0836512 -0.2135389 Largest eigenvalues: [1] 63600227 60522491 58172235 55890903 55116795 54617482 52792353 52355593 [9] 51564019 51377719 Smallest eigenvalues: [1] 0.5395627 0.4969850 0.4725656 0.4008540 0.3506297 0.3187900 [7] 0.2486233 0.1379814 -0.1586557 -3.6408846 Largest eigenvalues: [1] 65308883 60894089 57845627 55820089 55800405 54306633 52204139 52164038 [9] 52004589 51414024 Smallest eigenvalues: [1] 0.48776266 0.42660923 0.41964758 0.27900997 0.15372980 0.06051094 [7] 0.04615386 0.03363386 -0.44282030 -0.98324188 Largest eigenvalues: [1] 64127109 59514626 56570703 55316417 54641692 53116269 51745080 51484933 [9] 51407195 50627684 Smallest eigenvalues: [1] 0.4480195 0.4290202 0.3620698 0.3434233 0.2289225 0.2185495 [7] 0.2069439 0.1831452 -0.3371043 -0.7102083 Largest eigenvalues: [1] 64740647 60270422 57081019 55734153 55635788 53974028 52272544 52230024 [9] 51709908 51293591 Smallest eigenvalues: [1] 0.42985231 0.41042422 0.34230539 0.23361449 0.22150275 0.14118708 [7] -0.06674456 -0.10785911 -0.23598135 -1.44185056 Largest eigenvalues: [1] 63494786 60188033 57139279 55480965 54894605 53421251 52359781 51744015 [9] 51676020 51441694 Smallest eigenvalues: [1] 0.4120311 0.3530477 0.3252676 0.3194421 0.2684833 0.2350737 [7] 0.2124143 -0.2327599 -1.7259560 -2.9801417 Largest eigenvalues: [1] 65316751 60665054 57846664 56859640 55050516 53122244 52641226 52524708 [9] 51873115 51425983 Smallest eigenvalues: [1] 0.52949050 0.51977566 0.46030365 0.40256656 0.35034502 0.33285267 [7] 0.24269094 0.20226650 0.16547097 -0.01262839 Largest eigenvalues: [1] 65187895 60407227 57679795 56043085 55501186 53840607 52319963 52289786 [9] 52257984 51238223 Smallest eigenvalues: [1] 0.5355013 0.4866217 0.4790100 0.4635764 0.3058997 0.2970957 [7] 0.2919438 0.2288407 0.1453966 -3.0520384 Largest eigenvalues: [1] 65569100 60320504 57311932 57140365 55450412 53761219 53027667 52832023 [9] 52099835 51575430 Smallest eigenvalues: [1] 0.48432657 0.41722013 0.37305041 0.37101165 0.33759755 0.31536109 [7] 0.23168491 0.10351043 0.01477636 -1.72761011 Largest eigenvalues: [1] 63970672 59407406 56841595 55606637 54763370 53214451 51755641 51679362 [9] 51332227 50420492 Smallest eigenvalues: [1] 0.44908713 0.33672758 0.29858326 0.27079519 0.24723851 0.24280154 [7] 0.10900399 0.05530902 -0.18665752 -3.96915671 Largest eigenvalues: [1] 62826251 59780839 56951517 55170505 54967555 53287056 51909405 51533791 [9] 51047624 50584780 Smallest eigenvalues: [1] 0.4030885 0.3232050 0.3224300 0.3159119 0.1967794 0.1060946 [7] -0.2897242 -0.3686685 -1.4298307 -7.2426381 Largest eigenvalues: [1] 65759220 60303184 57770024 56244253 55241131 53816392 52653183 52439571 [9] 52234521 51364901 Smallest eigenvalues: [1] 0.5345002 0.4299528 0.4105145 0.4070320 0.4041669 0.3091196 [7] 0.2758072 0.2374550 0.0174245 -0.6222161 Largest eigenvalues: [1] 63727698 59807558 56994452 55703662 54611526 53082872 51973343 51831475 [9] 51644300 50924872 Smallest eigenvalues: [1] 0.5726498 0.5451262 0.3782607 0.3726637 0.3318796 0.3125551 [7] 0.2861111 0.2766571 0.2449393 -1.8759456 Largest eigenvalues: [1] 65742674 60936223 57944267 56924360 55434213 53981498 52850324 52456395 [9] 52027138 51468123 Smallest eigenvalues: [1] 0.38466282 0.34412500 0.31278743 0.30168756 0.23161936 -0.02942748 [7] -0.25532381 -0.45614524 -4.35004079 -5.87324734 Largest eigenvalues: [1] 65762066 60747064 57700127 56797864 55418049 54033630 52750361 52219799 [9] 51915712 51537272 Smallest eigenvalues: [1] 0.52767391 0.49658116 0.47108715 0.39378270 0.34990204 0.34411725 [7] 0.33183697 0.31351879 0.26861629 -0.05393078 Largest eigenvalues: [1] 63450183 60049111 57222506 55744530 54958459 53491121 51822211 51784969 [9] 51723151 50800995 Smallest eigenvalues: [1] 0.3995092 0.3728310 0.3359519 0.3328351 0.2261396 0.2118650 [7] 0.1919549 0.1627495 -0.6917800 -0.8362633 Largest eigenvalues: [1] 65287175 59755730 57164905 56180634 54982685 53480718 52292760 52168119 [9] 51420429 50551183 Smallest eigenvalues: [1] 0.18401539 0.14786746 0.06978497 0.04196946 -0.84799536 [6] -2.82244893 -2.91878869 -7.83955027 -10.48930386 -10.72465611 Largest eigenvalues: [1] 63015292 59343386 56806285 54941365 54676381 53133107 51948958 51370627 [9] 50939976 50505795 Smallest eigenvalues: [1] 0.4162112 0.3950567 0.3814943 0.3436694 0.3189936 0.2129440 [7] 0.1635790 -0.3169176 -0.3860692 -19.4047729 Largest eigenvalues: [1] 65649748 60371426 56967309 56704262 55039215 53297497 52701752 52199412 [9] 52005626 51578201 Smallest eigenvalues: [1] 0.5782234 0.4555175 0.3931808 0.3645335 0.3009528 0.2992097 [7] 0.2659478 0.2355635 0.1816481 -1.1072331 Largest eigenvalues: [1] 64933711 60068767 57613945 55830360 54769876 53494796 51992486 51883485 [9] 51870576 51180093 Smallest eigenvalues: [1] 0.3864456 0.3462517 0.3379102 0.3135665 0.1996375 0.1664430 [7] 0.1406302 -0.1032846 -0.7843584 -8.0654301 Largest eigenvalues: [1] 64984888 59654481 57039415 55800905 54704032 53336990 51936026 51840380 [9] 51777594 51076770 Smallest eigenvalues: [1] 0.4050711 0.3740097 0.3333073 0.2391651 0.1913153 0.1636822 [7] 0.1235815 -0.2511083 -1.3444760 -2.0810993 Largest eigenvalues: [1] 62823361 60091349 56781597 55657152 55344127 53850259 52184449 52093415 [9] 51217848 50950622 Smallest eigenvalues: [1] 0.4314467 0.4165944 0.4120417 0.4038097 0.4012641 0.3845278 [7] 0.3272880 0.2725798 0.2274015 -1.4135281 Largest eigenvalues: [1] 65653811 60055155 57417268 56343302 55034186 53681498 52401672 52220181 [9] 52020759 51258859 Smallest eigenvalues: [1] 0.4758727 0.4608726 0.4556556 0.4323938 0.3701018 0.2365879 [7] 0.2144270 0.1550570 0.1502910 -0.5561089 Largest eigenvalues: [1] 63738614 60369039 56690112 55442243 55213960 53556840 52328046 51690484 [9] 51385012 51218123 Smallest eigenvalues: [1] 0.56306153 0.52658127 0.47173434 0.45383100 0.42391527 0.42125430 [7] 0.20202586 0.19171824 0.11256320 -0.03131913 Largest eigenvalues: [1] 63656171 60871318 58012191 55488091 55388539 53966137 52083580 51992877 [9] 51481041 51059512 Smallest eigenvalues: [1] 0.5011419 0.4319145 0.4033364 0.4013300 0.3480772 0.2668091 [7] 0.2404480 0.1824264 0.1629935 -1.3841629 Largest eigenvalues: [1] 64912517 60749296 58085408 56624964 55472811 53995104 52562384 52418681 [9] 51998494 51274172 Smallest eigenvalues: [1] 0.020042392 -0.004704113 -0.073676077 -0.306308087 -0.827563103 [6] -1.333066779 -1.896066519 -4.566893032 -31.788612443 -95.315975672 Largest eigenvalues: [1] 64822268 60796234 57662204 57111115 55806840 53922927 53290073 52906370 [9] 52168635 52147320 Smallest eigenvalues: [1] 0.41169973 0.37842981 0.29016466 0.23843720 0.22037619 [6] 0.10446320 0.03065762 -3.20189543 -6.47881696 -20.93161279 Largest eigenvalues: [1] 64472378 60524225 56835352 55875543 55252204 53432428 52377265 51855424 [9] 51297033 51274609 Smallest eigenvalues: [1] 0.44767431 0.43901405 0.41997561 0.37608988 0.35429693 0.29154808 [7] 0.27659556 0.09143168 -0.21071695 -0.41305720 Largest eigenvalues: [1] 64216696 60158780 57132664 55841669 55023064 53131348 51899238 51828994 [9] 51677814 50817483 Smallest eigenvalues: [1] 0.5741196 0.5505421 0.4556008 0.4103342 0.4017258 0.3393958 [7] 0.3138406 0.2927986 0.2920543 -0.9103729 Largest eigenvalues: [1] 64753797 60531812 57880718 55843819 55816233 54306976 52496266 52454427 [9] 51908585 51597589 Smallest eigenvalues: [1] 0.3954106 0.3613995 0.3325060 0.3275516 0.2974220 0.2710702 [7] 0.2502615 0.2367582 -0.6378864 -1.1384685 Largest eigenvalues: [1] 63327263 60199961 57124033 55791567 55489946 53626769 51780834 51686690 [9] 51605775 50720783 Smallest eigenvalues: [1] 0.43212595 0.32741429 0.32567039 0.26011858 0.25440367 [6] 0.24957935 0.15788884 0.05547981 -1.68471039 -19.49401894 Largest eigenvalues: [1] 66625704 60475109 57803166 57116582 54846214 53455785 53159817 52109215 [9] 51885727 51418221 Smallest eigenvalues: [1] 0.5788304 0.4919517 0.4915447 0.4019376 0.3892566 0.3432942 [7] 0.2706531 0.2270635 0.2212239 -2.2417639 Largest eigenvalues: [1] 63714784 60193815 57566657 55528026 54809956 53380310 51738601 51726574 [9] 51665693 50873681 Smallest eigenvalues: [1] 0.4161256 0.3370086 0.2706851 0.2617583 0.2553429 0.2475482 [7] 0.1902336 0.1843731 0.1410241 -2.9327487 Largest eigenvalues: [1] 64423892 60500851 57670418 55968544 55437163 53889326 52529896 52031286 [9] 51790159 51348478 Smallest eigenvalues: [1] 0.48957690 0.47015299 0.46006675 0.37604773 0.30726435 0.29129516 [7] 0.27364006 0.04752531 -0.39124815 -2.31135055 Largest eigenvalues: [1] 62651510 59904429 56950294 55563333 54590043 53724832 51829871 51815446 [9] 50687549 50427098 Smallest eigenvalues: [1] 0.6039265 0.6017610 0.4566132 0.4070116 0.4021365 0.3577973 [7] 0.3567614 0.2973197 0.2168300 -0.2109041 Largest eigenvalues: [1] 62583035 60103371 57022040 55489174 54749865 53764644 52200558 51838826 [9] 50925905 50699356 Smallest eigenvalues: [1] 0.3847111 0.3608571 0.2838315 0.2586309 0.1807085 0.1160849 [7] -0.2037558 -0.9309813 -2.4501460 -7.1487017 Largest eigenvalues: [1] 63856990 59529917 57103437 55498374 54886353 52969433 52444737 51763721 [9] 51519941 51227290 Smallest eigenvalues: [1] 0.4643036 0.4563959 0.3411069 0.3097260 0.3085544 0.2178306 [7] 0.1817973 0.1560109 -0.1715189 -1.5199293 Largest eigenvalues: [1] 64265624 60475686 57731537 55879962 55602103 54342353 52472337 52274148 [9] 51857597 51075721 Smallest eigenvalues: [1] 0.53319784 0.48387200 0.43300546 0.41839598 0.39414981 0.28614480 [7] 0.26960483 0.16740033 0.01359703 -0.01666494 Largest eigenvalues: [1] 64780318 59968615 57461963 56077034 55154664 53411297 52749414 52175812 [9] 51776000 51697869 Smallest eigenvalues: [1] 0.5328656 0.5176262 0.4643269 0.4480038 0.4409601 0.4248786 [7] 0.3531666 0.1299633 -0.3455052 -6.7485879 Largest eigenvalues: [1] 65200333 60587153 57865091 57121154 55281982 53291432 53269892 53163590 [9] 51778087 51717128 Smallest eigenvalues: [1] 0.31608215 0.24069674 0.11354433 0.04292511 0.01785595 [6] -0.09365783 -0.28427092 -0.43040014 -0.58442752 -17.43913944 Largest eigenvalues: [1] 65373349 60285595 57009054 56624893 54527763 53111888 52493104 51968697 [9] 51378361 51278289 Smallest eigenvalues: [1] 0.58440307 0.56496377 0.42533665 0.38660801 0.32656081 0.30282690 [7] 0.26696556 0.26276361 0.22767641 -0.01716992 Largest eigenvalues: [1] 65697616 60555321 58192546 56877296 54969200 53739581 53002544 52134666 [9] 52075852 51494691 Smallest eigenvalues: [1] 0.44304822 0.37265766 0.29829633 0.23858726 0.22991867 0.21105634 [7] 0.19873996 0.11486178 0.03595543 -1.24070248 Largest eigenvalues: [1] 65342020 61300072 58005750 56454558 56428480 54779343 53309136 52659273 [9] 52450986 52106185 Smallest eigenvalues: [1] 0.38217472 0.36485588 0.35094592 0.26728381 0.23247778 0.16547567 [7] 0.09538476 0.02860731 -0.21735869 -7.72457098 Largest eigenvalues: [1] 63334095 59538581 56408176 54624483 54402005 52758295 51463953 50776258 [9] 50634070 50495323 Smallest eigenvalues: [1] 0.30397583 0.25558232 0.14471632 0.07601755 -0.60589255 [6] -0.61994491 -1.51095916 -2.95515444 -3.28992655 -10.47873558 Largest eigenvalues: [1] 65763203 60741780 58185593 55956732 55824054 54485045 52861625 52690921 [9] 52135509 51680100 Smallest eigenvalues: [1] 0.4991781 0.4334595 0.4152560 0.4009806 0.3702056 0.3682359 [7] 0.3159687 0.3019355 0.1282064 -0.4315340 Largest eigenvalues: [1] 62955938 60050256 57713871 55067021 54941557 53317947 52294149 51478923 [9] 51347523 51157836 Smallest eigenvalues: [1] 0.5323462 0.4857399 0.4214185 0.3833629 0.3711478 0.3337403 [7] 0.3203418 0.2487450 0.2050167 -0.7882811 Largest eigenvalues: [1] 62996951 59727261 56551448 55281072 54686373 53071931 51755436 51471138 [9] 51214747 50837088 Smallest eigenvalues: [1] 0.5946170 0.5183249 0.4916747 0.4180030 0.3871741 0.3863442 [7] 0.3564048 0.3301643 0.2541634 -0.3942726 Largest eigenvalues: [1] 63730409 60186546 57120299 55601606 55461010 53529881 52272292 52027080 [9] 51440718 51050315 Smallest eigenvalues: [1] 0.36330113 0.35735802 0.35020490 0.19922920 0.18943896 0.01681169 [7] -0.05716524 -0.47010158 -1.07214941 -6.99305943 Largest eigenvalues: [1] 63722148 60829231 58148699 55463999 55318700 53917759 52690089 52480727 [9] 51897707 51633096 Smallest eigenvalues: [1] 0.55222586 0.45823215 0.45177975 0.42486961 0.37224121 0.31678248 [7] 0.29644523 0.15944283 0.02937954 -3.19650320 Largest eigenvalues: [1] 63376026 59945953 56749059 55369233 55319556 53519502 52251627 51778446 [9] 51407958 51070679 Smallest eigenvalues: [1] 0.58592843 0.52194145 0.47764782 0.44381887 0.44376518 0.40030160 [7] 0.37257114 0.26480777 0.22298196 -0.07080257 Largest eigenvalues: [1] 63485082 60569211 57530077 55770973 55523739 54042364 52642565 52029172 [9] 51497996 51340575 Smallest eigenvalues: [1] 0.43136605 0.38550549 0.32649466 0.26778635 0.25121159 0.21327358 [7] 0.13904030 0.09686388 -0.27884036 -4.44577419 Largest eigenvalues: [1] 64448487 59833774 56855923 55369714 54605800 52882258 51626295 51474303 [9] 51108687 50964307 Smallest eigenvalues: [1] 0.54795927 0.53691621 0.52213423 0.46169288 0.39491044 0.36204463 [7] 0.34326572 0.31803810 0.23958644 -0.05511732 Largest eigenvalues: [1] 65491196 60107113 57099988 55892860 54944890 53350633 52059768 51820849 [9] 51759235 51251340 Smallest eigenvalues: [1] 0.39344414 0.37724984 0.34940665 0.27996271 0.12144554 0.00261382 [7] -0.02613744 -1.41686733 -1.68098458 -3.46434352 Largest eigenvalues: [1] 65277080 60941411 58112631 56686881 55668835 54300135 52824995 52493835 [9] 52304768 51892882 Smallest eigenvalues: [1] 0.6063189 0.5308484 0.3461956 0.3320219 0.2734973 0.2677669 [7] 0.2644860 0.2240272 -0.2719019 -1.2216412 Largest eigenvalues: [1] 64558238 60087415 57245728 56167307 55028116 53528956 52308840 52233006 [9] 51927752 51181048 Smallest eigenvalues: [1] 0.56291728 0.45060296 0.43171305 0.37414273 0.30983884 0.25363964 [7] 0.13281164 -0.03918815 -0.14024569 -1.60148114 Largest eigenvalues: [1] 65287755 60389075 56786491 56654701 54984713 53309914 52584893 51906870 [9] 51833710 50930864 Smallest eigenvalues: [1] 0.51487497 0.48276612 0.43027291 0.36304155 0.30814851 0.27853417 [7] 0.23836498 0.09051503 -0.05880217 -0.28942108 Largest eigenvalues: [1] 65860429 60418873 58047819 57069157 55026846 53186002 53070411 52928777 [9] 52127774 51922596 Smallest eigenvalues: [1] 0.38513789 0.35329402 0.30083898 0.23472265 0.17805962 [6] 0.13328944 0.09622418 0.03881459 -1.38401051 -48.34514255 Largest eigenvalues: [1] 65344881 60958579 57688499 56599388 56063322 54457052 52876054 52660175 [9] 52656877 52090257 Smallest eigenvalues: [1] 0.4312859 0.4173851 0.3891183 0.3484750 0.3449000 0.3259633 [7] 0.2577873 0.2073475 0.1676589 -5.2918387 Largest eigenvalues: [1] 63255498 59533713 56828169 55259564 54862849 53599530 51904267 51385857 [9] 50949594 50448282 Smallest eigenvalues: [1] 0.63734119 0.57445111 0.52384105 0.42092156 0.38533863 0.37679104 [7] 0.33042094 0.29810122 0.23653938 -0.02378385 Largest eigenvalues: [1] 63600365 60051132 57470063 55396019 55391954 53784579 52302689 51889047 [9] 51544347 51095898 Smallest eigenvalues: [1] 0.51994774 0.51639376 0.47663901 0.46760953 0.32900118 0.31842745 [7] 0.30924047 0.26801878 -0.03818643 -1.16756900 Largest eigenvalues: [1] 63662271 60485632 57527631 56326118 55614006 54584158 52731053 52344902 [9] 51634205 51146867 Smallest eigenvalues: [1] 0.48328920 0.42787750 0.36987557 0.30745724 0.30352216 0.27737620 [7] 0.26770761 0.04073542 -1.48947386 -2.50340650 Largest eigenvalues: [1] 64167773 59543924 56578038 56000180 54821535 53184462 52002393 51735733 [9] 51597789 50581031 Smallest eigenvalues: [1] 0.3837986 0.3189130 0.2606605 0.2598902 0.2277843 0.2170432 [7] 0.1256639 -0.1040040 -0.8911664 -1.0151174 Largest eigenvalues: [1] 64005904 61156880 58089652 56573854 55502220 54837168 52846203 52639711 [9] 51865067 51440816 Smallest eigenvalues: [1] 0.35742058 0.34568332 0.33108576 0.29742645 0.21909574 0.17427533 [7] 0.12305939 0.06227753 -0.13489715 -0.76433901 Largest eigenvalues: [1] 63232132 60131839 57142035 55517821 55100759 53803981 52586383 52193985 [9] 51617067 51315934 Smallest eigenvalues: [1] 0.5466208 0.4967246 0.3807028 0.3712237 0.2574054 0.2535420 [7] 0.2340367 0.2301929 0.1325831 -0.1254779 Largest eigenvalues: [1] 64052832 60691122 57469384 56026900 55660761 53956005 52736235 52131179 [9] 52114103 51282560 Smallest eigenvalues: [1] 0.4037012 0.3521072 0.3280791 0.2550376 0.2417018 0.2400799 [7] 0.2278215 0.1771234 -0.7800077 -6.1343407 Largest eigenvalues: [1] 62133088 59409572 56274144 54916464 54198771 53182483 51833913 50767242 [9] 50291487 50061494 Smallest eigenvalues: [1] 0.53718516 0.48817502 0.40652090 0.40084619 0.37524395 0.34283589 [7] 0.32066116 0.25596458 0.16594763 -0.03977973 Largest eigenvalues: [1] 64666573 59813277 56967995 55927469 54979719 53237422 52018191 51599059 [9] 51411081 50654344 Smallest eigenvalues: [1] 0.5863206 0.5540619 0.3660004 0.3357883 0.3308424 0.3035866 [7] 0.2564905 0.1926957 0.1348714 -0.6011687 Largest eigenvalues: [1] 64549217 60455773 57580895 55754282 55281208 53622331 52292144 51778729 [9] 51761486 51282293 Smallest eigenvalues: [1] 0.4233936 0.3923690 0.3565185 0.3522399 0.2706483 0.1992710 [7] 0.1937219 0.1574523 -0.4014794 -0.7171172 Largest eigenvalues: [1] 64772814 60561956 57355931 56220468 55725827 53578165 53198393 52350586 [9] 52340102 51879462 Smallest eigenvalues: [1] 0.06490486 -1.80228086 -2.69572036 -3.52033941 -3.55069947 [6] -3.84548309 -5.71278350 -31.46560668 -35.47167959 -63.46264795 Largest eigenvalues: [1] 64997748 59963960 57058946 56641242 54610984 53009910 52891822 52115119 [9] 51965522 51151556 Smallest eigenvalues: [1] 0.4831236 0.4593811 0.4016475 0.3778138 0.3434826 0.3240533 [7] 0.2739518 -0.2593484 -0.3011723 -1.0297635 Largest eigenvalues: [1] 65545649 60161552 57590318 56614626 55251940 53558575 52815210 52746128 [9] 51984869 51710529 Smallest eigenvalues: [1] 0.5499005 0.4761912 0.4751196 0.3409258 0.2214093 0.1936841 [7] 0.1374441 -0.2217093 -0.2720919 -0.4819296 Largest eigenvalues: [1] 64653491 59996375 57353618 56287928 54929199 53304119 52242095 52139553 [9] 51892960 51162272 Smallest eigenvalues: [1] 0.482074080 0.460566062 0.385325015 0.228719676 0.204170119 [6] 0.203174929 0.196435913 0.055128857 -0.005558804 -0.326605294 Largest eigenvalues: [1] 62768595 60424613 57366627 56084040 54315705 54177786 52396494 51857246 [9] 50831455 50780357 Smallest eigenvalues: [1] 0.33616348 0.30931887 0.24539654 0.21218479 0.19538602 0.16675887 [7] -0.04329842 -0.69152847 -3.69108248 -3.70084264 Largest eigenvalues: [1] 66730562 60734822 58651687 56911715 55320015 53843097 52873511 52833433 [9] 52210005 52131775 Smallest eigenvalues: [1] 0.3611995 0.3274914 0.3050859 0.3032461 0.2313873 0.1929277 [7] -0.6057555 -1.7203846 -6.0100409 -6.2851009 Largest eigenvalues: [1] 65276626 60435392 57738273 56471316 55756719 54336068 52382170 52308816 [9] 52272510 51459525 Smallest eigenvalues: [1] 0.4335927 0.3927939 0.3713157 0.3186559 0.2776129 0.2157777 [7] 0.1130594 -0.1613570 -0.4355709 -0.7732010 Largest eigenvalues: [1] 63031142 60317934 57502074 55434523 54969485 53726933 52281038 52160996 [9] 51554053 51441035 Smallest eigenvalues: [1] 0.5193983 0.4570162 0.3336109 0.2595471 0.2309372 0.1836258 [7] 0.1728076 0.1150490 -0.1525138 -0.9321288 Largest eigenvalues: [1] 65418361 61047491 58192914 56319833 56028300 54807647 53364910 52520563 [9] 52260960 52038206 Smallest eigenvalues: [1] 0.4268365 0.3927026 0.3802362 0.2556951 0.2540186 0.1327133 [7] -0.1691681 -0.1740369 -0.7788713 -7.8781130 Largest eigenvalues: [1] 62830070 60802078 56983708 55954913 55551738 53578210 52451131 51827853 [9] 51608119 50635326 Smallest eigenvalues: [1] 0.53814031 0.43750791 0.42313005 0.34093855 0.32466209 0.23680186 [7] 0.17705006 0.11334663 0.01340931 -0.08469750 Largest eigenvalues: [1] 63555464 60490871 57430637 55738280 54921299 53881775 52456179 52068906 [9] 51293499 51061757 Smallest eigenvalues: [1] 0.4333640 0.4317225 0.3928476 0.3572899 0.2367908 0.1986234 [7] 0.1922412 0.1784152 0.1477908 -1.9821548 Largest eigenvalues: [1] 65152205 59676858 57135198 56774622 54493271 53259100 52539180 51869170 [9] 51610097 51147730 Smallest eigenvalues: [1] 0.48435633 0.40264210 0.36446977 0.36301620 0.32316294 0.24950164 [7] 0.19704065 0.09462268 -0.96091428 -1.29952398 Largest eigenvalues: [1] 64065666 59934080 56998028 55770122 55225703 53370099 52637581 51871130 [9] 51796019 51531562 Smallest eigenvalues: [1] 0.4106107 0.3917283 0.3747283 0.2766745 0.2655919 0.2452429 [7] 0.1711048 -0.1104001 -0.5303969 -0.6167583 Largest eigenvalues: [1] 66347962 59627369 57501559 56844415 54610971 53257406 52851364 51812852 [9] 51751618 51205624 Smallest eigenvalues: [1] 0.3818560 0.3622534 0.3585395 0.3434945 0.3060358 0.2726398 [7] 0.1727128 0.1078282 -1.1614511 -6.9716373 Largest eigenvalues: [1] 65220544 60027510 57054620 55816913 55283493 53766530 51961272 51960431 [9] 51725012 50968240 Smallest eigenvalues: [1] 0.4059022 0.3530834 0.3361140 0.3195295 0.2869012 0.2324727 [7] 0.1811697 0.1787874 0.1682798 -1.3636802 Largest eigenvalues: [1] 62953397 60254564 57754141 55633894 55078550 53966077 51886474 51805769 [9] 51118635 50921819 Smallest eigenvalues: [1] 0.619214797 0.616442213 0.584535630 0.460510220 0.435279445 [6] 0.345675152 0.303333379 0.246263739 0.167528658 -0.002613377 Largest eigenvalues: [1] 63338416 60494701 57078485 55733066 54895248 53254074 52016268 51831658 [9] 51710907 51100720 Smallest eigenvalues: [1] 0.4716803 0.3844930 0.3749503 0.3587162 0.3251543 0.3150077 [7] 0.2847899 0.2483912 0.1770407 -2.3884923 Largest eigenvalues: [1] 65042623 60892258 57715940 56646422 56036754 54388616 52892757 52558994 [9] 52485842 51851005 Smallest eigenvalues: [1] 0.4895471 0.4573535 0.4067461 0.4025775 0.3292774 0.3281108 [7] 0.3122810 0.1748698 0.1436429 -2.3075010 Largest eigenvalues: [1] 64436462 60550646 57432767 56493112 55535528 53834227 52602911 52405994 [9] 52347225 51596706 Smallest eigenvalues: [1] 0.4855649 0.4806738 0.4493792 0.4257337 0.4082319 0.3735515 [7] 0.3304049 0.2607255 0.1915591 -0.9385318 Largest eigenvalues: [1] 64387570 59921530 57110558 55931866 55157099 53491320 51791941 51746275 [9] 51692209 50844819 Smallest eigenvalues: [1] 0.40843473 0.32427276 0.31404083 0.28269195 0.25819740 0.20088638 [7] 0.15872948 -0.05990638 -0.40760688 -1.56795718 Largest eigenvalues: [1] 61387319 59136736 56580228 54256121 54200180 52605164 51293670 51223159 [9] 50441478 50253623 Smallest eigenvalues: [1] 0.28950387 0.21357170 0.19234762 0.17185247 0.03154836 [6] -2.17331564 -4.86923620 -13.51039474 -20.12396804 -21.59833755 Largest eigenvalues: [1] 65245542 60127559 57761262 56001396 55146296 53612514 52432609 52082065 [9] 51579811 51486569 Smallest eigenvalues: [1] 0.39205837 0.31352983 0.30824127 0.18453919 0.13212866 0.12475500 [7] -0.03321208 -0.43045756 -1.82916584 -6.20041403 Largest eigenvalues: [1] 63583849 59890614 56364157 55975814 54306776 52795132 51825314 51663233 [9] 51222232 50367169 Smallest eigenvalues: [1] 0.4417341 0.4038176 0.2764126 0.2090916 0.1918436 0.1719696 [7] 0.1196186 -1.2944904 -3.1554940 -10.6048038 Largest eigenvalues: [1] 64910314 59780734 56499646 55538812 54685551 53039032 51768858 51550473 [9] 51236687 51055376 Smallest eigenvalues: [1] 0.49598739 0.47153020 0.38643072 0.32012031 0.29891131 0.28403887 [7] 0.19823060 0.10982614 -0.07062857 -1.37500070 Largest eigenvalues: [1] 64122822 60164936 57021753 56138603 54995170 53078490 52399287 52108555 [9] 51936459 51337943 Smallest eigenvalues: [1] 0.43790307 0.42965487 0.42093261 0.39689484 0.32490137 0.29326572 [7] 0.18560769 0.14404229 0.08376391 -5.96082852 Largest eigenvalues: [1] 62395166 59918541 56974262 55364335 54878954 53654648 52038522 52011692 [9] 51105441 50938925 Smallest eigenvalues: [1] 0.58033472 0.55348785 0.55319654 0.46123111 0.39062386 0.33984309 [7] 0.33279145 0.26923419 0.26738863 -0.02851748 Largest eigenvalues: [1] 63921647 60853449 57697019 56174340 55496605 53631706 52174747 52131082 [9] 52016515 50972321 Smallest eigenvalues: [1] 0.44672618 0.42344827 0.28009525 0.21728263 0.04270283 -0.24956196 [7] -0.38973148 -0.65082647 -1.04833091 -1.20644654 Largest eigenvalues: [1] 64033331 60440040 57434177 55940394 55471909 53570874 52698263 52079971 [9] 51945936 51654200 Smallest eigenvalues: [1] 5.229017e-01 4.872134e-01 4.091669e-01 3.871437e-01 3.374349e-01 [6] 2.724708e-01 2.646559e-02 4.953285e-05 -2.159932e-01 -1.022007e+01 Largest eigenvalues: [1] 64585766 60772815 57768232 55733029 55649730 54203728 52804990 52194973 [9] 51786908 51641055 Smallest eigenvalues: [1] 0.39485902 0.35743264 0.29258255 0.26565283 0.21072465 [6] 0.05240952 -0.52427941 -1.78479060 -3.69658365 -13.50641203 Largest eigenvalues: [1] 65252481 60701004 58545524 56854701 55362679 54052209 52863939 52717160 [9] 52422373 51850961 Smallest eigenvalues: [1] 0.4260388 0.3843881 0.3199751 0.2957491 0.2919985 0.2727853 [7] 0.2296530 0.1868074 -0.2691620 -33.6905296 Largest eigenvalues: [1] 64659464 60283454 57135113 56598090 54910010 53312651 52638118 51763427 [9] 51735213 50828911 Smallest eigenvalues: [1] 0.45245959 0.43137403 0.42789055 0.41377461 0.27000240 0.15589950 [7] 0.06469077 0.02853310 -0.55176870 -4.58658188 Largest eigenvalues: [1] 65043370 60333388 57283807 56284134 55269108 53172234 52410858 52087600 [9] 51866501 51260698 Smallest eigenvalues: [1] 0.39484097 0.32028836 0.28356366 0.26924378 0.16560932 0.02345127 [7] -0.29873418 -0.54655779 -1.30287880 -3.55914105 Largest eigenvalues: [1] 63300354 59384292 56769794 55386602 54802349 53057496 51936379 51613263 [9] 51292005 50570245 Smallest eigenvalues: [1] 0.5090463 0.4855877 0.4854849 0.4402381 0.3986666 0.3634851 [7] 0.3071932 0.2615275 0.1640894 -0.4264008 Largest eigenvalues: [1] 63605236 59899879 56995324 55933483 54689395 53049682 51927081 51768912 [9] 51065334 50474857 Smallest eigenvalues: [1] 0.4426110 0.3924150 0.3596015 0.3576191 0.2842544 0.2478722 [7] 0.2419023 0.2189636 -0.6422768 -1.0990688 Largest eigenvalues: [1] 65854651 60392332 58206567 57219409 54917368 53739538 53203900 51959474 [9] 51769853 51272527 Smallest eigenvalues: [1] 0.4949781 0.4140768 0.3787345 0.3448595 0.3333660 0.3259888 [7] 0.2844763 0.2524878 0.1310555 -1.6280998 Largest eigenvalues: [1] 64238811 60040281 57171062 56542604 54825437 53367394 52436649 52229641 [9] 51998420 51034604 Smallest eigenvalues: [1] 0.35386660 0.31129898 0.27713572 0.26879827 0.25843558 0.23912535 [7] 0.17438173 0.06320406 -0.12203291 -1.33315029 Largest eigenvalues: [1] 66317305 60312688 58051522 56936628 55235273 53884129 52940023 52699727 [9] 51739837 51548984 Smallest eigenvalues: [1] 0.5510319 0.5161116 0.5037409 0.4154655 0.4120026 0.3990238 [7] 0.3271287 0.2679941 0.2270957 -0.1703969 Largest eigenvalues: [1] 64154331 60503779 57492130 55541542 55345073 53710495 51905311 51791781 [9] 51718372 51017918 Smallest eigenvalues: [1] 0.4462222 0.4413162 0.3764029 0.3592977 0.2907381 0.2880201 [7] 0.2393497 0.1297328 -4.4514676 -15.6981149 Largest eigenvalues: [1] 63816159 60564082 57121921 55900641 55222074 54073102 51895720 51650771 [9] 51268021 50550616 Smallest eigenvalues: [1] 0.581633838 0.494953119 0.465368073 0.406638838 0.325886603 [6] 0.313158887 0.306838249 0.268819250 0.207593516 -0.009696508 Largest eigenvalues: [1] 65146062 60099226 56879229 56228445 54718501 52981955 52338662 51812001 [9] 51147366 51014058 Smallest eigenvalues: [1] 0.398131529 0.381355802 0.364193841 0.321923968 0.318962823 [6] 0.287641207 0.199177536 0.175516353 0.008682012 -13.697321706 Largest eigenvalues: [1] 62586258 59671900 56939990 55172669 54620691 53391229 51834535 51496248 [9] 50957699 50791267 Smallest eigenvalues: [1] 0.5373549 0.3872080 0.3834492 0.3232014 0.3185726 0.3099545 [7] 0.2930033 -0.3948456 -0.6872954 -0.7143613 Largest eigenvalues: [1] 65016429 60373698 57780454 56620777 55399207 53834880 52838026 52743138 [9] 52149093 51270082 Smallest eigenvalues: [1] 0.4628780 0.3568853 0.3260001 0.2822877 0.2800484 0.2474752 [7] 0.2427732 0.2266537 0.2103802 -46.3683064 Largest eigenvalues: [1] 63598151 59883891 57031902 55800920 54973653 53321992 51884066 51850233 [9] 51779028 51005041 Smallest eigenvalues: [1] 0.5545398 0.5217730 0.5112008 0.4545997 0.4518587 0.3429025 [7] 0.2798084 0.2561103 0.1991687 -0.1232933 Largest eigenvalues: [1] 64484433 60315178 57468264 55982883 54868379 53522754 52060384 52016813 [9] 51755214 51244827 Smallest eigenvalues: [1] 0.58673801 0.56720582 0.50854628 0.40485383 0.39769796 0.35089211 [7] 0.25830660 0.22392965 0.01674273 -0.93324220 Largest eigenvalues: [1] 63886977 60729946 57621728 55869068 55771665 54311748 52564797 52165203 [9] 51889929 51282359 Smallest eigenvalues: [1] 0.34698327 0.24479120 0.21234660 0.19986008 0.17859472 [6] 0.09196713 0.06446403 -0.22413795 -14.59909836 -21.32771476 Largest eigenvalues: [1] 64865361 60133172 56897101 56342744 55436304 53807472 52311100 52247735 [9] 51796752 51360835 Smallest eigenvalues: [1] 0.37312771 0.37184272 0.36667553 0.32592863 0.02734883 0.02222577 [7] -0.06980914 -0.16022570 -0.81788154 -1.96318679 Largest eigenvalues: [1] 64687280 59339129 56755609 55437233 53972644 52396293 51836459 51311588 [9] 50960750 50905212 Smallest eigenvalues: [1] 0.5897315 0.5828536 0.5721948 0.5049707 0.4852852 0.3320432 [7] 0.3168799 0.2096651 0.1794736 -0.9524993 Largest eigenvalues: [1] 64715781 60298513 56894736 56242623 55206968 53365362 52215443 52039307 [9] 51799506 50854229 Smallest eigenvalues: [1] 0.4642808 0.4515403 0.4476178 0.3966770 0.3521420 0.2985550 [7] 0.2366061 0.1849280 0.1127254 -0.6650059 Largest eigenvalues: [1] 65738517 60204478 57370096 56469144 55383243 53559289 52556160 52479965 [9] 51578968 51266802 Smallest eigenvalues: [1] 0.5572239 0.4581508 0.4485191 0.3912046 0.3837334 0.2791748 [7] 0.2131950 0.1473619 0.1430001 -0.2701492 Largest eigenvalues: [1] 65247883 60923462 57981055 56172890 56056063 54551032 52922420 52639435 [9] 52234702 51988180 Smallest eigenvalues: [1] 0.4278794 0.3476179 0.3183024 0.2369793 0.2132186 0.1871104 [7] -0.1011245 -0.2236885 -5.7885355 -5.9580871 Largest eigenvalues: [1] 64286370 60488102 57529748 55757762 55600341 54161487 52751630 52529613 [9] 51838513 51656311 Smallest eigenvalues: [1] 0.46965636 0.38818181 0.23838787 0.21927810 0.12616960 0.02622104 [7] -0.49254969 -0.58047406 -0.61184724 -0.66725288 Largest eigenvalues: [1] 62967702 59133922 56397725 55423130 54243728 52665853 51389320 51213887 [9] 51164835 50103864 Smallest eigenvalues: [1] 0.42825641 0.39942765 0.36942551 0.33032954 0.26166593 [6] 0.23420744 0.23011344 0.11908614 -0.09278426 -26.28260262 Largest eigenvalues: [1] 62750030 59768004 56684393 55236055 55054427 53387009 52023520 51215090 [9] 51066586 50587866 Smallest eigenvalues: [1] 0.4816451 0.4668635 0.2941645 0.2504987 0.2145759 0.1991994 [7] 0.1981649 0.1351890 0.1006855 -0.8509431 Largest eigenvalues: [1] 63257582 60351017 57108991 55608188 55059808 53621656 51913832 51618678 [9] 50875572 50648289 Smallest eigenvalues: [1] 0.54546501 0.51450324 0.48724536 0.45671083 0.39243157 0.36990241 [7] 0.34163215 0.05913585 -0.11125103 -0.11468128 Largest eigenvalues: [1] 64991354 59947584 57046232 56478948 54597889 53066801 52412655 51765989 [9] 51355717 50773118 Smallest eigenvalues: [1] 0.44728753 0.35795645 0.33933782 0.32804442 0.21225882 0.21049584 [7] 0.15980083 0.14846945 -0.06079634 -0.18078756 Largest eigenvalues: [1] 67266219 60669648 57623456 56922178 55185723 53488630 53024284 52573740 [9] 52055097 51973084 Smallest eigenvalues: [1] 0.4866668 0.4786676 0.4489369 0.3615731 0.3022249 0.2778196 [7] 0.2182407 -0.1331183 -0.2604480 -0.8549073 Largest eigenvalues: [1] 64523437 59928819 57432788 55326168 55255790 53452493 52103472 51758429 [9] 51592691 50858343 Smallest eigenvalues: [1] 0.43850409 0.38427917 0.25357374 0.24798042 -0.05440934 [6] -0.24140800 -0.71673711 -4.93092252 -8.02792029 -20.90923070 Largest eigenvalues: [1] 65249773 60106396 57294159 56064667 54739048 53252048 52352397 51677287 [9] 51463083 50458460 Smallest eigenvalues: [1] 0.5991883 0.5281029 0.5178836 0.4622291 0.4454491 0.4059809 [7] 0.2962903 0.1331650 -0.1296811 -1.1521993 Largest eigenvalues: [1] 64526084 60285005 57265766 56190777 55278706 53471709 52690261 52267597 [9] 51623127 51275306 Smallest eigenvalues: [1] 0.4188800 0.3487356 0.3279679 0.3269908 0.3075070 0.2495696 [7] 0.2208671 0.2091194 -1.3076344 -4.1788323 Largest eigenvalues: [1] 64366927 60693923 57820655 55579550 55544610 54149107 52438327 51997257 [9] 51667113 51598606 Smallest eigenvalues: [1] 0.4661149 0.4407696 0.3560121 0.3428487 0.3228056 0.2507656 [7] 0.1896730 0.1462090 -2.6825332 -28.2155618 Largest eigenvalues: [1] 61986590 59683254 56485676 55499970 54402611 53489888 51767450 51112500 [9] 50399418 50229598 Smallest eigenvalues: [1] 0.5329010 0.4513208 0.4414890 0.3713458 0.3555911 0.3053348 [7] 0.2269964 -0.2588324 -0.3180586 -0.4310804 Largest eigenvalues: [1] 65358608 60603954 58086456 56869578 55079701 53290685 52894107 52768550 [9] 51954210 51784438 Smallest eigenvalues: [1] 0.5617092 0.5354533 0.4306728 0.4148428 0.3158316 0.3071711 [7] 0.2266957 0.2207708 0.2206010 -0.5619875 Largest eigenvalues: [1] 64734970 60953231 57507971 56017674 55625522 54040222 52357535 52323881 [9] 52120162 51547714 Smallest eigenvalues: [1] 0.4700373 0.4265857 0.4048073 0.3963303 0.3359164 0.3233833 [7] 0.2706780 0.2436359 -0.2125806 -10.2950976 Largest eigenvalues: [1] 64422931 60170357 57548662 56342241 55244688 53709279 52339785 51944408 [9] 51928136 50815782 Smallest eigenvalues: [1] 0.596600063 0.580191868 0.541670645 0.530609083 0.497916460 [6] 0.436080669 0.306870086 0.241490864 0.169635234 -0.001726538 Largest eigenvalues: [1] 64294945 60516733 57663696 55909461 55163800 53264149 52199414 52112162 [9] 51571047 51089777 Smallest eigenvalues: [1] 0.4961910 0.4902026 0.4806140 0.4553746 0.4390719 0.2595080 [7] 0.1791196 -0.2440164 -0.6227254 -3.0845770 Largest eigenvalues: [1] 64387207 60315566 57771970 55909323 55112907 53611629 52287926 52091550 [9] 51807467 51117083 Smallest eigenvalues: [1] 0.3165348 0.2868056 0.2435300 0.2355389 0.1478802 0.1392101 [7] 0.1313882 -1.8590454 -7.4206405 -12.6158730 Largest eigenvalues: [1] 64169161 60745713 57632644 55876968 55282915 54205999 52662057 52153117 [9] 51798160 51468295 Smallest eigenvalues: [1] 0.4425852 0.4177886 0.3940021 0.2782246 0.1765252 -0.2251043 [7] -1.3219801 -2.1602911 -7.2638773 -16.2835269 Largest eigenvalues: [1] 65463398 59849089 57004151 56818991 54575699 52753964 52405633 51836765 [9] 51404133 50852713 Smallest eigenvalues: [1] 0.595002753 0.499714627 0.496328368 0.429235879 0.405218161 [6] 0.382180088 0.262937485 0.200909666 0.002652293 -0.499905603 Largest eigenvalues: [1] 64468475 60624678 57449008 55784301 55496268 53769662 52911557 51938199 [9] 51561082 51431505 Smallest eigenvalues: [1] 0.402866174 0.391950759 0.326876034 0.280944028 0.274173956 [6] 0.182973124 -0.005183514 -0.534444484 -1.481506686 -21.430849617 Largest eigenvalues: [1] 64859279 60681333 57672223 55802533 55648619 54313291 52602615 52348499 [9] 51829606 51524747 Smallest eigenvalues: [1] 0.4119543 0.4046272 0.3730116 0.3507124 0.3311649 0.2710863 [7] 0.1903433 0.1051565 -0.1564091 -0.1932710 Largest eigenvalues: [1] 65973088 60914917 57724318 56058834 55645614 53826329 52704344 52195036 [9] 51983071 51843962 Smallest eigenvalues: [1] 0.47219064 0.38574298 0.37339287 0.34166300 0.33395930 0.27276534 [7] 0.24513438 0.22089711 0.03058645 -1.93180410 Largest eigenvalues: [1] 65625374 60427104 57648340 56737618 55186455 53755204 52605260 52450966 [9] 51990118 51601657 Smallest eigenvalues: [1] 0.5020374 0.4191968 0.3869501 0.2561177 0.2272818 0.2118193 [7] -0.2205335 -0.3867581 -1.6421047 -2.6228899 Largest eigenvalues: [1] 66398218 61009272 58434454 56750705 55942717 54161086 53024288 52873617 [9] 52418817 52080028 Smallest eigenvalues: [1] 0.38320997 0.36041026 0.32108723 0.31321878 0.24711360 0.23687529 [7] 0.18993739 0.09900609 -0.11287443 -7.11540963 Largest eigenvalues: [1] 65209274 59383444 56863153 56030463 54684419 53108447 51999627 51305003 [9] 51194510 50584511 Smallest eigenvalues: [1] 0.44748223 0.41966422 0.40973741 0.29212575 0.24848101 0.24345831 [7] 0.20466526 0.09570455 -0.10115300 -0.28204296 Largest eigenvalues: [1] 66835808 61391501 58492227 56927542 55580044 53831180 53109222 52908205 [9] 52086839 52022214 Smallest eigenvalues: [1] 0.55870135 0.52577165 0.47899852 0.46535595 0.46441455 0.44421676 [7] 0.23913658 0.23565963 0.04982777 -0.05214577 Largest eigenvalues: [1] 62705148 60130743 56777315 55465905 55262063 53405581 52249528 51664529 [9] 51217419 50464234 Smallest eigenvalues: [1] 0.6335170 0.6058209 0.5532983 0.5524656 0.4573758 0.4543889 [7] 0.3424434 0.2313038 0.2235777 -0.8873691 Largest eigenvalues: [1] 64776839 60419149 57624121 56267497 55176198 53743129 52237618 52009423 [9] 51825588 50989582 Smallest eigenvalues: [1] 0.4809460 0.4000531 0.3643749 0.3633007 0.3445975 0.3377922 [7] 0.2070527 0.1865913 -0.5667321 -2.3734881 Largest eigenvalues: [1] 64019446 59980557 57263975 56189248 54889406 53251221 52132000 52064996 [9] 51700317 50635496 Smallest eigenvalues: [1] 0.6369606 0.5302138 0.5200224 0.4815634 0.4375574 0.3863850 [7] 0.3701213 0.3085190 0.2146247 -0.1748042 Largest eigenvalues: [1] 65155071 61211659 58338330 56544796 56325039 54708452 53472067 52642735 [9] 52528081 51940575 Smallest eigenvalues: [1] 0.4785571 0.4746846 0.4410983 0.4118512 0.3841887 0.3668965 [7] 0.3277161 0.1811739 0.1408216 -0.6609918 Largest eigenvalues: [1] 64909126 61115423 58179149 56212328 56057032 54498844 52544017 52510847 [9] 52190004 51690883 Smallest eigenvalues: [1] 0.47117178 0.46469081 0.41250110 0.34659523 0.34399625 0.32194163 [7] 0.31081005 0.12085568 0.06078797 -2.71815573 Largest eigenvalues: [1] 64350075 59518803 56663317 55984812 54508994 52817657 51998067 51519314 [9] 51497351 50560359 Smallest eigenvalues: [1] 0.4346896 0.3733635 0.3646124 0.3505277 0.2973378 0.2606022 [7] 0.2281173 0.1832396 -1.3018144 -6.9913078 Largest eigenvalues: [1] 64948744 60146340 57352168 56005045 55060614 53669277 52084438 51805155 [9] 51760344 50830627 Smallest eigenvalues: [1] 0.40427683 0.34842963 0.30804670 0.24481902 0.15717935 [6] 0.05892585 -0.00211258 -0.78667016 -1.56359745 -12.26724365 Largest eigenvalues: [1] 65621086 60871049 58196565 56339127 55622847 54115936 52829808 52349538 [9] 52103273 51605139 Smallest eigenvalues: [1] 0.51651388 0.48494782 0.46418786 0.46389734 0.44118384 0.41089926 [7] 0.40272391 0.30869897 0.09280225 -0.11407244 Largest eigenvalues: [1] 63662340 59634720 57365275 55432102 54967724 53265366 51598050 51544271 [9] 51452041 50482966 Smallest eigenvalues: [1] 0.32354642 0.32169932 0.26056856 0.25879940 0.21499204 0.11053373 [7] -0.08515092 -0.54543152 -1.41498525 -2.72793053 Largest eigenvalues: [1] 65450136 59518139 57091560 56065267 54313443 52782946 52178448 51804085 [9] 51517405 51122820 Smallest eigenvalues: [1] 0.4367802 0.3624695 0.3374817 0.3349788 0.2379174 0.2035338 [7] -1.1352942 -1.7838715 -3.0375818 -8.8461238 Largest eigenvalues: [1] 65747952 60107712 57451055 57318072 54778518 53192069 53168751 52449707 [9] 52265871 51682659 Smallest eigenvalues: [1] 0.37074622 0.32964236 0.25232790 0.23409043 0.14494076 [6] 0.13759617 0.11152770 0.07757987 -0.57253582 -13.93100786 Largest eigenvalues: [1] 65781897 59924479 57497598 56680141 54718461 53090438 52722620 51923643 [9] 51659170 51122536 Smallest eigenvalues: [1] 0.5831168 0.5639826 0.3837977 0.3826191 0.3035591 0.2863617 [7] 0.2745112 0.2731092 0.2431454 -1.4086800 Largest eigenvalues: [1] 65137463 60643966 57849733 56184126 55552678 54203133 52339115 52319215 [9] 52256902 51332130 Smallest eigenvalues: [1] 0.3683887 0.3512420 0.3408925 0.3232900 0.2787079 0.2724606 [7] 0.2245215 0.1846142 -0.2622792 -1.5402836 Largest eigenvalues: [1] 64623202 60783323 57881613 56446604 55995575 54235915 52386160 52236666 [9] 52109384 51197995 Smallest eigenvalues: [1] 0.46198582 0.45573780 0.43610679 0.36581319 0.35699677 0.34375384 [7] 0.25456610 0.14674583 0.08096377 -0.26255144 Largest eigenvalues: [1] 64448147 61161415 57735874 56329391 55854340 54270310 52482906 52143619 [9] 52012443 51288637 Smallest eigenvalues: [1] 0.4454687 0.4390658 0.4226786 0.3351076 0.3039356 0.2955374 [7] 0.2863432 0.2531215 0.1173429 -0.3254932 Largest eigenvalues: [1] 63319878 59730634 56756909 55304533 54739660 53105694 51500323 51455907 [9] 51228466 50587355 Smallest eigenvalues: [1] 0.50226669 0.45125814 0.41137682 0.33723767 0.33328902 0.21965764 [7] 0.12710130 0.04384981 -0.12613060 -1.86189819 Largest eigenvalues: [1] 61730491 59517124 56837496 54670470 54418834 52959528 51681618 51557314 [9] 50819779 50630242 Smallest eigenvalues: [1] 0.4082084 0.3809722 0.3175078 0.3117375 0.3034126 0.2684511 [7] 0.2369499 0.2207037 -0.3627658 -0.9675033 Largest eigenvalues: [1] 64127099 60297681 57598985 55669821 55220419 53732401 51926088 51745300 [9] 51737051 51057534 Smallest eigenvalues: [1] 0.472090059 0.457929953 0.372775765 0.320080079 0.255523639 [6] 0.234289583 0.228135878 0.005882272 -0.007653789 -0.180203494 Largest eigenvalues: [1] 65302765 60951090 58156776 55806616 55607269 54387828 52698923 52422608 [9] 51864350 51707824 Smallest eigenvalues: [1] 0.5217158 0.4826237 0.3938609 0.3764443 0.3246314 0.2812599 [7] 0.2804431 0.2751018 -0.8850331 -1.4925676 Largest eigenvalues: [1] 64889062 59795307 57211664 55956867 54999276 53616969 52016384 51972910 [9] 51716295 51143142 Smallest eigenvalues: [1] 0.42296270 0.41268900 0.40888269 0.37646961 0.31108342 0.27795950 [7] 0.19224440 0.16648144 0.15671339 -0.09273714 Largest eigenvalues: [1] 64267331 60084489 57393624 55524141 55430005 53850331 52270825 52006573 [9] 51570610 51225934 Smallest eigenvalues: [1] 3.193495e-01 2.013858e-01 9.200554e-02 8.926988e-02 9.936771e-04 [6] -2.215423e-02 -1.101043e-01 -8.727731e-01 -1.565285e+01 -1.840693e+01 Largest eigenvalues: [1] 62460189 60161864 56292925 55248765 55189474 53442812 51989511 51885954 [9] 50976871 50455187 Smallest eigenvalues: [1] 0.5385928 0.4965616 0.4868131 0.4751368 0.4265040 0.4066629 [7] 0.3680893 0.3539590 0.2986524 -0.9663422 Largest eigenvalues: [1] 65287550 60627157 57758124 56718238 55491871 53974496 52592540 52320014 [9] 51865157 51279229 Smallest eigenvalues: [1] 0.56935255 0.56354283 0.54377823 0.53103914 0.47037046 0.37939205 [7] 0.36660544 0.33274338 0.31475206 -0.05407509 Largest eigenvalues: [1] 65572468 61072960 58293329 57137740 55616490 53992113 53098514 52812922 [9] 52335700 51810663 Smallest eigenvalues: [1] 0.39771853 0.36605174 0.35853521 0.28550846 0.22965467 -0.06847966 [7] -0.30470030 -1.54637995 -2.25399036 -9.44133852 Largest eigenvalues: [1] 63105488 60083343 57030489 55284656 55239587 53482165 52226953 51869946 [9] 51269099 51061421 Smallest eigenvalues: [1] 0.5171361 0.4865891 0.4518466 0.4104234 0.3556949 0.2574824 [7] 0.2164616 0.1135890 -0.4051819 -0.4166858 Largest eigenvalues: [1] 64173327 60655314 58378402 55888399 55454987 54630121 52780321 52214480 [9] 51606673 51422334 Smallest eigenvalues: [1] 0.4029243 0.4018202 0.3899124 0.3105355 0.2693868 0.2628813 [7] 0.2519655 0.2371773 0.2353172 -0.7939161 Largest eigenvalues: [1] 64607546 60727005 57790348 55740800 55681926 54315022 52456711 52037329 [9] 51845447 51196923 Smallest eigenvalues: [1] 0.366884917 0.275665985 0.218540002 0.007691799 -0.006153075 [6] -0.191619157 -0.672055184 -0.864089060 -0.901121715 -1.334254853 Largest eigenvalues: [1] 62099733 60216656 56901223 55598598 55188973 53763432 52376058 51891639 [9] 50930336 50819007 Smallest eigenvalues: [1] 0.42610577 0.33129939 0.32683798 0.26952448 0.25144868 0.24254517 [7] 0.11172515 0.07045316 -2.62996106 -6.92126661 Largest eigenvalues: [1] 63799434 60628491 57881872 55808186 55791607 54155629 52676672 52200287 [9] 51794047 51657184 Smallest eigenvalues: [1] 0.5487412 0.4565224 0.4462112 0.4244772 0.4183680 0.3785733 [7] 0.3549216 0.3367931 0.3349219 -0.4078569 Largest eigenvalues: [1] 63489102 59887664 56903379 55705661 54786918 53210919 51700762 51474477 [9] 51185618 50363963 Smallest eigenvalues: [1] 0.5405838 0.4536518 0.4077796 0.3958012 0.3701455 0.3227531 [7] 0.2808164 0.2673987 0.1986518 -1.3182308 Largest eigenvalues: [1] 64164268 60062226 56977050 56058612 55020514 53400863 52003669 51861822 [9] 51733894 51039032 Smallest eigenvalues: [1] 0.4270398 0.2864364 0.2571402 0.2373492 0.2039900 0.1876548 [7] 0.1817205 -2.1896355 -3.1294113 -6.5270451 Largest eigenvalues: [1] 64892434 59937071 56962640 56583702 54665060 53176919 52351480 52247487 [9] 51744908 51006328 Smallest eigenvalues: [1] 0.5341144 0.4107927 0.4005878 0.3090971 0.2481083 0.2461680 [7] -0.1281613 -0.2992312 -0.6081750 -19.7901473 Largest eigenvalues: [1] 65382267 60099102 57087956 55870202 54976591 53418825 52080401 52032896 [9] 51658714 51250411 Smallest eigenvalues: [1] 0.51259405 0.50985427 0.46812844 0.38045732 0.36816855 0.36809214 [7] 0.27374988 0.23827465 -0.02485813 -0.38040892 Largest eigenvalues: [1] 62650980 59780044 56743963 55194066 54722693 53315350 51948454 51735596 [9] 50874021 50628503 Smallest eigenvalues: [1] 0.50521696 0.46510991 0.43458252 0.39244545 0.38267005 0.35211441 [7] 0.34020312 0.09802594 0.04738960 -0.02482130 Largest eigenvalues: [1] 63739581 60305508 57361615 55468862 54863352 53439318 51993580 51522328 [9] 51517327 51152138 Smallest eigenvalues: [1] 0.46761774 0.42545473 0.42043402 0.38920906 0.30095922 0.27767208 [7] 0.25500262 0.17357523 0.17339234 -0.07817236 Largest eigenvalues: [1] 64608709 61206609 58213748 56061023 55700191 54158954 52831963 52208762 [9] 52180561 51948289 Smallest eigenvalues: [1] 0.4989402 0.4619286 0.3987685 0.3691881 0.3585004 0.2764301 [7] 0.2401817 -0.1596020 -0.2613991 -0.5504757 Largest eigenvalues: [1] 63736179 59813801 57434454 55337619 54933574 53661507 51936093 51500664 [9] 51226749 50693658 Smallest eigenvalues: [1] 0.48503699 0.43655895 0.40992494 0.38106473 0.34250827 0.32877577 [7] 0.28788444 0.21054488 0.16162259 -0.03885352 Largest eigenvalues: [1] 64206663 59447133 57262210 55571173 54493701 53059324 51848335 51729715 [9] 51275121 50839147 Smallest eigenvalues: [1] 0.4441993 0.4173982 0.4049454 0.3850415 0.3815862 0.3424496 [7] 0.3171507 0.2675028 -0.3561928 -33.5318669 Largest eigenvalues: [1] 66225916 60488782 57869109 57080502 55102329 53714415 53090096 51956956 [9] 51913401 51097694 Smallest eigenvalues: [1] 0.4457368 0.3469112 0.3111173 0.2777945 0.2741597 0.2596741 [7] -0.1852783 -0.4284197 -3.5392829 -4.9668615 Largest eigenvalues: [1] 65313613 59957328 57855888 56466579 55224343 54015896 52719527 52402783 [9] 52395980 51834450 Smallest eigenvalues: [1] 0.3377719 0.3016237 0.2998872 0.2683010 0.2435994 0.2341296 [7] -0.6551704 -0.7253914 -1.4010014 -9.6362314 Largest eigenvalues: [1] 62368185 59927158 57522380 55937590 54214348 54102724 52385871 52107340 [9] 51047245 50735455 Smallest eigenvalues: [1] 0.260392160 0.246198173 0.186251639 0.137679517 0.081803619 [6] 0.044102629 0.018894230 0.005853617 -0.990973008 -17.603513577 Largest eigenvalues: [1] 62908863 60733371 57767519 55569707 55207542 53982085 52193411 51845545 [9] 51372746 51224998 Smallest eigenvalues: [1] 0.6131991 0.5135985 0.5011057 0.4633477 0.3946598 0.3463550 [7] 0.3091917 0.2928958 0.2560634 -1.0221547 Largest eigenvalues: [1] 65238470 61076332 57875594 56809465 55393005 53901856 52814122 52722993 [9] 52182180 51926616 Smallest eigenvalues: [1] 0.5355943 0.4957699 0.4848498 0.4499409 0.4378068 0.3363424 [7] 0.2886285 0.2509242 0.2167049 -0.1989357 Largest eigenvalues: [1] 65458743 60026275 57834345 56593570 54697921 53062377 52831881 51795006 [9] 51477791 50890314 Smallest eigenvalues: [1] 0.4387782 0.4277284 0.4100086 0.3495594 0.3489280 0.2971214 [7] 0.1925726 0.1919807 -0.5387739 -21.0813380 Largest eigenvalues: [1] 65004417 60376581 57702056 56532773 55130848 53414412 52714241 52001861 [9] 51906824 50990053 Smallest eigenvalues: [1] 0.5256431 0.4572065 0.4491234 0.4113677 0.3850087 0.3790004 [7] 0.3171255 0.1960669 0.1807790 -1.9247137 Largest eigenvalues: [1] 62940405 60269618 57575250 55412373 54921097 53843621 51914001 51808395 [9] 51081605 50929350 Smallest eigenvalues: [1] 0.6205814 0.5906973 0.5541414 0.5475933 0.4521749 0.3755399 [7] 0.2649637 0.2049598 0.1841806 -0.8680196 Largest eigenvalues: [1] 64353659 60059015 56872269 55844029 55007882 53352383 51725673 51651644 [9] 51422861 50519991 Smallest eigenvalues: [1] 0.12920234 0.07653261 0.06371167 -0.04779952 -0.34083850 [6] -1.92409911 -9.72468340 -27.61676598 -33.29934368 -44.89290360 Largest eigenvalues: [1] 65180621 60207937 56484016 56340252 55208204 53330429 52327657 52303894 [9] 52194607 51147638 Smallest eigenvalues: [1] 0.37429053 0.34924468 0.34516069 0.34213494 0.28880090 0.09359304 [7] 0.07296078 0.05012915 -1.28637025 -3.38288881 Largest eigenvalues: [1] 62689806 59049125 56601700 55003811 54732128 53093561 51879078 51489399 [9] 50876470 50486287 Smallest eigenvalues: [1] 0.47232773 0.45977329 0.43119076 0.36240963 0.32969283 0.25910272 [7] 0.23378894 0.02993916 -0.18171418 -0.24359475 Largest eigenvalues: [1] 62234920 59332481 56892529 54813651 54477956 52900682 51874847 51266706 [9] 50945506 50799773 Smallest eigenvalues: [1] 0.4153222 0.3721074 0.3648583 0.3597596 0.3279138 0.2510410 [7] 0.2327371 0.1508180 0.1263878 -0.7126174 Largest eigenvalues: [1] 63577332 60097602 57111281 55502187 55245232 53909106 52332234 51916698 [9] 51393220 51173762 Smallest eigenvalues: [1] 0.5033041 0.5028158 0.3602542 0.3423207 0.3097934 0.2378690 [7] 0.2302833 0.1502926 -1.0370043 -5.8579513 Largest eigenvalues: [1] 64680500 60901910 57293572 56249877 55814252 54005386 52474461 52274526 [9] 51954039 51479185 Smallest eigenvalues: [1] 0.4363476 0.4250772 0.3885742 0.3249050 0.2703968 0.2699337 [7] 0.2582783 -0.1438690 -0.3453970 -0.7135927 Largest eigenvalues: [1] 64614830 60386060 57820301 56550732 55390296 53923850 52997069 52582632 [9] 52169874 51713304 Smallest eigenvalues: [1] 0.4570453 0.4069215 0.3449191 0.3265189 0.3156249 0.2754068 [7] 0.2434499 0.1960337 -0.2192655 -2.0999734 Largest eigenvalues: [1] 64012457 60461494 57354408 56073168 55690807 54014159 52241063 52112263 [9] 52017083 50998877 Smallest eigenvalues: [1] 0.4798902 0.4523935 0.3724019 0.3239674 0.2783808 0.2624360 [7] 0.2622589 0.1560630 0.1261194 -0.1911510 Largest eigenvalues: [1] 63582006 60115770 57810428 55284706 55250052 53883565 52254894 52162502 [9] 51444836 51278298 Smallest eigenvalues: [1] 0.473308256 0.401127285 0.334910641 0.322614510 0.286410878 [6] 0.283300887 0.194000008 0.047672795 -0.004845634 -0.292629510 Largest eigenvalues: [1] 64558938 61130217 57782812 56540130 55437595 53800198 52441661 52407814 [9] 51749690 51345857 Smallest eigenvalues: [1] 0.4848754 0.4563133 0.4359468 0.3283973 0.3072911 0.2526044 [7] 0.1913358 -0.1546851 -0.2407034 -4.5787521 Largest eigenvalues: [1] 61991750 60031365 56568428 55263409 54337442 53486483 52057173 51534840 [9] 50573657 50333762 Smallest eigenvalues: [1] 0.4570738 0.3474239 0.3350057 0.2766244 0.2600711 0.2315790 [7] 0.2209667 0.1974956 -1.7134918 -5.2846710 Largest eigenvalues: [1] 64274292 60140438 57252366 56165528 54930888 53579782 52358009 52237435 [9] 52197215 51365213 Smallest eigenvalues: [1] 0.49670168 0.49394717 0.44829228 0.36448408 0.32831097 0.31792781 [7] 0.10269757 0.07532116 -0.15397033 -0.20599405 Largest eigenvalues: [1] 64363426 59878684 57104908 56088550 54249504 52786876 52087835 51823916 [9] 51434253 50963480 Smallest eigenvalues: [1] 0.5167286 0.4824251 0.3597968 0.3111099 0.2555201 0.2021249 [7] 0.1219693 -0.1239433 -0.8158369 -6.6270137 Largest eigenvalues: [1] 63320238 60817045 57641719 56159222 55196536 54326377 52965386 52316766 [9] 51996043 51352786 Smallest eigenvalues: [1] 0.50290442 0.47585084 0.47098028 0.40679262 0.33466914 0.31840766 [7] 0.30616957 0.25841052 0.02244975 -1.47613820 Largest eigenvalues: [1] 65447523 60485006 57435826 56876586 55352013 53730149 52920697 52447010 [9] 51860555 51438062 Smallest eigenvalues: [1] 0.3383644 0.2979536 0.2618785 0.2103490 0.2046308 0.1647281 [7] -0.2224727 -4.2857895 -6.4515612 -8.6066024 Largest eigenvalues: [1] 66507608 61108059 58847356 57035193 55712819 54346549 53014014 52925881 [9] 52581974 52269794 Smallest eigenvalues: [1] 0.4252840 0.3423662 0.3336869 0.3323679 0.2306571 0.2033730 [7] 0.1020442 -0.2578452 -1.5659658 -5.8674456 Largest eigenvalues: [1] 66077594 59809813 56904559 56805066 54488160 52998364 52539768 51375897 [9] 51336507 50597457 Smallest eigenvalues: [1] 0.63793933 0.52631474 0.43413163 0.41457364 0.32760467 0.32722992 [7] 0.29616832 0.17152286 0.05353258 -0.46194262 Largest eigenvalues: [1] 63828026 60126248 57351873 55447429 54739545 53282513 51977171 51636795 [9] 51497797 50927279 Smallest eigenvalues: [1] 0.5222351 0.4562282 0.4485056 0.4196149 0.4015466 0.3842206 [7] 0.3312612 0.2452085 0.2279085 -0.7680761 Largest eigenvalues: [1] 64024180 61105254 57827067 56250724 55873003 54252140 52567359 52415834 [9] 52111082 51355014 Smallest eigenvalues: [1] 0.5519751 0.4872064 0.4747355 0.4578739 0.4470574 0.4217565 [7] 0.2450505 0.1807670 0.0219168 -4.1126368 Largest eigenvalues: [1] 63577667 59716110 57128273 55359317 55340230 53770377 52120032 52087750 [9] 51340085 51059569 Smallest eigenvalues: [1] 0.1186554 0.0825284 0.0529728 -0.0372975 -0.1339336 -0.5006408 [7] -0.6340608 -5.3942508 -9.0506397 -10.7815102 Largest eigenvalues: [1] 60197593 59660633 57177402 55554625 53771355 53535568 51798011 51774512 [9] 50876604 50181561 Smallest eigenvalues: [1] 0.6035463 0.5954294 0.5759948 0.5109591 0.4127615 0.2858684 [7] 0.2626945 0.2203413 -0.7094681 -0.9064164 Largest eigenvalues: [1] 65283980 60389947 57340141 56593202 55224555 53487125 52489125 52288459 [9] 52051476 51226028 Smallest eigenvalues: [1] 0.33051335 0.32947440 0.32208165 0.28144278 0.20115887 [6] 0.10026024 0.02786063 -1.57545617 -5.72180767 -13.01099703 Largest eigenvalues: [1] 66766159 60644655 58073269 57145833 55261515 53464085 53400369 52299392 [9] 52034857 51386274 Smallest eigenvalues: [1] 0.1787263 0.1694780 -0.1508300 -0.1618422 -0.2092064 -2.6735940 [7] -10.8811268 -13.9918489 -16.1152760 -45.2920170 Largest eigenvalues: [1] 64181573 60385359 57681995 55624559 55139120 53978694 52483650 52397406 [9] 51458610 51359352 Smallest eigenvalues: [1] 0.55709940 0.44304761 0.43967077 0.24651467 0.21007720 [6] 0.07587060 0.03942532 -0.06699987 -1.22521144 -13.42529864 Largest eigenvalues: [1] 63738121 60120180 57069934 55617674 55327418 53629248 52393111 52082738 [9] 51650625 51243038 Smallest eigenvalues: [1] 0.31741735 0.29445243 0.26649249 0.15290198 0.14590069 0.01748872 [7] -0.02409168 -0.97643113 -2.48616229 -2.69990715 Largest eigenvalues: [1] 64645061 60039385 56551220 56093698 54579275 52924085 52139720 51588420 [9] 51466508 50635687 Smallest eigenvalues: [1] 0.1898011 0.1779258 -0.2048827 -0.3105301 -0.3244568 -0.6612220 [7] -0.7574761 -9.0586112 -12.3224468 -45.5009116 Largest eigenvalues: [1] 63169532 61208265 57581156 56074674 55009955 54392361 52306164 52170824 [9] 51041471 50923017 Smallest eigenvalues: [1] 0.4469115 0.4369492 0.3852842 0.3410604 0.2868728 0.2702469 [7] 0.1745803 -0.0855023 -0.3849818 -0.9510035 Largest eigenvalues: [1] 65252960 60425611 58126205 56877061 54898749 53225959 52740829 52410286 [9] 51893976 51624976 Smallest eigenvalues: [1] 0.5096993 0.4690237 0.3976463 0.3880216 0.3637760 0.3054254 [7] 0.2829234 0.2599532 0.1933149 -0.7891419 Largest eigenvalues: [1] 65924624 59684389 56611975 56340959 54443394 52705533 52350657 51798634 [9] 51530241 51042740 Smallest eigenvalues: [1] -0.1306257 -0.2182491 -0.4359008 -0.5852863 -1.1135423 -1.6209949 [7] -1.8196521 -2.2606164 -2.4056539 -11.1826519 Largest eigenvalues: [1] 63929336 60765465 57684461 56001098 55794429 54214258 52600603 52521789 [9] 51943063 51675518 Smallest eigenvalues: [1] 0.3996114 0.3851469 0.3834856 0.3747796 0.3739012 0.2204755 [7] -0.6547359 -0.7969780 -3.7007032 -4.6063026 Largest eigenvalues: [1] 65111569 59930882 57508501 56327488 54775501 53097587 52410190 52366181 [9] 51636071 51499959 Smallest eigenvalues: [1] 0.49717037 0.44398068 0.33357902 0.32290876 0.16551153 0.11560995 [7] 0.01621756 -0.31879867 -0.43762964 -6.27493168 Largest eigenvalues: [1] 64756233 59566271 57041714 55570610 54146153 52653235 52048032 51750849 [9] 51214058 51075972 Smallest eigenvalues: [1] 0.5280886 0.5229860 0.5163932 0.4758649 0.4746665 0.4543488 [7] 0.3745868 0.2968540 0.2602990 -0.5961865 Largest eigenvalues: [1] 64009321 60606589 57143668 56323018 55377409 53661104 52287254 52082333 [9] 52009968 51226181 Smallest eigenvalues: [1] 0.42972082 0.37327617 0.32616719 0.25645898 0.25346892 0.20537717 [7] 0.07521011 -0.02827733 -0.11018006 -0.51743350 Largest eigenvalues: [1] 61290100 60031369 57133066 55819832 53867922 53851609 52174240 51635254 [9] 50746817 50707498 Smallest eigenvalues: [1] 0.4838751 0.4833004 0.4393723 0.3841969 0.2933796 0.2815018 [7] 0.2175510 0.1997441 -1.7149451 -28.3217400 Largest eigenvalues: [1] 63829585 59968574 57081574 55657127 55174927 53322796 52153221 51690406 [9] 51555364 51042939 Smallest eigenvalues: [1] 0.46707631 0.46191817 0.36168906 0.29191823 0.28113160 0.27180736 [7] 0.19479707 0.04415995 -0.18954797 -1.97918844 Largest eigenvalues: [1] 64718511 59452673 56622443 55988099 54291841 52823758 52016166 51700274 [9] 51213750 50847463 Smallest eigenvalues: [1] 0.4660506 0.4599969 0.4131064 0.3923726 0.3892344 0.3143654 [7] 0.2647937 0.2221240 -0.1185449 -3.4275015 Largest eigenvalues: [1] 63537445 60421480 57546608 55664746 55451003 54147554 52344905 52314703 [9] 51575202 51251961 Smallest eigenvalues: [1] 0.4056294 0.3800859 0.3677871 0.3472109 0.2619507 0.2334085 [7] 0.1778901 0.1465146 -0.3718325 -0.6810458 Largest eigenvalues: [1] 65145399 61156549 58473966 56551354 55873371 54296463 53116771 52557560 [9] 52053291 51930585 Smallest eigenvalues: [1] 0.4047533 0.3961447 0.3761853 0.3121273 0.3105423 0.2957181 [7] 0.2280731 0.2215193 -0.7267893 -1.1710817 Largest eigenvalues: [1] 64978227 59900672 57844393 56155312 55024515 53940857 52191911 52158163 [9] 51779626 51200255 Smallest eigenvalues: [1] 0.5094213 0.4887179 0.4350756 0.3718631 0.3454801 0.3173984 [7] 0.2981974 0.2455020 0.1727210 -1.0740660 Largest eigenvalues: [1] 64660658 59901449 57277046 55567244 54947603 53478410 52105215 51708121 [9] 51680084 51284710 Smallest eigenvalues: [1] 0.23666775 0.19696834 0.16535025 0.13610663 0.07894434 [6] -0.06924628 -0.15111873 -2.95676465 -12.11895385 -12.66048797 Largest eigenvalues: [1] 63078323 58732346 56016653 55248847 53883715 52688534 51431821 51127713 [9] 50889641 50050161 Smallest eigenvalues: [1] 0.4052114 0.3977633 0.3518903 0.3464258 0.3031983 0.2768000 [7] 0.2580313 0.2407707 0.1873606 -2.9965878 Largest eigenvalues: [1] 65124315 60438801 57102924 57043930 54950138 53450674 52805348 52546452 [9] 52017693 51660801 Smallest eigenvalues: [1] 0.5477875 0.4588957 0.4520199 0.3379817 0.2525528 0.2217774 [7] 0.1773967 0.1738130 0.1545247 -0.2604269 Largest eigenvalues: [1] 63736110 60366337 57321776 55295173 55274215 53485717 52936781 51827820 [9] 51765377 51497498 Smallest eigenvalues: [1] 0.4816732 0.4739031 0.4259841 0.4072189 0.3362325 0.2803447 [7] 0.1677723 0.1128676 -0.6205316 -1.3516641 Largest eigenvalues: [1] 65095020 59765952 57366970 56114894 54864578 53368385 52159709 52067841 [9] 51932334 51221450 Smallest eigenvalues: [1] 0.29010428 0.24140761 0.20818745 0.11323732 0.02074865 [6] -0.33961604 -13.07879631 -16.28979150 -56.76642877 -70.64630226 Largest eigenvalues: [1] 63027284 59421479 56231444 54706048 54562277 53028310 51814327 51507339 [9] 50830466 50597701 Smallest eigenvalues: [1] 0.5647435 0.3920006 0.3366998 0.2980104 0.2973342 0.2718065 [7] 0.2709506 -0.1080825 -1.0100542 -1.1747386 Largest eigenvalues: [1] 62408256 59614678 57393694 55353284 54565459 53588408 52406147 51886748 [9] 50863848 50740281 Smallest eigenvalues: [1] 0.57144900 0.52921040 0.52911305 0.50753726 0.48910617 0.45276255 [7] 0.37900531 0.07620250 0.05655370 -0.01034054 Largest eigenvalues: [1] 65419041 59907847 57169638 56226242 54652356 52926350 52404559 51574323 [9] 51552065 50761521 Smallest eigenvalues: [1] 0.371271890 0.330851213 0.307232654 0.281531137 0.256668163 [6] 0.232274056 0.193993701 0.182034178 -0.005417974 -0.302951598 Largest eigenvalues: [1] 63789800 59241096 57039615 55103653 54506807 53149607 51400099 51336439 [9] 51092612 50372391 Smallest eigenvalues: [1] 0.4909831 0.4549253 0.4099944 0.3741369 0.3719137 0.2222549 [7] 0.1747840 -0.3199870 -4.0824018 -4.3992507 Largest eigenvalues: [1] 63554601 60075734 56807171 55074291 54931844 53146499 51787747 51057811 [9] 51009623 50725826 Smallest eigenvalues: [1] 0.57592619 0.54454884 0.50724665 0.36937398 0.36003625 0.31825666 [7] 0.25611902 0.23308721 0.22615272 -0.04615426 Largest eigenvalues: [1] 63053855 60229365 56868888 55576619 55183520 53737069 52080177 51891840 [9] 51300620 50879257 Smallest eigenvalues: [1] 0.5589331 0.4863285 0.4112946 0.3783604 0.3362585 0.2128650 [7] 0.1215538 -0.2453996 -0.4138166 -1.0953834 Largest eigenvalues: [1] 64953052 60249766 57455140 56518763 55019934 53460661 52457286 52097709 [9] 51611383 50985717 Smallest eigenvalues: [1] 0.5972178 0.5456131 0.4455389 0.4226966 0.3205695 0.3148668 [7] 0.2679887 0.2527282 0.1654921 -0.5227497 Largest eigenvalues: [1] 65243761 60006447 56832069 56368450 54727375 53024001 52441960 51826070 [9] 51778153 51063630 Smallest eigenvalues: [1] 0.38359621 0.36222014 0.35961793 0.26874270 0.20798768 [6] 0.08574142 -0.41520101 -5.17263069 -11.23711291 -38.95989049 Largest eigenvalues: [1] 62789801 59712578 56427323 54950722 54868390 52852027 51819028 51118818 [9] 50854511 50411281 Smallest eigenvalues: [1] 0.4909796 0.4570228 0.4066567 0.3032244 0.2554636 0.2424323 [7] 0.2384851 -0.4434140 -0.8030490 -2.3378398 Largest eigenvalues: [1] 67150421 60669272 58591803 57408161 55274280 53620116 53564825 52896289 [9] 52227571 52064083 Smallest eigenvalues: [1] 0.5579982 0.5051204 0.3622174 0.3388242 0.2910276 0.2906055 [7] 0.2526001 0.1288093 0.1058786 -0.9665361 Largest eigenvalues: [1] 65983704 60976055 58410422 57315994 55543214 54136413 53258475 52768257 [9] 52473207 51747584 Smallest eigenvalues: [1] 0.4335797 0.4310832 0.3973678 0.3264764 0.2949178 0.2167845 [7] 0.1722916 0.1245493 0.1232390 -0.3697616 Largest eigenvalues: [1] 63363120 60481686 57178352 55545719 55256142 53928166 52441585 52338007 [9] 51405894 51281093 Smallest eigenvalues: [1] 0.5092447 0.4580002 0.4432456 0.3791556 0.2967002 0.2387923 [7] 0.2172654 0.1813795 -0.1203716 -0.3629448 Largest eigenvalues: [1] 63005277 59507447 56539402 54936544 54658541 52937044 51505806 51095008 [9] 50982621 50339473 Smallest eigenvalues: [1] 0.46291563 0.38719190 0.31786026 0.29318455 0.19211782 0.16450483 [7] -0.04082186 -0.12421561 -0.83118975 -2.12806154 Largest eigenvalues: [1] 65394117 60275985 57693786 56521421 55051914 53605746 52458415 52410567 [9] 52337765 51609474 Smallest eigenvalues: [1] 0.44524083 0.33245889 0.32462086 0.25437299 0.24604660 0.23578911 [7] 0.17555370 0.09603666 -0.01507374 -0.19263204 Largest eigenvalues: [1] 64906064 59519019 57160557 55722279 54727460 53363251 51797701 51737353 [9] 51250806 50731940 Smallest eigenvalues: [1] 0.41492594 0.29416226 0.28393718 0.28006142 0.18150681 0.14976376 [7] 0.14608236 0.07471617 -0.77893733 -1.07189272 Largest eigenvalues: [1] 64983449 60648684 57972259 55649599 55561426 54057784 53003278 52137233 [9] 52052877 51781663 Smallest eigenvalues: [1] 0.4577545 0.4522391 0.4027851 0.3863218 0.3476765 0.3327155 [7] 0.2706671 0.2129754 -1.0122043 -20.5550455 Largest eigenvalues: [1] 63515113 60002132 57141020 55851145 55311790 53615514 51988878 51967686 [9] 51778499 50941847 Smallest eigenvalues: [1] 0.54853294 0.50670621 0.43630769 0.42127703 0.39077436 0.28047300 [7] 0.27437091 0.27193397 0.25827140 -0.09679595 Largest eigenvalues: [1] 65329281 60762509 57832429 56852817 55367283 53742499 52927568 52432303 [9] 52172398 51360320 Smallest eigenvalues: [1] 0.5483294 0.5379973 0.5170185 0.3726293 0.3230770 0.3121718 [7] 0.2450974 0.2203398 0.0599361 -5.3187898 Largest eigenvalues: [1] 62669562 60249016 56921224 55580776 54825988 53797765 52224272 51661710 [9] 51005158 50788887 Smallest eigenvalues: [1] 0.30186246 0.25588873 0.22552097 0.17886503 0.04501903 [6] -0.17855591 -0.48106412 -10.43718676 -13.43292393 -24.39000393 Largest eigenvalues: [1] 62345266 59068683 56452822 54424568 54355514 52693592 51603877 51499862 [9] 50607549 50361774 Smallest eigenvalues: [1] 0.5029969 0.4924368 0.4343908 0.4127689 0.3936988 0.3684727 [7] 0.3423737 0.2358618 -0.1057755 -0.2538911 Largest eigenvalues: [1] 64414116 60106720 57646132 56283123 54645963 53203514 52327673 51834114 [9] 51693769 51057981 Smallest eigenvalues: [1] 0.5258422 0.4687241 0.4557539 0.4278174 0.3596955 0.3399936 [7] 0.3066862 0.1886756 -0.2935807 -0.4541939 Largest eigenvalues: [1] 65254733 60385691 57041037 56303551 55570412 53723274 52300271 52221783 [9] 51738451 51113930 Smallest eigenvalues: [1] 0.238454453 0.095073277 -0.007738026 -0.161267824 -0.368006568 [6] -1.702313950 -6.342835540 -18.344036839 -23.197898678 -95.354781700 Largest eigenvalues: [1] 65296510 60911543 57177145 57000834 55917603 53967696 53321942 52893030 [9] 51963347 51883159 Smallest eigenvalues: [1] 0.4991829 0.4818742 0.3902265 0.3703390 0.3133894 0.2937669 [7] 0.1900952 0.1659271 0.1239934 -0.5915255 Largest eigenvalues: [1] 64302211 60716873 57685295 56023991 55870578 54208739 52796191 52538021 [9] 52020759 51807013 Smallest eigenvalues: [1] 0.429156932 0.368938493 0.325209364 0.241678838 0.226363620 [6] 0.153614750 -0.003838937 -0.130597834 -1.006863253 -2.150462474 Largest eigenvalues: [1] 62477984 59853835 57105826 55674597 54204036 53824487 52107679 51568295 [9] 50698970 50496817 Smallest eigenvalues: [1] 0.2789917 0.2225079 0.1954517 0.1855275 -0.2659694 [6] -0.6825136 -0.7343493 -1.7496139 -6.4743192 -100.3148702 Largest eigenvalues: [1] 66884428 60727530 57939227 56612360 55508821 53538982 52925127 52178014 [9] 52109953 51010463 Smallest eigenvalues: [1] 0.5461506 0.4823923 0.4672295 0.3512405 0.3175798 0.2802527 [7] 0.2663688 0.2644027 0.2258517 -0.4020982 Largest eigenvalues: [1] 62906218 60603242 57310859 55776414 55097754 54178427 52751712 51888506 [9] 51265792 50969062 Smallest eigenvalues: [1] 0.4625740 0.4010580 0.3619648 0.3291956 0.3288281 0.2895016 [7] 0.2553185 0.2263961 0.2109011 -3.3883164 Largest eigenvalues: [1] 64932886 60317744 57475822 56630719 55104380 53516737 52474525 52437673 [9] 52419629 51452034 Smallest eigenvalues: [1] 0.52715344 0.43580318 0.38113151 0.32608084 0.31390926 0.19302616 [7] -0.05792133 -0.93230301 -1.91622521 -6.09469851 Largest eigenvalues: [1] 64517255 60109472 57331116 56545376 54876978 53172348 52340385 52301442 [9] 51780712 51186017 Smallest eigenvalues: [1] 0.44887669 0.42603683 0.41961486 0.41196201 0.37011495 0.17941008 [7] 0.14942029 0.14904827 0.05206293 -1.94679354 Largest eigenvalues: [1] 64203103 60492865 57359657 56044722 55344547 53440895 52741323 52071351 [9] 51698724 51591883 Smallest eigenvalues: [1] 0.3892820 0.3487393 0.3113848 0.2719389 0.2204615 0.0496663 [7] -0.2384710 -0.5021606 -0.5821858 -3.1487417 Largest eigenvalues: [1] 65609042 60671337 58168512 56122139 55410158 53825258 52993446 52289341 [9] 52052802 51959624 Smallest eigenvalues: [1] 0.3921902 0.3769315 0.3519380 0.3496981 0.2686873 0.2389682 [7] 0.1381529 0.1366931 -0.9824289 -1.0151289 Largest eigenvalues: [1] 65782954 60798656 58210469 56374832 55633437 54264241 52434761 52415451 [9] 52353673 51677285 Smallest eigenvalues: [1] 0.59710702 0.54076646 0.52405931 0.49091527 0.42684775 0.39801605 [7] 0.27760095 0.14651228 0.11536004 -0.02958352 Largest eigenvalues: [1] 64891688 60407884 57291069 55306151 55149069 53551103 52079719 51520547 [9] 51514934 51198273 Smallest eigenvalues: [1] 0.53794929 0.42607518 0.30905173 0.26351827 0.21458911 0.02477885 [7] -0.02717911 -0.16207734 -1.02056580 -2.80488081 Largest eigenvalues: [1] 63291348 59431319 56748974 55163999 54910435 53023954 51818178 51532302 [9] 51263653 50697319 Smallest eigenvalues: [1] 0.5318254 0.4674420 0.3899673 0.3229714 0.2784848 0.2699827 [7] 0.1655744 -0.1108428 -0.1673049 -1.1428309 Largest eigenvalues: [1] 64448618 60730551 57304818 56627205 55459424 53505813 52740090 52501294 [9] 51901187 51070646 Smallest eigenvalues: [1] 0.25243659 0.21358580 0.19323473 0.18336026 0.09014207 -0.71495101 [7] -1.16325950 -2.01383008 -4.18354226 -5.26476507 Largest eigenvalues: [1] 65518080 59796194 57316053 56510531 55031019 53501384 52611474 52060676 [9] 51870141 50819031 Smallest eigenvalues: [1] 0.4910755 0.4891466 0.4774769 0.4365560 0.4104876 0.3207398 [7] 0.3188411 0.3007056 0.2665099 -0.2975243 Largest eigenvalues: [1] 64208698 59919816 57112887 55732158 55158474 53411081 52265271 51740662 [9] 51638936 50902639 Smallest eigenvalues: [1] 0.5101966 0.4951504 0.4665691 0.3619481 0.3521903 0.3331943 [7] 0.2803387 -0.3407573 -1.5429698 -2.1064550 Largest eigenvalues: [1] 67419690 60898653 58684381 57775396 55279604 53791756 53763943 52741421 [9] 52232406 51983087 Smallest eigenvalues: [1] 0.5696144 0.5590046 0.4389156 0.3974480 0.3645191 0.3583544 [7] 0.3416514 0.2737678 0.1813640 -1.8833488 Largest eigenvalues: [1] 64871755 60282387 57177814 56218951 55325217 53843399 52221401 52102718 [9] 52018948 50934637 Smallest eigenvalues: [1] 0.4693469 0.4518112 0.3918816 0.3859981 0.3344764 0.3247012 [7] 0.2740529 0.2253304 0.1303382 -0.0675637 Largest eigenvalues: [1] 65381241 59405266 56627087 56373903 54257151 52803392 52403884 51544328 [9] 51286517 50622072 Smallest eigenvalues: [1] 0.5149883 0.4299325 0.4092290 0.3678656 0.3144539 0.2852062 [7] 0.2502052 -0.2123847 -0.5578747 -1.5390840 Largest eigenvalues: [1] 64785318 60554602 57631317 56480150 55190970 53384658 52500148 52281630 [9] 52105357 51159596 Smallest eigenvalues: [1] 0.4722795 0.4650883 0.4566886 0.4523340 0.4111263 0.4048655 [7] 0.3561046 0.3181576 0.3020069 -0.2281016 Largest eigenvalues: [1] 64963433 60252594 57667626 56279449 55156992 53719120 52367111 52129632 [9] 51905101 51220596 Smallest eigenvalues: [1] 0.4813249 0.4633643 0.4425030 0.3960609 0.3827651 0.3703349 [7] 0.3567444 0.3300237 -0.2133325 -3.0614927 Largest eigenvalues: [1] 63039208 59986948 57170072 55602980 55163735 53530057 51909456 51679701 [9] 51416241 50544673 Smallest eigenvalues: [1] 0.33992788 0.33117354 0.24444898 0.16244912 0.16041558 0.02198482 [7] -0.03019142 -0.04202999 -0.69409640 -4.92509489 Largest eigenvalues: [1] 64303371 60012434 57103694 55855808 55827790 53966460 52150433 51788493 [9] 51760883 50690858 Smallest eigenvalues: [1] 0.3739392 0.3400950 0.3374348 0.2752155 0.2492474 0.2432026 [7] 0.2187203 0.2043097 -3.0246086 -9.9196261 Largest eigenvalues: [1] 64510963 60626035 57711355 55719739 55574296 54148691 52370501 52177869 [9] 51655977 51564711 Smallest eigenvalues: [1] 0.5550998 0.4613133 0.3985648 0.3393245 0.3329940 0.3010023 [7] 0.2456954 0.1834303 -0.5305284 -2.3738032 Largest eigenvalues: [1] 66580830 59676158 57142087 56878847 54361913 53231395 52558753 51759258 [9] 51380248 51058168 Smallest eigenvalues: [1] 0.4774911 0.4439654 0.4332345 0.3126872 0.3014802 0.2551789 [7] 0.1868672 0.1186505 -2.1765488 -4.3838795 Largest eigenvalues: [1] 63389818 59813482 57254308 55899256 54896559 53372822 52739198 52192275 [9] 51700891 51484188 Smallest eigenvalues: [1] 0.43328845 0.38719455 0.37674980 0.27752984 0.12302446 [6] -0.07760758 -0.11254720 -0.41678797 -3.89305747 -14.39757724 Largest eigenvalues: [1] 63721875 59221417 56626464 55014390 54261307 52626148 51366186 51048924 [9] 51001995 50472366 Smallest eigenvalues: [1] 0.5049877 0.4139814 0.3794518 0.3507782 0.3320662 0.2714831 [7] 0.2431447 0.2112054 0.1881777 -0.2357201 Largest eigenvalues: [1] 63363523 59721126 57030640 55540033 54812756 53299844 51787395 51676671 [9] 51585476 50791837 Smallest eigenvalues: [1] 0.4198794 0.3204345 0.3035517 0.2641293 0.2438497 0.2095091 [7] 0.1592699 0.1364110 -1.1454457 -4.0666950 Largest eigenvalues: [1] 65093158 59097482 56547614 56075054 53901870 52596559 52102653 51245021 [9] 51099102 50486599 Smallest eigenvalues: [1] 0.5227194 0.5059859 0.4981923 0.4457535 0.3767528 0.3616820 [7] 0.2974851 0.2890158 -0.4473132 -2.1675098 Largest eigenvalues: [1] 66617715 61003702 58140449 57788429 55209434 53823945 53382298 52434736 [9] 52113933 51524019 Smallest eigenvalues: [1] 0.445328417 0.385286421 0.364609395 0.315363511 0.273160561 [6] 0.261115992 0.254419890 0.203082302 -0.004028773 -1.052138807 Largest eigenvalues: [1] 65084793 60246996 57372672 56263051 55367276 53722296 52323883 52022610 [9] 51834624 51014821 Smallest eigenvalues: [1] 0.4341606 0.3577792 0.3255446 0.3157514 0.2818044 0.2334308 [7] 0.2146404 -0.4799234 -1.6754531 -4.5124258 Largest eigenvalues: [1] 63383427 60232910 57210838 55661666 55578067 53675023 51953631 51771568 [9] 51471919 51237151 Smallest eigenvalues: [1] 0.42093704 0.37580775 0.31111732 0.29431373 0.27486582 0.24140553 [7] 0.19546482 0.03669958 -0.14103699 -5.23249640 Largest eigenvalues: [1] 65359462 60576357 57823392 56572610 56182118 54262181 52595117 52410399 [9] 51955369 51251053 Smallest eigenvalues: [1] 0.2729783 0.2706867 0.2384592 0.2278426 0.1235578 -0.4504019 [7] -0.5971150 -1.4395688 -16.3249884 -34.0914851 Largest eigenvalues: [1] 64901160 59759172 56958042 56667693 54905439 53217128 52489484 51370122 [9] 51198887 50426340 Smallest eigenvalues: [1] 0.4554501 0.3550554 0.3425412 0.3238883 0.2681186 0.2454067 [7] -0.1319494 -0.3589444 -1.5479449 -8.7067886 Largest eigenvalues: [1] 63402451 59613515 56936391 54913542 54746845 52954454 51685464 51163980 [9] 51013426 50560135 Smallest eigenvalues: [1] 0.50499464 0.50237240 0.46944764 0.45110610 0.28366685 0.26981990 [7] 0.12573600 -0.01493711 -0.43155697 -9.48172877 Largest eigenvalues: [1] 64984141 60068182 57095392 55869088 54885385 53134114 52120017 51964467 [9] 51894852 51237814 Smallest eigenvalues: [1] 0.43274085 0.40635116 0.39121924 0.38072803 0.33036984 0.28694404 [7] 0.21678863 0.20260673 0.06202214 -1.07354130 Largest eigenvalues: [1] 64923661 61194443 58218019 56469070 56263877 54855320 53132086 52796651 [9] 52185622 51983742 Smallest eigenvalues: [1] 0.48516217 0.36710366 0.29781240 0.20398797 -0.07905503 [6] -0.36319719 -0.37410108 -1.24833610 -2.03155426 -24.59923755 Largest eigenvalues: [1] 65748158 60418040 57699642 56553541 55557636 53669555 52679027 52323301 [9] 52193404 51390377 Smallest eigenvalues: [1] 0.5499865 0.4208013 0.4102624 0.3910351 0.3840838 0.2929361 [7] 0.2620767 0.1673236 0.1459602 -1.1357819 Largest eigenvalues: [1] 65232715 60516047 57818024 56383629 55534259 54121014 52830329 52455888 [9] 52364252 51829765 Smallest eigenvalues: [1] 0.24334952 0.22008136 0.20946134 0.20289071 0.19768708 -0.01684957 [7] -0.05938816 -0.07341618 -1.40394549 -3.74934048 Largest eigenvalues: [1] 68040001 60681448 58564870 57737275 54968708 53959572 53753965 52351765 [9] 51793378 51688121 Smallest eigenvalues: [1] 0.4822019 0.4618066 0.3679673 0.3482136 0.3172875 0.3096675 [7] 0.2920842 0.2557456 0.2378626 -0.1069289 Largest eigenvalues: [1] 64715112 60386260 57290028 56280337 54909910 53360729 52496448 51746698 [9] 51714526 50854797 Smallest eigenvalues: [1] 0.40366129 0.35584743 0.34893782 0.26607788 0.25617216 0.24545336 [7] 0.23088991 0.07835972 -0.06808716 -0.71303065 Largest eigenvalues: [1] 64418227 60272024 57538448 55416779 55135472 53764506 52055857 51945465 [9] 51643290 51106653 Smallest eigenvalues: [1] 0.6458670 0.5290819 0.4215005 0.3536802 0.3200041 0.2503895 [7] 0.2296752 0.1531097 -0.1155864 -0.5435428 Largest eigenvalues: [1] 63183821 59985908 57502172 55322395 55038142 53752840 52348876 51810737 [9] 51198202 50840139 Smallest eigenvalues: [1] 0.4640593 0.4377243 0.3644144 0.3194029 0.3104610 0.2795312 [7] 0.2055138 0.1923308 -1.2375955 -12.4058702 Largest eigenvalues: [1] 64573106 59936877 56722379 55809260 55104462 53406175 52353098 51918984 [9] 51852662 51219078 Smallest eigenvalues: [1] 0.45384324 0.37035798 0.35794837 0.32435794 0.25690769 0.25328091 [7] 0.24230546 0.05948428 -0.75149526 -1.32151493 Largest eigenvalues: [1] 64449102 60377059 57220185 55480173 55462660 53830333 52192780 51873629 [9] 51413374 51156962 Smallest eigenvalues: [1] 0.49027024 0.44953124 0.42905935 0.42731675 0.36738142 0.30615057 [7] 0.24320575 0.21787247 0.16608311 -0.08800963 Largest eigenvalues: [1] 63324737 59538915 56864243 55083026 55073825 53210917 51888727 51500722 [9] 51158414 50660139 Smallest eigenvalues: [1] 0.5442891 0.5004407 0.4789799 0.4641114 0.3300991 0.3097456 [7] 0.3088163 0.2767147 0.2209505 -0.8225658 Largest eigenvalues: [1] 64463616 59933708 57098043 55853022 54863078 53391108 52313894 51896564 [9] 51627284 51003963 Smallest eigenvalues: [1] 0.4654656 0.4138306 0.3295331 0.2914700 0.2825199 0.2504557 [7] 0.2406395 0.2264968 0.1826636 -4.7170459 Largest eigenvalues: [1] 66806578 60182174 57652106 57160939 54902998 53537384 53148556 52223214 [9] 52068645 51477767 Smallest eigenvalues: [1] 0.49404084 0.43808708 0.37417089 0.35002741 0.34270305 0.30349633 [7] 0.28832401 0.18733932 -0.04115719 -0.38155206 Largest eigenvalues: [1] 65596407 60748616 57948171 56464715 55692419 54062004 53442958 52657923 [9] 52140380 51994919 Smallest eigenvalues: [1] 0.43767714 0.41360798 0.29450200 0.26490822 0.24130288 0.20592951 [7] 0.16103586 0.07000476 -0.41737411 -0.50971827 Largest eigenvalues: [1] 67168498 60566866 57849403 57404401 54764190 53469202 53123933 52272941 [9] 51948122 51711059 Smallest eigenvalues: [1] 0.4287099 0.4282514 0.3973804 0.3892213 0.3123146 0.2358853 [7] 0.1612999 0.1605497 -0.2688335 -5.8299995 Largest eigenvalues: [1] 65084274 59743409 56896469 56346631 54535488 52725316 52411718 51643999 [9] 51561855 50930849 Smallest eigenvalues: [1] 0.3082562 0.3047844 0.2716003 0.2579050 0.1788843 -0.2576115 [7] -0.3452661 -0.9506603 -2.0562081 -2.6868315 Largest eigenvalues: [1] 65264885 60778802 57708336 56415326 55899069 54367923 52810124 52405618 [9] 52093863 51653800 Smallest eigenvalues: [1] 0.59600416 0.53213548 0.51288707 0.47686931 0.46248450 0.38031461 [7] 0.30797385 0.30478171 0.20292123 -0.01065626 Largest eigenvalues: [1] 65765198 60987537 58210608 56764277 55471310 53732148 52709991 52519562 [9] 52020629 51685092 Smallest eigenvalues: [1] 0.6034738 0.5556320 0.5199809 0.4999030 0.4861337 0.4641957 [7] 0.4211815 0.3063336 0.2672209 -0.2760835 Largest eigenvalues: [1] 64124588 59773195 56768950 55984895 54821312 53177997 51973039 51811308 [9] 51628959 50833276 Smallest eigenvalues: [1] 0.4404908 0.4034500 0.3996555 0.3893506 0.3052125 0.2917697 [7] 0.1438516 -0.3118468 -9.3989921 -18.2183983 Largest eigenvalues: [1] 65500943 60219216 57519340 56635008 54742896 53386022 52744574 51496580 [9] 51475777 50514245 Smallest eigenvalues: [1] 0.46474102 0.37507310 0.36475399 0.28321383 0.23768977 0.23375274 [7] 0.19428444 0.05959832 0.04432313 -6.34832757 Largest eigenvalues: [1] 61708688 59864826 57140470 56000404 54333436 53803108 52122637 51134929 [9] 50551509 50525734 Smallest eigenvalues: [1] 0.4706150 0.4617676 0.4283637 0.4041858 0.3622399 0.3478138 [7] 0.2470418 0.2353118 -0.6615252 -1.0302431 Largest eigenvalues: [1] 65180634 60288309 58247009 56440038 55256285 54039406 52539085 52509700 [9] 52187060 51768085 Smallest eigenvalues: [1] 0.47066771 0.38953935 0.35319067 0.29865405 0.04963312 0.01243067 [7] -0.12960261 -0.13251663 -1.29890621 -2.15787959 Largest eigenvalues: [1] 65055322 59994988 56704071 56240372 54695048 53018451 52309600 52188075 [9] 51422350 51171086 Smallest eigenvalues: [1] 0.42271475 0.37708931 0.36209363 0.33430741 0.28253021 0.24862574 [7] 0.20156792 0.15752430 0.08164249 -3.32906415 Largest eigenvalues: [1] 61367940 59582945 56825009 55424000 53504078 53409756 51673331 50917345 [9] 50245675 50109295 Smallest eigenvalues: [1] 0.28327777 0.27753930 0.10578123 0.07314426 -0.16387648 [6] -0.88582894 -1.55372743 -2.32373572 -2.52625439 -27.40042386 Largest eigenvalues: [1] 63004957 60612180 57156802 55952653 55483519 54309703 52438970 52367865 [9] 51399196 51253812 Smallest eigenvalues: [1] 0.47750982 0.46956939 0.44915818 0.42281053 0.35592319 0.19446157 [7] 0.18962537 0.16803872 0.08330244 -0.32227640 Largest eigenvalues: [1] 65523492 60063624 56901120 56376583 55001407 53157168 52437940 52200364 [9] 51999228 51485916 Smallest eigenvalues: [1] 0.4571964 0.3238459 0.2648202 0.2493922 0.2049719 0.2019953 [7] 0.1837542 -0.5546926 -2.1066588 -21.2173276 Largest eigenvalues: [1] 65229683 60393280 57768877 56105495 54799568 53196929 52388765 52113475 [9] 51972804 51710292 Smallest eigenvalues: [1] 0.41078896 0.35949319 0.34406070 0.32722415 0.31474933 [6] 0.29921865 0.27754639 0.09137449 -0.02184615 -29.39202358 Largest eigenvalues: [1] 63022377 59484776 57100237 55226959 55194210 53428889 51724593 51475606 [9] 51288230 50596320 Smallest eigenvalues: [1] 0.36847322 0.34207286 0.33981044 0.27570306 0.25959508 0.22660283 [7] 0.17982102 0.03736938 -0.33792894 -2.94218894 Largest eigenvalues: [1] 64995722 60254030 57290980 55896512 55322786 53625187 51823965 51548462 [9] 51526877 50883196 Smallest eigenvalues: [1] 0.4955103 0.4726134 0.4609949 0.3370033 0.3052478 0.3018187 [7] 0.2919358 0.2790933 0.2225502 -0.4303885 Largest eigenvalues: [1] 61920249 59872713 56871954 55567620 54250349 53663278 52162575 51672359 [9] 50790756 50459394 Smallest eigenvalues: [1] 0.48895418 0.46394416 0.45855480 0.42888069 0.41184146 0.31492873 [7] 0.28350104 0.27625885 0.09075314 -3.54530943 Largest eigenvalues: [1] 64043044 60509385 57318820 55474611 55434749 53804844 52156129 51656538 [9] 51607360 50997015 Smallest eigenvalues: [1] 0.452059327 0.450230083 0.399109587 0.240694255 0.173602166 [6] 0.154327437 0.066358713 -0.008891906 -1.682021539 -3.384752104 Largest eigenvalues: [1] 63903868 60786594 57278680 56008697 55397039 53990673 52489251 52194596 [9] 51931905 51254613 Smallest eigenvalues: [1] 0.3655935 0.3329792 0.2606046 0.2589456 0.2511102 0.2165988 [7] 0.2043469 -0.6491771 -8.5410615 -16.9960753 Largest eigenvalues: [1] 64497420 61351850 57931601 56981107 56359736 55256138 53113711 52663058 [9] 52255885 51664821 Smallest eigenvalues: [1] 0.46277828 0.45676796 0.44092611 0.43662052 0.35244114 0.28151719 [7] 0.23070772 0.19887279 0.04933185 -1.02341151 Largest eigenvalues: [1] 65890518 59920846 57251140 57034471 54819032 53363671 52921575 52189240 [9] 52064594 51554353 Smallest eigenvalues: [1] 0.11801268 0.09489184 0.08466386 0.07295297 -0.22823110 [6] -0.63592599 -1.93349065 -6.46042397 -17.86811655 -67.45496709 Largest eigenvalues: [1] 63867038 59435600 56543078 54968586 54542654 52832065 51947736 51299224 [9] 51285669 51006173 Smallest eigenvalues: [1] 0.5278092 0.4939030 0.4748969 0.4338467 0.4239038 0.4017272 [7] 0.3793102 0.3614124 0.3346325 -0.5934390 Largest eigenvalues: [1] 63959375 60847791 57545913 56281084 55855382 54118737 52261688 52190027 [9] 52085476 51105563 Smallest eigenvalues: [1] 0.6247623 0.5476715 0.4598102 0.4455974 0.4411331 0.4318708 [7] 0.3728331 0.2579648 -0.1275022 -0.1724734 Largest eigenvalues: [1] 64797134 60195553 57625071 56073197 55273474 53481629 52518988 52242795 [9] 51812093 51410050 Smallest eigenvalues: [1] 0.5584616 0.5545359 0.4930952 0.4839450 0.3540002 0.3452527 [7] 0.3301492 0.3117685 0.2383850 -0.1593142 Largest eigenvalues: [1] 63363949 59670131 57190772 55369679 55204815 53698423 52031428 51669022 [9] 51246827 50811008 Smallest eigenvalues: [1] 0.47844117 0.41895707 0.40023332 0.39309687 0.35261705 0.33232005 [7] 0.05061357 0.01728149 -0.14966521 -4.74192526 Largest eigenvalues: [1] 64413604 59608540 56700461 56022953 54331782 52694243 52069234 51614090 [9] 51250684 50674572 Smallest eigenvalues: [1] 0.5676876 0.5214993 0.4597463 0.3925009 0.3615232 0.3507187 [7] 0.2664203 0.1855388 0.1679822 -0.6563396 Largest eigenvalues: [1] 65042474 60765130 57521496 56683838 55783312 53960441 52919359 52613443 [9] 52462212 51773650
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.595585 | 0.8824614 | 15.19461 | 0 | 2.738447 | 6.767316 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + acc + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_acc_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 664 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.3603906 0.3206480 0.2860769 0.2596945 0.2094575 0.1474205 [7] 0.1147731 -0.1408713 -0.1589878 -3.8942672 Largest eigenvalues: [1] 64042812 60125820 57559805 55670773 55051760 53392896 52138209 51717479 [9] 51678901 51142828 Smallest eigenvalues: [1] 0.19308764 0.17015664 0.10711512 0.02288223 -0.01647957 -0.01698404 [7] -0.02461813 -0.18648999 -0.18929676 -2.45392676 Largest eigenvalues: [1] 63355450 61056600 57701327 55871095 55332918 53938763 52739427 52427972 [9] 51869486 51615887 Smallest eigenvalues: [1] 0.313184927 0.299904415 0.297226800 0.272611956 0.223798356 [6] 0.129874123 0.067220822 -0.005984975 -0.153001156 -0.633852607 Largest eigenvalues: [1] 64140129 61112687 58366275 55856481 55741450 54327511 53206043 52322060 [9] 52089966 51897926 Smallest eigenvalues: [1] 0.486435822 0.484210632 0.414051726 0.353098383 0.346720503 [6] 0.259123560 0.251768800 -0.006308419 -0.043910305 -0.102562167 Largest eigenvalues: [1] 61984148 60501986 57601754 55831981 54968196 54066883 52461370 52415988 [9] 51222636 51000972 Smallest eigenvalues: [1] 0.3567004 0.3285938 0.2976389 0.2334785 0.2046435 0.1983599 [7] 0.1705519 0.1184595 -0.1281541 -3.2064522 Largest eigenvalues: [1] 65163173 59818161 57293665 56025018 54719041 53144375 52121514 51967281 [9] 51426274 51120415 Smallest eigenvalues: [1] 0.41800093 0.41103957 0.37141810 0.28186811 0.27306749 0.14039522 [7] 0.05665045 -0.02675393 -0.10474338 -0.33093004 Largest eigenvalues: [1] 64358283 60638162 57254916 56045643 55652612 53846201 52740030 52017768 [9] 51714901 51420528 Smallest eigenvalues: [1] 0.2635689 0.1968254 0.1840918 0.1463388 0.1367938 0.0774332 [7] -0.1700209 -0.1777492 -0.3643735 -0.4571581 Largest eigenvalues: [1] 65013751 60998681 57648795 56151025 55480723 53867210 52962816 52135892 [9] 52042929 51761050 Smallest eigenvalues: [1] 0.34805612 0.31317840 0.23050060 0.22377275 0.18881466 -0.05365539 [7] -0.12786940 -0.30029511 -0.38798873 -0.65147113 Largest eigenvalues: [1] 64870413 59853259 56521056 56464943 54495022 52690414 52475124 52167009 [9] 51688408 51233785 Smallest eigenvalues: [1] 0.4924669167 0.4224823921 0.4110749524 0.3006899051 0.2739084512 [6] 0.2118511766 0.2073970513 0.0566545630 0.0004435585 -1.9697097632 Largest eigenvalues: [1] 63897554 59811350 57221227 55815994 54681379 53175611 52229504 51781375 [9] 51653218 51043701 Smallest eigenvalues: [1] 0.37594417 0.35853443 0.33685754 0.32689900 0.23091090 0.22691332 [7] 0.22173925 0.10436881 0.06168631 -0.03016414 Largest eigenvalues: [1] 64507451 60409949 58002489 55634486 55321207 54073815 52718494 52110591 [9] 51872357 51712245 Smallest eigenvalues: [1] 0.44564453 0.40144457 0.35814751 0.33064016 0.20256703 0.06430269 [7] -0.43919089 -0.45225889 -1.04595515 -3.72937176 Largest eigenvalues: [1] 64699010 60039590 57230094 55798586 55200344 52971868 52186125 51956598 [9] 51697452 51235547 Smallest eigenvalues: [1] 0.3637690 0.3179382 0.2953825 0.2815649 0.2708426 0.1716318 [7] 0.1256518 0.0709207 -0.2944240 -1.8981729 Largest eigenvalues: [1] 63315355 59864465 57107461 55193265 54822933 53603761 52141302 52028246 [9] 51338200 51002270 Smallest eigenvalues: [1] 0.38703956 0.38204369 0.35914554 0.27981298 0.27351546 0.21683480 [7] 0.20852930 -0.05007726 -0.21218630 -1.18122172 Largest eigenvalues: [1] 64864962 59719156 57151947 56535418 54774457 53303421 52543399 52172525 [9] 51483342 50767655 Smallest eigenvalues: [1] 0.5666210 0.5128652 0.5047648 0.4344818 0.3820561 0.3682778 [7] 0.2593738 0.2163635 0.1474606 -0.0161257 Largest eigenvalues: [1] 65018802 59485575 56759327 55961013 54888526 53236899 52142138 51950984 [9] 51851831 51205014 Smallest eigenvalues: [1] 0.49674605 0.38986244 0.36977487 0.32981922 0.22408674 0.21679872 [7] 0.14659607 0.09302246 -0.08805735 -0.11807157 Largest eigenvalues: [1] 66291866 59307802 57238030 56639429 54034094 53259521 52543575 51326778 [9] 51117772 50519245 Smallest eigenvalues: [1] 0.5048780 0.5018486 0.4783975 0.4409971 0.4168265 0.3654423 [7] 0.2558727 0.1582258 -0.1423267 -0.2183561 Largest eigenvalues: [1] 63345416 60087174 56783771 55243839 54976033 53456167 51999856 51371631 [9] 50839683 50520652 Smallest eigenvalues: [1] 0.3680907 0.2673715 0.2556593 0.2264717 0.2032561 0.1806324 [7] 0.1578470 0.1348485 -0.1274604 -0.5267096 Largest eigenvalues: [1] 66512102 60534115 57855623 57260735 55043218 53384080 53184007 52933113 [9] 51654632 51496812 Smallest eigenvalues: [1] 0.46250142 0.40812451 0.38320941 0.23381370 0.21528419 0.12381999 [7] 0.10875845 0.07737656 0.06233337 -0.79995766 Largest eigenvalues: [1] 65753544 60501423 56960768 56753694 55112839 53464936 52724815 52234591 [9] 52020426 51263068 Smallest eigenvalues: [1] 0.48720891 0.47571582 0.45112471 0.39529391 0.33727289 0.27785494 [7] 0.15250768 0.02060553 -0.07968460 -0.71683640 Largest eigenvalues: [1] 63421109 59880816 57059970 55351813 54886550 53781939 52421157 51800205 [9] 50989232 50887761 Smallest eigenvalues: [1] 0.39905433 0.36072808 0.34246557 0.30407559 0.29587872 0.27107999 [7] 0.24143192 0.11505289 0.11430622 -0.06455022 Largest eigenvalues: [1] 64281762 61489955 58090710 56617451 55655382 54025692 52788376 52530737 [9] 52474244 51781334 Smallest eigenvalues: [1] 0.4524249 0.4297710 0.3758639 0.3483349 0.3256069 0.2992669 [7] 0.2661505 0.2370527 0.1072519 -0.1315416 Largest eigenvalues: [1] 64822507 61097914 58013734 56414784 56408389 54708214 53058937 52587644 [9] 52315629 51706456 Smallest eigenvalues: [1] 0.30172964 0.25823254 0.15310404 0.09629276 0.09252563 0.01557363 [7] -0.06069795 -0.11263539 -0.43452943 -1.44370508 Largest eigenvalues: [1] 64743454 60218965 56999694 55926177 54883767 53329324 51982796 51929633 [9] 51562484 50890426 Smallest eigenvalues: [1] 0.49313171 0.43804805 0.40373882 0.32104682 0.27865145 0.26023728 [7] 0.18798723 0.16612590 0.07420535 -0.06207839 Largest eigenvalues: [1] 63228762 60339728 57141445 55692928 54834423 53103843 51918880 51757665 [9] 51683771 50766304 Smallest eigenvalues: [1] 0.3815686 0.2937906 0.2934616 0.2672913 0.2637593 0.2198001 [7] 0.2107763 0.1004381 -0.4090973 -0.5188172 Largest eigenvalues: [1] 63894586 59758694 57239506 55185835 54421974 52959164 51919518 51354950 [9] 51113528 51070084 Smallest eigenvalues: [1] 0.34347383 0.27432736 0.26188890 0.23710049 0.22722438 0.21810667 [7] 0.19475320 0.01777969 -0.18448097 -0.26251265 Largest eigenvalues: [1] 65754532 60415101 57841584 56729040 55100359 53409275 52978023 52750692 [9] 51987324 51898316 Smallest eigenvalues: [1] 0.4341985 0.3725930 0.3666928 0.3291824 0.2923235 0.2614658 [7] 0.1960324 0.1268017 0.1227838 -1.4700311 Largest eigenvalues: [1] 64976715 59836961 57158468 56027573 55025189 53202778 52093152 52054413 [9] 51493984 51140531 Smallest eigenvalues: [1] 0.49515698 0.44302564 0.35624174 0.34921851 0.33763801 0.29688016 [7] 0.26949354 0.14490958 -0.08477671 -1.05720891 Largest eigenvalues: [1] 63539838 59124913 56986340 55537837 54439466 52891167 51600459 51493504 [9] 51429997 50568226 Smallest eigenvalues: [1] 0.43287209 0.39230530 0.33789149 0.31164282 0.26393407 0.19947962 [7] -0.03676008 -0.07383353 -0.08369749 -0.22410323 Largest eigenvalues: [1] 61127531 59035791 56117928 54820812 54126598 52912263 51797545 50841255 [9] 50128339 49932966 Smallest eigenvalues: [1] -0.2460616 -0.3330930 -0.3729782 -0.3737812 -0.4331279 -0.5176597 [7] -0.5487857 -0.9669094 -1.1436436 -1.2282288 Largest eigenvalues: [1] 64858128 61061489 58209202 55631681 55550754 54216186 52454133 51974642 [9] 51671098 51419047 Smallest eigenvalues: [1] 0.27058774 0.23880427 0.23389710 0.20867380 0.17934001 0.02470653 [7] -0.01126291 -0.21387908 -0.34756716 -0.76965295 Largest eigenvalues: [1] 64842719 61059995 57733046 56630744 55598746 54004868 52775192 52599737 [9] 52376831 51802623 Smallest eigenvalues: [1] 0.39886268 0.30092224 0.25846460 0.24828442 0.21635403 0.11846062 [7] 0.09696379 -0.05399715 -1.18493062 -1.22707519 Largest eigenvalues: [1] 64505280 60140247 56638533 56268165 55292871 53292063 52537867 52240039 [9] 52193336 51205387 Smallest eigenvalues: [1] 0.468809909 0.374803091 0.341744479 0.286649767 0.249555276 [6] 0.189182536 0.142985110 -0.009777275 -0.622729528 -1.012807441 Largest eigenvalues: [1] 64029117 58805802 56461250 55821379 53978132 52250512 51751027 51256342 [9] 51020191 49960559 Smallest eigenvalues: [1] 0.424019349 0.324891136 0.238578223 0.228276122 0.226693893 [6] 0.206355120 0.186955433 0.149452847 0.003521582 -7.045044203 Largest eigenvalues: [1] 61832975 59825418 56886563 55066069 54669400 53472166 52120498 51468919 [9] 50728614 50525906 Smallest eigenvalues: [1] 0.26833906 0.22044811 0.21640131 0.21348019 0.07544258 0.04953039 [7] -0.12830040 -0.17947132 -1.00590867 -2.90901045 Largest eigenvalues: [1] 66492448 60572966 57389874 56426197 55331903 53686182 52545385 52417101 [9] 51793282 51658011 Smallest eigenvalues: [1] 0.43086981 0.35695808 0.34527069 0.34409043 0.25809766 0.24956918 [7] 0.22633378 0.18869623 0.04441534 -0.06619720 Largest eigenvalues: [1] 64569776 60746734 58209546 55780995 55604053 54234904 52757165 52437905 [9] 51782170 51522448 Smallest eigenvalues: [1] 0.3199920 0.3085092 0.2815040 0.2192651 0.2166413 0.1703417 [7] 0.1068566 -0.1781967 -0.2262937 -2.1929220 Largest eigenvalues: [1] 65075273 60567053 57749733 55895980 55826053 54154201 52434478 52240629 [9] 52204402 51355481 Smallest eigenvalues: [1] 0.36679593 0.36204198 0.30321159 0.27852106 0.20601523 0.09675696 [7] 0.02474611 -0.08693992 -0.22011251 -1.60236497 Largest eigenvalues: [1] 63877916 59888506 57013986 55192226 55033924 53438740 52166670 51471107 [9] 51344018 51183333 Smallest eigenvalues: [1] 0.474959591 0.388621819 0.357229674 0.342993411 0.324167216 [6] 0.310567632 0.241170437 0.013774104 -0.006679943 -0.073915400 Largest eigenvalues: [1] 65237018 60365372 57467544 56411339 54843198 53060364 52541326 52121609 [9] 51296529 50886352 Smallest eigenvalues: [1] 0.34471929 0.32909510 0.30661962 0.25509392 0.24737358 0.20364714 [7] 0.06887637 0.05206281 -0.10369626 -2.43385066 Largest eigenvalues: [1] 63171106 59821566 56965008 55146968 54994103 53372462 51709603 51671283 [9] 51149930 50895599 Smallest eigenvalues: [1] 0.48916970 0.39957389 0.38312140 0.35914591 0.25344685 0.21311593 [7] 0.18543280 0.12980339 0.03028597 -0.77720909 Largest eigenvalues: [1] 65238373 59942593 57167130 57130370 54517661 53085943 52858254 52016865 [9] 51906367 51073233 Smallest eigenvalues: [1] 0.37306304 0.32342526 0.32011327 0.17822441 0.14853715 0.14105478 [7] -0.06471892 -0.22865453 -0.57631561 -0.71568892 Largest eigenvalues: [1] 65070191 60984772 58054948 56780020 55345357 53402084 53005991 52656621 [9] 51832038 51704852 Smallest eigenvalues: [1] 0.28908031 0.24141226 0.22387002 0.15346420 0.10963183 0.07682236 [7] -0.03741547 -0.04481323 -0.79968007 -0.82843491 Largest eigenvalues: [1] 64853322 60580673 58070284 56409408 55069526 53499647 52708025 52469870 [9] 52087559 51785470 Smallest eigenvalues: [1] 0.33057720 0.28530559 0.27569552 0.22232186 0.13690152 0.02835007 [7] -0.10745943 -0.36032917 -0.40872622 -1.11880970 Largest eigenvalues: [1] 64155923 59585147 56853874 54875791 54761907 53058820 51286058 51238972 [9] 51113988 50490770 Smallest eigenvalues: [1] 0.39960852 0.23095879 0.21918600 0.16759046 0.08511106 0.06018156 [7] -0.03117794 -0.05202401 -0.09417116 -1.33545675 Largest eigenvalues: [1] 63335509 59835216 56962529 55206734 54747277 53152608 51682359 51488730 [9] 51309686 50888761 Smallest eigenvalues: [1] 0.5364285 0.5353717 0.4451344 0.4384927 0.4352319 0.3925692 [7] 0.3231796 0.2993528 0.2874640 -0.2740327 Largest eigenvalues: [1] 64168402 60433535 57581693 55838796 55364991 53658423 51735558 51697195 [9] 51564242 50652737 Smallest eigenvalues: [1] 0.54477934 0.53961058 0.46571162 0.40663906 0.37828691 0.34767162 [7] 0.20242885 0.10694160 0.01386924 -0.32716346 Largest eigenvalues: [1] 62134351 59525841 56632421 55230589 54338034 53394068 51681453 51589397 [9] 50455817 50289707 Smallest eigenvalues: [1] 0.44576428 0.32286257 0.31535376 0.25187381 0.14262545 0.12887404 [7] 0.06061520 0.04429567 -0.05580773 -2.15177198 Largest eigenvalues: [1] 63505411 59554332 56760102 55289636 55039486 53369357 52378995 51839392 [9] 51441216 51216217 Smallest eigenvalues: [1] 0.5205121 0.5028372 0.4369018 0.3663844 0.3630000 0.3339224 [7] 0.3291279 0.2937270 0.2668510 -0.4076816 Largest eigenvalues: [1] 63812606 59626039 57210590 55512293 54681728 52916285 51692881 51525854 [9] 51044999 50389901 Smallest eigenvalues: [1] 0.37353636 0.31628203 0.24671127 0.23271970 0.21987027 0.12945540 [7] -0.01279438 -0.20582004 -0.29160393 -0.86838223 Largest eigenvalues: [1] 64246167 60069298 57089796 56026719 55078598 53558221 52425139 51965156 [9] 51934191 51448378 Smallest eigenvalues: [1] 0.387618700 0.350842220 0.313729781 0.274074025 0.230364909 [6] 0.201045632 0.191965046 0.005931078 -0.145759565 -0.261922357 Largest eigenvalues: [1] 64812748 61049897 58348316 56108538 55789309 54391289 52461537 52307812 [9] 52019069 51537906 Smallest eigenvalues: [1] 0.35843234 0.35473116 0.33890849 0.32846012 0.31521429 0.28887962 [7] 0.22239760 0.01641749 -0.23299799 -0.32896698 Largest eigenvalues: [1] 65476519 60479513 57689154 56575188 55216963 53689845 52491133 52169096 [9] 51982746 51247026 Smallest eigenvalues: [1] 0.46052563 0.43961626 0.41741332 0.40072946 0.30383083 0.25091436 [7] 0.19061881 0.16642050 0.07783223 -0.13221950 Largest eigenvalues: [1] 65440331 60869551 57965413 56422599 55596541 54095370 52633987 52530999 [9] 52022117 51526187 Smallest eigenvalues: [1] 0.48360484 0.47577667 0.42888151 0.42256623 0.34681360 0.34478007 [7] 0.27721432 0.25140540 0.22366972 -0.03321141 Largest eigenvalues: [1] 65390979 60730666 57959144 56619766 56027558 54435551 52608311 52367810 [9] 52286101 51354269 Smallest eigenvalues: [1] 0.3373224 0.3266732 0.2598420 0.2295445 0.2081416 0.1724380 [7] 0.1444689 -0.5320565 -0.6962719 -0.7924707 Largest eigenvalues: [1] 66333537 60712971 57981165 57139470 55098263 53523924 53274765 52331288 [9] 51896990 51522859 Smallest eigenvalues: [1] 0.358128201 0.321289787 0.306916866 0.273582428 0.264583667 [6] 0.191468149 0.163286958 -0.005859051 -0.391608586 -0.424768896 Largest eigenvalues: [1] 63886544 60503146 57149465 55781985 55736539 54049574 52905981 52206455 [9] 51954925 51687018 Smallest eigenvalues: [1] 0.48178954 0.40723983 0.39895801 0.38145384 0.31096653 0.25125948 [7] 0.23717507 0.19727587 0.06835951 -0.09234222 Largest eigenvalues: [1] 64917614 59570925 57013438 56450765 54200155 52678059 52445773 51409487 [9] 51177865 50346307 Smallest eigenvalues: [1] 0.49139837 0.47513540 0.44025141 0.42538513 0.36614629 0.30053951 [7] 0.28887771 0.07024903 -0.02697186 -0.46653374 Largest eigenvalues: [1] 65266549 60192459 57627485 56337903 55479689 53456239 52604307 52102947 [9] 51738313 51063413 Smallest eigenvalues: [1] 0.28076112 0.22395012 0.22355702 0.21288323 0.15382624 0.03527388 [7] -0.13569635 -0.42121597 -0.59959270 -5.43688229 Largest eigenvalues: [1] 66269055 60853321 57240954 57222216 55622334 53782052 53247162 52414815 [9] 52221674 51469603 Smallest eigenvalues: [1] 0.27821730 0.19862006 0.19819928 0.13485490 0.07339599 -0.13500070 [7] -0.28586167 -0.40306937 -0.99114765 -1.90357430 Largest eigenvalues: [1] 64427041 60545555 57908962 56640833 55541517 53868869 52600700 52428444 [9] 52259322 51271379 Smallest eigenvalues: [1] 0.14068416 0.09121334 -0.02220390 -0.06431161 -0.21434716 -0.26956082 [7] -0.60929578 -1.21714060 -1.34764833 -1.48726618 Largest eigenvalues: [1] 66219887 60093450 57918014 55880813 54851939 53048982 52343802 51705149 [9] 51278967 50943662 Smallest eigenvalues: [1] 0.46875744 0.43413460 0.37802219 0.37219335 0.27783285 0.23231523 [7] 0.17196609 0.15705356 0.05810619 -0.18960095 Largest eigenvalues: [1] 65498045 61244736 58057107 56841727 55886177 54275404 53471337 52840763 [9] 52377361 52076991 Smallest eigenvalues: [1] 0.30065156 0.28012827 0.24835356 0.24701815 0.13455353 0.12902444 [7] 0.12729337 0.03730063 -0.78035003 -2.06242905 Largest eigenvalues: [1] 63508021 59788113 56961370 55547485 54800061 53196096 51960334 51743953 [9] 51524377 50954353 Smallest eigenvalues: [1] 0.29180419 0.27555984 0.24628449 0.22956510 0.20239016 0.18006428 [7] 0.11235817 0.09156804 -0.04272696 -5.83561262 Largest eigenvalues: [1] 63345500 60597202 57177419 55826058 54903460 53904659 51950536 51776875 [9] 51023165 50725203 Smallest eigenvalues: [1] 0.51898108 0.51190742 0.49346421 0.45000858 0.44590826 0.40245592 [7] 0.26890601 0.17226099 0.01089595 -0.01735811 Largest eigenvalues: [1] 65450490 60164291 57661918 56539077 54888937 53282850 52370456 52311259 [9] 51956350 51530022 Smallest eigenvalues: [1] 0.3058265 0.2989377 0.2661292 0.1974696 0.1739128 0.1180772 [7] 0.1179815 0.1047524 -0.0267872 -1.6321315 Largest eigenvalues: [1] 65868486 60961942 58268142 56642964 55654836 53985039 53045952 52600567 [9] 52474029 52195419 Smallest eigenvalues: [1] 0.29353112 0.26421254 0.24069880 0.21331116 0.14220334 0.13595383 [7] 0.08201721 -0.02624704 -1.37526050 -1.59779590 Largest eigenvalues: [1] 66324597 60409218 57749827 56802431 55062561 53910980 52636040 52490835 [9] 52366116 51812154 Smallest eigenvalues: [1] 0.3238356 0.2496848 0.2159286 0.1849888 0.1712111 0.1618124 [7] -0.1586719 -0.2831307 -0.3315398 -0.9900699 Largest eigenvalues: [1] 66198155 59954691 57371542 56871274 54652198 53037627 52860533 52456301 [9] 51650825 51589338 Smallest eigenvalues: [1] 0.28030410 0.23164345 0.16569131 0.14974950 0.07352849 -0.04166859 [7] -0.04956359 -0.38941178 -0.44200870 -0.53847499 Largest eigenvalues: [1] 63973941 60192981 57661301 55427909 54774789 53571659 51624257 51540728 [9] 51529087 50945402 Smallest eigenvalues: [1] 0.42430077 0.37351528 0.36916465 0.33133912 0.22922266 0.22083748 [7] 0.14874419 0.08477195 0.06912904 -0.16018647 Largest eigenvalues: [1] 64611572 60355340 57490467 56329037 55303275 53826454 52384693 52383575 [9] 52180474 51306512 Smallest eigenvalues: [1] 0.50171588 0.46687751 0.45267226 0.39188347 0.34826348 0.32061463 [7] 0.31232823 0.12021224 0.09798791 -0.13610437 Largest eigenvalues: [1] 64772381 59660125 57134377 55753136 54904515 53502594 51926088 51854032 [9] 51320852 50429195 Smallest eigenvalues: [1] 0.38531642 0.34042368 0.23556259 0.20364124 0.17823409 -0.04027302 [7] -0.04702928 -0.05179629 -0.07915303 -1.30598756 Largest eigenvalues: [1] 64284780 60462140 57269798 55685606 55474462 53795416 52884626 51973386 [9] 51892705 51644598 Smallest eigenvalues: [1] 0.4215706 0.4121962 0.3736347 0.3310153 0.2855394 0.2404173 [7] 0.2231569 0.2040454 0.1198840 -0.1835219 Largest eigenvalues: [1] 62627336 60759937 57180116 55433331 55365360 53677334 52273855 52176674 [9] 51348637 51157193 Smallest eigenvalues: [1] 0.4916969 0.4845972 0.4465242 0.4170723 0.3137256 0.3047418 [7] 0.2508813 0.2288577 0.2121150 -0.0672257 Largest eigenvalues: [1] 64235432 59578502 57258443 55447346 54628133 53072705 51695272 51402215 [9] 51306666 50653162 Smallest eigenvalues: [1] 0.3842260 0.3788244 0.3093946 0.2491844 0.2410652 0.1990001 [7] 0.1674324 -0.4061881 -0.6413068 -1.5163069 Largest eigenvalues: [1] 62641300 59213911 56765481 55065029 54852673 53142059 51877363 51746645 [9] 50950153 50613542 Smallest eigenvalues: [1] 0.60627072 0.59890510 0.54791023 0.44315392 0.38616628 0.35894897 [7] 0.26408105 0.22032031 0.12442103 -0.01300647 Largest eigenvalues: [1] 62810815 60171645 57072618 55771058 54808337 54115070 52447664 52203238 [9] 51068261 50844478 Smallest eigenvalues: [1] 0.28762597 0.27535851 0.27197888 0.24981564 0.22488444 0.15031248 [7] 0.02205735 -0.64347616 -0.90645808 -1.62884934 Largest eigenvalues: [1] 64811016 60261258 57815952 56154256 55134026 53305000 52437683 52147419 [9] 52080975 51590695 Smallest eigenvalues: [1] 0.43939866 0.38067198 0.30842538 0.29381131 0.25166320 0.14475968 [7] 0.10947469 0.08465491 -0.13708031 -1.16591922 Largest eigenvalues: [1] 65503611 60526228 57455322 56213183 55119027 53370079 52370235 52310403 [9] 51914938 51329582 Smallest eigenvalues: [1] 0.114355585 -0.004635647 -0.008848434 -0.159913929 -0.164976422 [6] -0.246746159 -0.336428536 -0.475751998 -0.693432413 -1.421451540 Largest eigenvalues: [1] 63031583 59916935 57118657 55164654 54726760 53107658 52182645 51350157 [9] 51156730 50926974 Smallest eigenvalues: [1] 0.45998872 0.41580810 0.39184842 0.33953891 0.33800481 0.33182469 [7] 0.27681551 0.25551057 0.21870749 -0.02127224 Largest eigenvalues: [1] 61723181 59132596 56775358 54843397 54310412 53083041 51443760 51092701 [9] 50398566 50087078 Smallest eigenvalues: [1] 0.4124039 0.3006569 0.2514511 0.2511782 0.2249729 0.2143911 [7] 0.1778251 0.1097218 -0.1895180 -0.2528983 Largest eigenvalues: [1] 64547811 60215328 57630273 56368777 54897717 53369060 52518681 51626623 [9] 51478585 50467374 Smallest eigenvalues: [1] 0.3579867 0.3538659 0.3065763 0.2799404 0.2398964 0.2322097 [7] 0.1360400 0.1043339 -0.4957799 -1.1937904 Largest eigenvalues: [1] 65307097 60270620 58356998 55588030 55510642 54424149 52858980 52693364 [9] 51851792 51550041 Smallest eigenvalues: [1] 0.4043210 0.3438279 0.3292763 0.3054532 0.2274421 0.1681585 [7] 0.1507635 0.1159263 -0.2828722 -0.4291482 Largest eigenvalues: [1] 63682380 59316459 57318296 55877214 54162732 52832241 51785944 51713349 [9] 51387607 50693001 Smallest eigenvalues: [1] 0.431394797 0.420844315 0.360916333 0.359955744 0.346086671 [6] 0.339005585 0.285401444 0.257995076 -0.002866243 -5.545150798 Largest eigenvalues: [1] 64216750 60061595 57117564 55598064 55108613 53333083 52120494 51716823 [9] 51626127 50854276 Smallest eigenvalues: [1] 0.4608246 0.3841535 0.3712152 0.3627737 0.2946871 0.2719265 [7] 0.2047346 0.1746251 0.1477002 -0.1509604 Largest eigenvalues: [1] 64045586 59697654 57065280 55967590 54704728 53200363 52078906 51823622 [9] 51804903 50923302 Smallest eigenvalues: [1] 0.522567142 0.508919326 0.412642972 0.352535295 0.307459818 [6] 0.302199698 0.158631452 0.134830209 0.024603845 -0.002993484 Largest eigenvalues: [1] 63177302 59624004 57131831 54773680 54626686 53134592 51864442 51348919 [9] 50898124 50539322 Smallest eigenvalues: [1] 0.51385050 0.45614854 0.42400424 0.35775865 0.33238024 0.28848757 [7] 0.24921755 0.16494337 0.02533496 -0.02961978 Largest eigenvalues: [1] 61446744 59820695 56948255 56035796 54095329 53944818 52733495 51624963 [9] 50741235 50665946 Smallest eigenvalues: [1] 0.46139118 0.44187490 0.39909965 0.33792925 0.31125959 0.29159161 [7] 0.27961396 0.17456575 0.14171066 -0.03839334 Largest eigenvalues: [1] 63714964 60702691 57312911 55907357 55824463 54108635 52535897 52011540 [9] 51875612 51479550 Smallest eigenvalues: [1] 0.42639968 0.39559155 0.36525013 0.34761243 0.34320671 0.28718473 [7] 0.26210578 0.21108925 0.05909535 -0.14595074 Largest eigenvalues: [1] 61834668 60856656 57519513 55647639 55020232 53877479 52142949 52131096 [9] 51248404 50990330 Smallest eigenvalues: [1] 0.30001491 0.29098047 0.26735308 0.20674120 0.16650157 0.12895381 [7] 0.08717612 -0.13805674 -0.42287786 -0.51276924 Largest eigenvalues: [1] 64617957 61378016 58295062 56594013 55839873 54005981 53775110 52832017 [9] 52238143 52083503 Smallest eigenvalues: [1] 0.4068207 0.4065248 0.3910243 0.3167281 0.2799650 0.2734857 [7] 0.2637625 0.2035177 -0.1255357 -4.0310711 Largest eigenvalues: [1] 64923755 60501512 57783306 56311142 55204456 53720725 52398973 52116895 [9] 52065385 51204325 Smallest eigenvalues: [1] 0.284458278 0.239570607 0.161864226 0.078653164 0.001354026 [6] -0.049783775 -0.107340000 -0.436127485 -0.590370738 -1.137575036 Largest eigenvalues: [1] 64891547 59770522 56935810 55457870 54649439 52996751 51960321 51644092 [9] 51297891 51122953 Smallest eigenvalues: [1] 0.3988811 0.3785343 0.3597117 0.3264402 0.3187563 0.3079406 [7] 0.2994325 0.1886132 0.1358960 -0.1118437 Largest eigenvalues: [1] 65289964 60791535 57433230 57124862 55243598 53653674 52871165 52665504 [9] 52329115 51409997 Smallest eigenvalues: [1] 0.42503823 0.39471310 0.26896249 0.23419675 0.23267573 0.19209878 [7] 0.18739692 -0.06811077 -0.54508634 -0.63416543 Largest eigenvalues: [1] 65320022 61025858 57394836 56222003 56006665 54116520 53056581 52540694 [9] 52208895 51664922 Smallest eigenvalues: [1] 0.5547804 0.4796298 0.4590903 0.4184093 0.3740510 0.3720161 [7] 0.3422207 0.3344018 0.2337584 -0.2264861 Largest eigenvalues: [1] 64118028 60212374 57337982 56028139 55373081 53506169 52063641 51965326 [9] 51773277 50799994 Smallest eigenvalues: [1] 0.29195785 0.26514031 0.22143992 0.21376256 0.16918389 0.15121911 [7] 0.12781814 0.05062987 -0.04063535 -0.26847746 Largest eigenvalues: [1] 62134203 58916993 56411820 54813421 54712013 53001419 51976627 51491648 [9] 50715303 50466484 Smallest eigenvalues: [1] 0.57420020 0.53871151 0.48216025 0.44775400 0.39620996 0.39488092 [7] 0.36739665 0.22070880 0.13224398 -0.06623388 Largest eigenvalues: [1] 63968624 60037365 56660136 55413056 55287549 53582239 52220309 51450455 [9] 51410823 50580619 Smallest eigenvalues: [1] 0.352742067 0.337433782 0.334528432 0.270141273 0.265758769 [6] 0.173941368 0.162504619 0.062101215 0.006925509 -0.129423609 Largest eigenvalues: [1] 64924472 59172526 56684532 56374077 54581068 53022179 52416933 51606833 [9] 50762362 50190823 Smallest eigenvalues: [1] 0.397795416 0.375662603 0.335943325 0.311856821 0.294155796 [6] 0.204684635 0.003725602 -0.216922536 -0.242593855 -2.926670356 Largest eigenvalues: [1] 65461585 60376823 57493288 56042344 55495960 53954256 52660679 52163290 [9] 51972204 51782551 Smallest eigenvalues: [1] 0.18194292 0.08483852 -0.06535354 -0.23098375 -0.23570552 -0.29365374 [7] -0.43288915 -0.71670623 -0.83823223 -4.91196316 Largest eigenvalues: [1] 62451671 59615497 56787975 55366325 54455170 53447420 52074444 51802714 [9] 51036027 50681459 Smallest eigenvalues: [1] 0.637143917 0.538830483 0.513684301 0.504624488 0.431139853 [6] 0.386743562 0.303686175 0.217925661 0.156696251 -0.001484799 Largest eigenvalues: [1] 65111852 60550941 57706261 56389305 55355203 53864406 52454220 52406028 [9] 52019443 51352038 Smallest eigenvalues: [1] 0.4381370 0.4163145 0.3968833 0.3435968 0.2781574 0.2569211 [7] 0.1466814 0.1412468 0.1271378 -1.8012059 Largest eigenvalues: [1] 63956777 60373091 57520828 55380189 55318216 53820383 52203252 52113608 [9] 51522971 51319108 Smallest eigenvalues: [1] 0.4074957 0.3736822 0.3610401 0.3152661 0.2545363 0.2487171 [7] 0.1374125 0.1346574 -0.3316199 -0.4561040 Largest eigenvalues: [1] 63134456 60483048 56862999 55826770 54949694 53260382 52170498 51709374 [9] 51536848 50733833 Smallest eigenvalues: [1] 0.3730152 0.3535112 0.3378832 0.3305521 0.2481641 0.2221549 [7] 0.1935049 0.1100101 -0.1051907 -1.9676151 Largest eigenvalues: [1] 61936147 59599615 56855775 54932905 54400927 53029978 51361980 51207151 [9] 50618151 50410146 Smallest eigenvalues: [1] 0.46423913 0.40073847 0.36553243 0.34260564 0.32537861 0.29811718 [7] 0.28135759 0.18887851 0.12339765 -0.04777045 Largest eigenvalues: [1] 64927043 59830651 57435423 56049643 54706435 53080973 52191417 51846698 [9] 51758212 51008885 Smallest eigenvalues: [1] 0.53378569 0.52429601 0.48888533 0.48028643 0.44036744 0.33179848 [7] 0.18613807 0.11911690 0.06998202 -0.11580793 Largest eigenvalues: [1] 63563802 60240938 57434281 55583602 55165952 53637103 52165471 51917817 [9] 51678109 51046726 Smallest eigenvalues: [1] 0.4625514 0.4098466 0.3950050 0.3897157 0.3592403 0.1428243 [7] 0.1260283 0.1138990 -0.1988930 -1.3626917 Largest eigenvalues: [1] 64519744 59214123 56732450 54844362 54837469 53120083 52147075 51286113 [9] 51212950 50596867 Smallest eigenvalues: [1] 0.44985555 0.43340665 0.39665318 0.37379911 0.29793721 0.17104380 [7] 0.16079471 0.10643018 0.06518246 -1.59781987 Largest eigenvalues: [1] 64446842 60147472 56881250 55975115 55313850 53315808 52367494 52052142 [9] 51597967 51215915 Smallest eigenvalues: [1] 0.269956889 0.168703941 0.128518350 0.045044792 0.039120644 [6] 0.003191129 -0.116530282 -0.330270907 -0.590093810 -0.851078350 Largest eigenvalues: [1] 64240755 60878508 57548537 55651574 55272276 53572096 52107573 51850581 [9] 51539419 51213731 Smallest eigenvalues: [1] 0.41871591 0.38195318 0.35698294 0.32602633 0.29134595 0.24158548 [7] 0.22386232 0.19775791 -0.05521472 -2.23561446 Largest eigenvalues: [1] 63191346 60076232 57326240 55869687 54709059 53356190 52177186 51715577 [9] 51652003 51200595 Smallest eigenvalues: [1] 0.39243812 0.37778438 0.29793035 0.25610061 0.22433754 0.22185230 [7] 0.01741347 -0.03202508 -0.08575769 -5.24342707 Largest eigenvalues: [1] 63363168 59695982 56724347 55117036 54980511 52899753 51465013 51446686 [9] 51224826 50449030 Smallest eigenvalues: [1] 0.49175672 0.40112003 0.36323426 0.29570560 0.27596625 0.23047658 [7] 0.19690478 0.17238320 0.04136418 -0.98022697 Largest eigenvalues: [1] 64944767 59798967 57647056 55922501 54627372 53456253 52215664 51699038 [9] 51483015 50796357 Smallest eigenvalues: [1] 0.35680785 0.33378388 0.25902892 0.23487622 0.23211194 0.21514133 [7] 0.16171935 0.09826078 -0.22083617 -0.80487036 Largest eigenvalues: [1] 62464811 60246060 57279819 55640718 55052970 53486891 52297287 52177961 [9] 51454446 50813074 Smallest eigenvalues: [1] 0.21809328 0.17766232 0.17054201 0.16118970 0.07402816 0.07078496 [7] -0.10071888 -0.28095705 -1.46274409 -1.55358804 Largest eigenvalues: [1] 63606322 59473104 56973373 54813005 54695710 53216161 51599122 51123121 [9] 50987209 50443197 Smallest eigenvalues: [1] 0.36202829 0.35079600 0.24234965 0.20275350 0.16940017 0.10203958 [7] 0.02006566 -0.04535303 -0.23270112 -3.57495525 Largest eigenvalues: [1] 64980942 59705304 56925347 56302661 54872859 53152064 52460402 52262021 [9] 51759935 51262943 Smallest eigenvalues: [1] 0.31840516 0.20177103 0.15939058 0.13932871 -0.02069221 -0.03142577 [7] -0.11038247 -0.22070981 -1.09169964 -2.05762710 Largest eigenvalues: [1] 65888465 59784264 57060916 56618711 54568943 53057364 52664335 52188248 [9] 51414871 51391962 Smallest eigenvalues: [1] 0.46273726 0.36205484 0.22338922 0.19390587 0.18597176 0.15130079 [7] 0.11961507 -0.06721433 -0.36030320 -1.67870313 Largest eigenvalues: [1] 63818053 59417184 56343085 55084596 54632459 52934193 51713555 51286134 [9] 51128063 50371408 Smallest eigenvalues: [1] 0.416692834 0.364815114 0.240203085 0.191391103 0.118741762 [6] 0.063732697 0.004530815 -0.015170372 -0.077513604 -0.632270320 Largest eigenvalues: [1] 63359283 59430167 56752892 54791207 54516702 53005746 51683104 51252831 [9] 51073236 50643275 Smallest eigenvalues: [1] 0.48314931 0.39699723 0.38656114 0.36852205 0.31081783 0.29669520 [7] 0.28052225 -0.03951312 -0.04482099 -2.32612212 Largest eigenvalues: [1] 64308431 60612838 56984282 55689644 55565238 53620448 52189609 51984478 [9] 51817341 51126469 Smallest eigenvalues: [1] 0.255893637 0.255496711 0.222270377 0.034376715 -0.009442275 [6] -0.140263386 -0.433526406 -0.723518822 -1.077376241 -1.454730069 Largest eigenvalues: [1] 65895119 59530534 56850827 56252136 54400012 52998113 52314320 51750849 [9] 51363202 50943201 Smallest eigenvalues: [1] 0.31448537 0.31089953 0.24469739 0.18495554 0.12219551 0.02676088 [7] -0.30076956 -0.85848804 -1.58658861 -1.85757015 Largest eigenvalues: [1] 66457410 60426487 58459040 56947635 55141540 53193619 52890811 52219571 [9] 51797093 51481297 Smallest eigenvalues: [1] 0.39882907 0.36988662 0.34962567 0.34640457 0.32618712 0.30297334 [7] 0.25496569 0.19267631 0.18536449 -0.01011802 Largest eigenvalues: [1] 64526635 60723027 58150356 55814539 55688479 54371589 52435290 52057851 [9] 51923014 51186804 Smallest eigenvalues: [1] 0.10331314 0.09411901 -0.05479243 -0.10662159 -0.12199998 -0.31617443 [7] -0.32968892 -0.38409834 -0.74752024 -1.24051087 Largest eigenvalues: [1] 66153630 60398999 57972392 57252778 54850598 53367460 53112243 52797847 [9] 51888651 51518140 Smallest eigenvalues: [1] 0.38241794 0.35423516 0.33731761 0.30472545 0.30069783 0.20922189 [7] 0.10869108 -0.08314438 -0.15020855 -1.32186369 Largest eigenvalues: [1] 63638549 60277715 57401201 56276972 55013923 53339215 52519683 52066540 [9] 51829671 51332714 Smallest eigenvalues: [1] 0.49799915 0.44928913 0.44581410 0.41499356 0.33121849 0.27941617 [7] 0.23813911 0.20386552 0.05577655 -0.06201129 Largest eigenvalues: [1] 66259222 60049795 57766631 57093564 54859826 53569324 53193417 51933343 [9] 51746823 50986621 Smallest eigenvalues: [1] 0.38344711 0.33708112 0.33666557 0.27678748 0.26551530 0.21773843 [7] 0.20135358 0.05200353 -0.02940766 -0.41362848 Largest eigenvalues: [1] 64948306 60119483 57028828 56571925 54897534 53300319 52546207 52486640 [9] 51982007 51535200 Smallest eigenvalues: [1] 0.20179198 0.19685450 0.18101021 0.13777247 -0.03113217 -0.23597599 [7] -0.51116234 -1.00738849 -1.38620527 -1.51914677 Largest eigenvalues: [1] 65295663 60301423 57699408 56512384 54765000 53432575 52643772 52164124 [9] 51620770 51354129 Smallest eigenvalues: [1] 0.5354128 0.5036787 0.4995127 0.4318419 0.3589464 0.3519149 [7] 0.1788749 0.1578994 0.1156847 -0.2320354 Largest eigenvalues: [1] 64203162 59266658 56591366 55558831 54351875 52286714 51617249 51118063 [9] 51098441 50270800 Smallest eigenvalues: [1] 0.5313828 0.4991924 0.4406278 0.4039710 0.3529575 0.2939176 [7] 0.2645401 0.0338451 -0.3570618 -4.0684087 Largest eigenvalues: [1] 65487650 59825436 56828623 56436953 54550995 52546916 52259940 51470609 [9] 51418905 50639626 Smallest eigenvalues: [1] 0.21519902 0.15399032 0.10489712 -0.02301297 -0.05059752 -0.12224821 [7] -0.13170798 -0.77349678 -1.06153459 -1.88610184 Largest eigenvalues: [1] 66332553 60411304 57380203 57188388 54998345 53277662 53126460 52821210 [9] 51854920 51802795 Smallest eigenvalues: [1] 0.3746854 0.3275190 0.3178091 0.2250618 0.1771928 0.1572432 [7] 0.1093535 -0.1651058 -0.3501318 -0.9610655 Largest eigenvalues: [1] 64128097 59864698 56886956 55135106 54682539 53092378 51768006 51661962 [9] 51289161 51044492 Smallest eigenvalues: [1] 0.39885408 0.37649569 0.36196943 0.28037889 0.26043615 0.20837866 [7] 0.18578268 0.05003467 0.04163188 -1.45146658 Largest eigenvalues: [1] 64616076 60324247 56857436 56039624 55398832 53639036 51908081 51784943 [9] 51716899 50874203 Smallest eigenvalues: [1] 0.376280719 0.307968800 0.270685000 0.171366752 0.160953665 [6] 0.108070901 0.072151884 0.020834484 0.002786508 -1.987170405 Largest eigenvalues: [1] 63983121 60170079 57266457 55482300 55072229 53896826 52008947 51582188 [9] 51111977 50789597 Smallest eigenvalues: [1] 0.24094082 0.16113435 0.07831721 0.04222213 -0.03530437 -0.04026649 [7] -0.07239794 -0.12900239 -0.35897698 -0.82937782 Largest eigenvalues: [1] 66149144 60763201 58175050 56352719 55258555 53761435 52584161 52274386 [9] 51911871 51441598 Smallest eigenvalues: [1] 0.45072375 0.44930617 0.42707307 0.33227141 0.27608788 0.25176901 [7] 0.05342844 0.04366002 -0.05559960 -2.35706928 Largest eigenvalues: [1] 65316235 60092150 57101572 56471027 55207253 53717852 52384138 52138233 [9] 51965542 51267309 Smallest eigenvalues: [1] 0.46426041 0.43155913 0.39258429 0.37299448 0.36460008 0.30936865 [7] 0.28669020 0.17339815 0.13165021 -0.07712913 Largest eigenvalues: [1] 64447110 59828114 56546209 55860706 54700493 53110423 51915110 51875719 [9] 51444778 50799338 Smallest eigenvalues: [1] 0.32180708 0.30948438 0.28262209 0.22483686 0.19245215 -0.05613209 [7] -0.09511850 -0.17865712 -0.56782904 -2.91985104 Largest eigenvalues: [1] 65494462 60770984 57409712 55881813 55367889 53448261 51999398 51898515 [9] 51631644 51150789 Smallest eigenvalues: [1] 0.4215955 0.3830922 0.3608919 0.3411174 0.3170894 0.3020075 [7] 0.2732070 0.2585327 0.2136132 -0.0904391 Largest eigenvalues: [1] 64170768 60128314 57281690 55445678 55411005 53774799 51903407 51567664 [9] 51325856 50429510 Smallest eigenvalues: [1] 0.41027462 0.34991550 0.33201372 0.28719242 0.23969036 0.17322448 [7] 0.08775426 -0.03237588 -0.07105975 -0.25147471 Largest eigenvalues: [1] 65732569 60345982 57423459 56437619 55366065 53937114 52478352 51988905 [9] 51832965 50614801 Smallest eigenvalues: [1] 0.30067100 0.25692767 0.17869120 0.14802603 0.13641694 0.11662896 [7] 0.02789947 -0.76134603 -0.96719689 -1.04722745 Largest eigenvalues: [1] 65316550 59817144 57643068 55937888 55004182 53727770 52529449 52012799 [9] 52006955 51646610 Smallest eigenvalues: [1] 0.4718204 0.3725984 0.3688057 0.3619263 0.3417680 0.2895856 [7] 0.2668145 0.2288515 0.1696846 -0.0419761 Largest eigenvalues: [1] 65430252 60186549 57902544 56708130 54799905 53182629 52727318 51983730 [9] 51787673 51207025 Smallest eigenvalues: [1] 0.16163110 0.10226022 0.07016115 0.01021784 -0.01938875 -0.15511759 [7] -0.20201882 -0.28235975 -0.83649657 -1.41196324 Largest eigenvalues: [1] 63589651 60474192 57779315 55120910 54979755 53748396 51942201 51879761 [9] 51166026 50946444 Smallest eigenvalues: [1] 0.43652355 0.42026365 0.39998526 0.39097169 0.31227609 0.27948034 [7] 0.26460260 0.19855633 0.06991435 -0.03640425 Largest eigenvalues: [1] 65120762 60300018 58019377 55737396 55382700 53653209 52427660 52078487 [9] 51952404 51482757 Smallest eigenvalues: [1] 0.365817485 0.253268375 0.245423941 0.174328665 0.139668327 [6] 0.035727625 0.009370155 -0.049486401 -0.160140997 -0.538150752 Largest eigenvalues: [1] 66174484 60557071 57955294 56600992 54988746 53595055 52667171 52608848 [9] 51925991 51758373 Smallest eigenvalues: [1] 0.37421177 0.37286524 0.36146869 0.27574148 0.24273759 0.16643424 [7] 0.16437171 0.10164275 0.03150259 -0.41895148 Largest eigenvalues: [1] 66555193 61015849 57875134 57278162 56051532 54362047 53313086 53219235 [9] 52404952 52003054 Smallest eigenvalues: [1] 0.42999126 0.39400374 0.32997726 0.30741752 0.29716140 0.24433894 [7] 0.17649854 0.13992982 0.09912456 -0.68463267 Largest eigenvalues: [1] 65480565 59535569 57271541 56789497 54602543 53325300 52731957 51867612 [9] 51482190 50987039 Smallest eigenvalues: [1] 0.56084345 0.49043668 0.48142433 0.41932512 0.36428754 0.26911925 [7] 0.25576346 0.21769094 -0.04888047 -3.80561657 Largest eigenvalues: [1] 64832032 60105255 57402449 56089024 55128969 53440947 52201383 51955887 [9] 51932038 50968290 Smallest eigenvalues: [1] 0.43845323 0.42975066 0.39989268 0.38468818 0.34356178 0.22839252 [7] 0.20607929 0.08697602 0.07640505 -5.50472005 Largest eigenvalues: [1] 63794133 60633576 57902608 56019595 55698928 54404253 52707114 52662581 [9] 51882010 51585602 Smallest eigenvalues: [1] 0.4624995 0.3755231 0.3703261 0.3592630 0.3440499 0.3248258 [7] 0.2752419 0.2409431 0.1158476 -0.7668570 Largest eigenvalues: [1] 64221205 60318583 57709171 55619533 55531237 54156202 52544302 52282630 [9] 51618503 51105844 Smallest eigenvalues: [1] 0.45448890 0.42029267 0.39848239 0.29456969 0.20575790 0.15607533 [7] 0.13126174 0.08395056 0.01181098 -1.42544809 Largest eigenvalues: [1] 63006324 60062214 56941706 55361428 54650641 53614751 51778485 51688758 [9] 50917214 50820470 Smallest eigenvalues: [1] 0.51249200 0.45822914 0.40281296 0.39870987 0.36076613 0.35794471 [7] 0.34564490 0.14319905 0.10718640 -0.07663943 Largest eigenvalues: [1] 65176484 61281441 57663689 56588514 56289128 54564393 53434200 52573449 [9] 52280838 51819554 Smallest eigenvalues: [1] 0.42829448 0.41753283 0.38087157 0.36199592 0.33765541 0.29052853 [7] 0.26068976 0.01377166 -0.20060367 -0.87768029 Largest eigenvalues: [1] 64144509 60444007 57639448 56127475 55400155 53856133 52361648 52171013 [9] 51806209 51182076 Smallest eigenvalues: [1] 0.308025995 0.206761619 0.203216503 0.186286851 0.113052555 [6] 0.076307466 0.006604131 -0.181839664 -0.291542576 -21.811795757 Largest eigenvalues: [1] 65871585 59810854 57759104 56107180 54956920 53792945 52488773 52300045 [9] 51995030 51435775 Smallest eigenvalues: [1] 0.4434678 0.3933192 0.3548960 0.2414716 0.2047585 0.1569187 [7] 0.1048188 -0.1947996 -0.3046727 -0.7510127 Largest eigenvalues: [1] 65753249 60422185 57651871 56907886 54849631 52897648 52848862 52433092 [9] 51726218 51532197 Smallest eigenvalues: [1] 0.5779033 0.5601017 0.4521349 0.4358426 0.3057825 0.2802577 [7] 0.2698895 0.2403582 -0.2231736 -0.2502104 Largest eigenvalues: [1] 65495792 60740763 57667770 56644212 55475239 53738347 52781202 52599364 [9] 51953171 51400325 Smallest eigenvalues: [1] 0.39276884 0.35729847 0.34816612 0.30998125 0.27557320 0.22853905 [7] 0.14775489 0.11577115 0.08818914 -3.10563628 Largest eigenvalues: [1] 63716726 59893907 57517720 55575251 54941132 53477474 51870779 51750287 [9] 51570194 50904700 Smallest eigenvalues: [1] 0.34195849 0.24133060 0.21694165 0.19503112 0.10672832 0.02787603 [7] -0.10118311 -0.21591306 -0.67050739 -1.28075896 Largest eigenvalues: [1] 65171880 60592546 57871300 56212817 55299538 53882689 52342246 52080007 [9] 51797614 51116417 Smallest eigenvalues: [1] 0.40662046 0.38647370 0.33170701 0.33162997 0.30318397 0.22392881 [7] 0.20000899 0.08068127 0.05883845 -0.39544448 Largest eigenvalues: [1] 65145845 60237238 57688219 56369463 55097132 53466215 53217061 52567880 [9] 51852069 51605759 Smallest eigenvalues: [1] 0.4959148 0.4117465 0.3925934 0.3892781 0.2854885 0.2722464 [7] 0.1915873 0.1864380 -0.1529678 -0.1771534 Largest eigenvalues: [1] 64485225 60417703 57274239 55921359 55124532 53399009 51904648 51825347 [9] 51797969 50898568 Smallest eigenvalues: [1] 0.6139020 0.5804288 0.5208425 0.5147206 0.4563544 0.3409322 [7] 0.2962343 0.2506831 0.2447080 -0.6830423 Largest eigenvalues: [1] 64533801 59843461 57051366 55700044 55026546 53588815 52152621 51836739 [9] 51632093 50798520 Smallest eigenvalues: [1] 0.38089860 0.36074590 0.30022144 0.28137132 0.27443576 0.18334242 [7] 0.17583582 0.16014067 0.13095374 -0.07063696 Largest eigenvalues: [1] 65799156 60657443 58331932 56359963 55470306 53900753 52569202 52415561 [9] 52330166 51790033 Smallest eigenvalues: [1] 0.3616097 0.3286228 0.3181877 0.3007739 0.2525987 0.2037673 [7] 0.1977944 0.1026287 -0.5029078 -3.1767412 Largest eigenvalues: [1] 65431182 59830413 57109716 56758413 54850195 52841188 52646603 52424251 [9] 51838168 51478743 Smallest eigenvalues: [1] 0.4471657 0.4327267 0.3227875 0.2972009 0.2606796 0.2331267 [7] 0.2251395 0.1442445 0.1034761 -0.6873129 Largest eigenvalues: [1] 61983548 59479073 56151308 54809728 54805144 53062109 51964424 51953472 [9] 50874982 50679640 Smallest eigenvalues: [1] 0.38179778 0.29670344 0.26829412 0.21802983 0.15912084 0.07662484 [7] -0.02784264 -0.12456120 -0.57823318 -0.78838126 Largest eigenvalues: [1] 65278982 61455893 58255280 57242291 55362965 53669651 53381839 52675368 [9] 52285646 51440846 Smallest eigenvalues: [1] 0.4701700 0.4498259 0.4130603 0.3694225 0.3263399 0.2567731 [7] 0.2288796 0.1915548 0.1630194 -0.6071124 Largest eigenvalues: [1] 62909426 59399446 56885421 54818310 54707668 53234116 51921570 51200939 [9] 50850083 50466636 Smallest eigenvalues: [1] 0.24025026 0.23284841 0.21419365 0.18911631 0.13054411 0.01454168 [7] -0.13678224 -0.19889759 -0.32694998 -1.22316880 Largest eigenvalues: [1] 64079599 59956866 57537982 55733631 54838047 53561966 51793740 51766962 [9] 51707695 50824179 Smallest eigenvalues: [1] 0.41558011 0.37971485 0.23767634 0.07841913 0.07488108 0.04916357 [7] -0.02906305 -0.08548154 -0.30606844 -2.11074582 Largest eigenvalues: [1] 63827165 60265287 57422937 55607886 55498858 53761653 52625950 51818676 [9] 51735138 51284014 Smallest eigenvalues: [1] 0.206281423 0.186940906 0.184822632 0.164652584 0.156494196 [6] 0.147955263 0.058202108 -0.007530551 -0.279125147 -0.352152164 Largest eigenvalues: [1] 63593910 59314045 56383037 55532901 54778798 53085053 51773136 51495649 [9] 50830776 50198942 Smallest eigenvalues: [1] 0.47735267 0.38922739 0.38311668 0.37983251 0.34968656 0.28385840 [7] 0.19040160 0.16099142 -0.08795911 -0.44315592 Largest eigenvalues: [1] 64537503 60757877 57781254 55942695 55358972 53760801 52792436 52172156 [9] 52105396 51884014 Smallest eigenvalues: [1] 0.36681956 0.33198055 0.33129214 0.32368534 0.24858332 0.21126190 [7] 0.20711594 0.19122726 -0.08568089 -1.58808715 Largest eigenvalues: [1] 64961779 60717350 58030721 55773400 55687200 54230392 52235425 52002581 [9] 51934151 51336714 Smallest eigenvalues: [1] 0.23151387 0.16549267 0.15482562 0.08237195 0.03596431 -0.06702173 [7] -0.37048212 -0.38894702 -1.34481634 -1.70611943 Largest eigenvalues: [1] 64597605 59563841 56882993 55986066 54643173 53036149 52238462 51993337 [9] 51601370 51022888 Smallest eigenvalues: [1] 0.43433141 0.41408769 0.29875081 0.29814096 0.23928795 0.23167230 [7] 0.18174241 0.16648653 -0.06203392 -1.23436719 Largest eigenvalues: [1] 64440736 60560603 57212631 56259889 55598767 53962329 52232686 52090257 [9] 51934081 51051546 Smallest eigenvalues: [1] 0.3042010065 0.2028350908 0.1740175163 0.1612815640 0.1369131970 [6] 0.0001836193 -0.0677540862 -0.2490146759 -0.4799055444 -1.0698131028 Largest eigenvalues: [1] 64993726 60428037 57374522 56547352 54849189 53550509 52484664 52412518 [9] 51789101 51646571 Smallest eigenvalues: [1] 0.27330582 0.23265980 0.20692219 0.12274527 0.07847066 -0.19807447 [7] -0.25987368 -0.30761489 -0.51152650 -1.38724883 Largest eigenvalues: [1] 64121480 59235452 57025321 55467561 54263155 53170667 51844510 51643615 [9] 51464198 50938521 Smallest eigenvalues: [1] 0.22199018 0.21752864 0.17762979 0.16634727 0.12907103 -0.04799962 [7] -0.09461652 -0.13949955 -0.17537962 -1.50600064 Largest eigenvalues: [1] 64803510 60825577 57752098 56073264 55661494 54323780 52679780 52602585 [9] 52017695 51827638 Smallest eigenvalues: [1] 0.529283596 0.519283179 0.490264063 0.434428678 0.422483895 [6] 0.342396511 0.313743248 0.261834375 0.078963518 -0.009048804 Largest eigenvalues: [1] 62319757 59863546 56791761 54995234 54701300 53307653 51698147 51593220 [9] 50666779 50490874 Smallest eigenvalues: [1] 0.37679206 0.36717120 0.32350101 0.31689581 0.29871551 [6] 0.25686390 0.25632731 -0.01333862 -0.06789774 -10.12314265 Largest eigenvalues: [1] 64411516 59932779 57280277 55653920 55068576 53505755 52217133 51758458 [9] 51549442 50961953 Smallest eigenvalues: [1] 0.33992151 0.33773102 0.33052832 0.24759088 0.17865735 0.16725219 [7] 0.13009824 0.12557393 0.06940252 -0.05708416 Largest eigenvalues: [1] 62687074 60046225 57096819 55454949 55099931 53311649 52429309 52254927 [9] 51307310 51079840 Smallest eigenvalues: [1] 0.3734285 0.3578477 0.3031081 0.2387319 0.2306287 0.2039266 [7] 0.1485060 -0.1171986 -0.3440188 -1.6214314 Largest eigenvalues: [1] 65486043 60113924 57079185 56666044 55185757 53628727 52574929 52359392 [9] 52009107 51585582 Smallest eigenvalues: [1] 0.49486609 0.47791572 0.45526315 0.38861004 0.26367715 0.24308695 [7] 0.16907081 0.12584112 0.02471961 -0.01684104 Largest eigenvalues: [1] 62945545 60794518 57637850 56261031 54882770 54402627 52808606 52517634 [9] 51566391 51069462 Smallest eigenvalues: [1] 0.40440121 0.33971828 0.32780829 0.26849468 0.18441321 0.14547299 [7] 0.03445263 -0.35447099 -0.44357899 -4.96304851 Largest eigenvalues: [1] 65527053 60207613 57375006 56259761 55115688 53212988 52481602 52032514 [9] 51617348 51241593 Smallest eigenvalues: [1] 0.2201364 0.1930468 0.1874791 -0.1227888 -0.1273022 -0.2719032 [7] -0.2880179 -0.3875469 -0.4994241 -1.0144298 Largest eigenvalues: [1] 65057256 61275334 57637187 56391357 56306501 54331565 53877199 52564757 [9] 52190753 51824437 Smallest eigenvalues: [1] 0.4518062 0.3811479 0.3427248 0.3200841 0.2817578 0.2711405 [7] 0.2704352 0.1788838 -0.2115723 -0.4633926 Largest eigenvalues: [1] 64165066 60755183 58081525 56166649 55246195 53722459 52005370 51939202 [9] 51843830 50931778 Smallest eigenvalues: [1] 0.25074725 0.20080264 0.10458999 0.08528284 0.07400013 0.01865420 [7] -0.02934871 -0.12047732 -0.15615536 -3.60260821 Largest eigenvalues: [1] 65005210 59847985 57578032 56482285 55144388 53920519 52943505 52327741 [9] 52276216 51892719 Smallest eigenvalues: [1] 0.45241489 0.44066831 0.35509133 0.32710229 0.31067170 0.25264288 [7] 0.18197227 -0.07615371 -0.23499493 -2.00386152 Largest eigenvalues: [1] 65575740 59738799 56726747 56287922 54373976 52617790 52310861 51390303 [9] 51134809 50635299 Smallest eigenvalues: [1] 0.4649903 0.4474241 0.4294076 0.3502424 0.3471955 0.2751184 [7] 0.2261942 0.1726147 0.1328097 -0.3506693 Largest eigenvalues: [1] 64730132 59805212 57428042 55376687 55297960 53809419 51715412 51587904 [9] 51486614 50723969 Smallest eigenvalues: [1] 0.53888156 0.45745730 0.39162100 0.36546596 0.32729226 0.24969499 [7] 0.22215482 0.09068120 0.03596904 -0.16543456 Largest eigenvalues: [1] 64285560 60171025 57302773 55878871 55708304 54134687 52378623 52314474 [9] 51809959 51710390 Smallest eigenvalues: [1] 0.30722470 0.26472251 0.20720361 0.17229991 0.08035100 [6] 0.06282899 -0.13471021 -0.24564233 -0.84712211 -19.78156914 Largest eigenvalues: [1] 63373225 60139956 57612673 55372237 55048578 53712521 52590324 51754877 [9] 51208079 50960488 Smallest eigenvalues: [1] 0.45094110 0.43401422 0.40202821 0.37104549 0.28886965 0.28196224 [7] 0.19893324 0.14721583 0.05688805 -0.63896127 Largest eigenvalues: [1] 65752212 59703940 57233182 56738997 54613908 53095906 52639259 52129237 [9] 51608316 51128829 Smallest eigenvalues: [1] 0.538572136 0.515976379 0.469945128 0.430167322 0.366027608 [6] 0.317178642 0.142653151 0.084944324 0.041586483 -0.008741183 Largest eigenvalues: [1] 64580174 60202693 57517011 55442585 55231930 53796502 52481055 52135800 [9] 51571013 51344194 Smallest eigenvalues: [1] 0.36606927 0.35714062 0.29389149 0.23647287 0.21072451 0.18678329 [7] 0.09481632 -0.06747963 -0.23553946 -1.14394497 Largest eigenvalues: [1] 64461719 59735997 56821507 56081272 54957468 53379231 52166592 52112757 [9] 51622284 51044612 Smallest eigenvalues: [1] 0.46249793 0.43717746 0.40706058 0.30474117 0.27275971 0.26185734 [7] 0.22445666 0.19572387 0.03786895 -1.21038559 Largest eigenvalues: [1] 63452371 59579523 57298204 55281584 54737329 53529528 52205879 51839523 [9] 51449580 51030156 Smallest eigenvalues: [1] 0.44583460 0.43792066 0.38713001 0.34232814 0.32319399 0.30532744 [7] 0.20429410 0.03224634 -0.10057823 -0.38382236 Largest eigenvalues: [1] 62820107 59663631 57056598 55572069 54853961 53197441 51612340 51509818 [9] 51435912 50413943 Smallest eigenvalues: [1] 0.48627473 0.48486213 0.44672818 0.33133222 0.29116410 0.24938516 [7] 0.17885290 0.15383709 0.03918108 -0.32173457 Largest eigenvalues: [1] 64044075 60455779 57302207 55913636 55661146 53944846 52678631 52321508 [9] 52078249 51483432 Smallest eigenvalues: [1] 0.5002047 0.4877379 0.4363611 0.3618692 0.2871384 0.2837144 [7] 0.2813088 0.2140507 -0.4797941 -0.9148599 Largest eigenvalues: [1] 63638083 59431396 56612639 55357256 54698638 52886140 52464489 51393630 [9] 51193909 50785635 Smallest eigenvalues: [1] 0.40686541 0.40339525 0.38322734 0.35472292 0.31792274 0.14749524 [7] 0.10558648 0.01705676 -0.01633554 -1.35660784 Largest eigenvalues: [1] 65858758 59719838 57339255 56055788 54743702 53212222 52241443 51955715 [9] 51846048 50763179 Smallest eigenvalues: [1] 0.43457226 0.39821612 0.39522916 0.33260903 0.30360549 0.27909684 [7] 0.09056232 0.07132009 -0.03331028 -0.15457582 Largest eigenvalues: [1] 64720423 59776526 57054000 55910283 55196154 53571753 51959316 51679796 [9] 51182446 50133327 Smallest eigenvalues: [1] 0.39260874 0.33435365 0.30692710 0.30182919 0.18902775 0.18174103 [7] 0.12612453 -0.01734765 -0.23787213 -1.24284197 Largest eigenvalues: [1] 63199803 60239464 57177048 55512057 54614668 53577085 51846545 51628947 [9] 51002896 50764446 Smallest eigenvalues: [1] 0.50145166 0.48650096 0.38400414 0.34200567 0.24375922 0.17251154 [7] 0.15953227 0.12035749 0.02524313 -0.77626865 Largest eigenvalues: [1] 62208651 59439404 56257202 54771859 54608922 52944998 51956172 51311175 [9] 50736905 50573517 Smallest eigenvalues: [1] 0.56872319 0.55253719 0.52510494 0.38457499 0.37944957 0.32946291 [7] 0.14578330 0.06764163 -0.02156755 -0.08872731 Largest eigenvalues: [1] 65497041 59685859 56909482 56792229 54671221 52837401 52798023 51602580 [9] 51214826 50555018 Smallest eigenvalues: [1] 0.45195098 0.33012824 0.32135000 0.24388514 0.20623307 0.06529955 [7] 0.04877222 -0.10096606 -0.42589629 -1.64607516 Largest eigenvalues: [1] 65073717 61262736 57555699 57004377 56014142 54035441 53623577 52585375 [9] 52541897 52021777 Smallest eigenvalues: [1] 0.36025654 0.26378349 0.21604217 0.21202484 0.10607797 0.08405659 [7] -0.07731024 -0.60904395 -0.67791686 -1.48559029 Largest eigenvalues: [1] 66083921 59610777 56943449 56626455 54251470 52778248 52755492 51933327 [9] 51177987 51122943 Smallest eigenvalues: [1] 0.49283605 0.48350648 0.37031427 0.34334530 0.34313966 0.24508915 [7] 0.22922330 0.02242962 -0.07046072 -0.09086812 Largest eigenvalues: [1] 64279055 59176574 56610448 55358905 54514337 52907435 51709124 51318291 [9] 50987734 50327076 Smallest eigenvalues: [1] 0.59273904 0.45494010 0.43849772 0.42920931 0.31278377 0.31257013 [7] 0.26006999 0.15085641 -0.01491967 -0.18238095 Largest eigenvalues: [1] 63841274 59410326 56573212 55552144 54267231 52710932 51581156 51387589 [9] 50842338 49968115 Smallest eigenvalues: [1] 0.32548894 0.28259775 0.26385580 0.25170916 0.18768399 0.17611072 [7] 0.13279673 0.05586095 0.01349406 -0.62425734 Largest eigenvalues: [1] 65491052 60679702 58281654 56793204 55238631 54039033 52738094 52398507 [9] 52174768 51299871 Smallest eigenvalues: [1] 0.26999467 0.24067227 0.18690195 0.17381151 0.15689405 0.06549953 [7] 0.02325153 -0.01391736 -0.02708347 -1.39803260 Largest eigenvalues: [1] 65084599 59667335 56795187 55302314 54541184 52989902 51781746 51415711 [9] 51288702 50928691 Smallest eigenvalues: [1] 0.481809313 0.463455723 0.380058870 0.303092990 0.297394438 [6] 0.296393546 0.260159155 0.245311660 0.001545766 -5.653291840 Largest eigenvalues: [1] 65444898 60920182 58162050 56492742 55877988 54191029 52776147 52371895 [9] 52288088 51327756 Smallest eigenvalues: [1] 0.42724661 0.36254226 0.26973931 0.24610441 0.18356294 0.17923246 [7] 0.11800548 0.09199347 -0.04562304 -2.16147899 Largest eigenvalues: [1] 64443860 59692638 56612346 55302251 54601411 53081073 51565075 51394645 [9] 51080771 50329756 Smallest eigenvalues: [1] 0.127079620 0.121829523 -0.009105345 -0.098734966 -0.175533379 [6] -0.252872943 -0.275911775 -0.311978659 -0.407907347 -2.161574917 Largest eigenvalues: [1] 65166770 60394479 57775083 55548521 55184248 53636282 52218048 51709664 [9] 51565684 51504031 Smallest eigenvalues: [1] 0.498621018 0.482464932 0.464719120 0.367635146 0.357574127 [6] 0.281352521 0.156715382 0.137070219 -0.002578572 -0.026560631 Largest eigenvalues: [1] 63739908 60064686 56938842 55368735 55233402 53695629 52270016 52120536 [9] 51489855 51181683 Smallest eigenvalues: [1] 0.4550115 0.4339077 0.4096776 0.4083677 0.2809894 0.2704890 [7] 0.2332062 0.1926729 0.1642633 -0.3350256 Largest eigenvalues: [1] 65597075 60361315 57620003 56372938 54974286 53558960 52533581 51877096 [9] 51684126 51062125 Smallest eigenvalues: [1] 0.59293228 0.58439590 0.46079415 0.45680111 0.32576455 0.30668977 [7] 0.26509910 0.22948079 0.08844987 -0.19775837 Largest eigenvalues: [1] 66080229 60433448 57848196 56491531 55229555 53883980 52610828 52405954 [9] 51883012 51441355 Smallest eigenvalues: [1] 0.37981832 0.36038541 0.35522910 0.32377308 0.27366214 0.22163999 [7] 0.17251062 0.13792477 -0.08273076 -0.55500850 Largest eigenvalues: [1] 65121254 60782164 58069287 56509829 55274120 53986842 52427337 52286661 [9] 52056309 51143008 Smallest eigenvalues: [1] 0.4922655 0.4512300 0.4361336 0.3612484 0.3577866 0.3213488 [7] 0.3003183 0.2121997 0.1652579 -0.2157578 Largest eigenvalues: [1] 64907340 59573935 56568121 56394720 54398209 52937925 52218787 51739831 [9] 51448563 50468316 Smallest eigenvalues: [1] 0.5408972 0.5211180 0.5062630 0.4059827 0.3587215 0.3547026 [7] 0.1936218 0.1909158 0.1808374 -0.1337813 Largest eigenvalues: [1] 63808887 60205071 56991351 55354761 55284676 53747266 52290576 52010319 [9] 51451656 51267976 Smallest eigenvalues: [1] 0.3447919987 0.3307802435 0.2989218221 0.2922549215 0.2223076358 [6] 0.1546549790 0.1139861743 0.0701401505 0.0005542438 -0.0658164069 Largest eigenvalues: [1] 62031393 60336994 57417077 55937013 55018472 54168102 52646816 52352086 [9] 51505789 51012184 Smallest eigenvalues: [1] 0.6018108 0.5702971 0.5446860 0.4811291 0.4214358 0.4008453 [7] 0.3032235 0.2026565 0.1251318 -0.6339919 Largest eigenvalues: [1] 64140185 60661946 57032731 55678399 55601213 53980704 52335225 52178298 [9] 51534697 51069349 Smallest eigenvalues: [1] 0.4444439 0.4202566 0.3568545 0.3111323 0.2645969 0.2453223 [7] 0.1863267 0.1122573 0.1027479 -0.2382730 Largest eigenvalues: [1] 65917226 60080011 57518928 57227433 54856524 53449453 53203666 52068827 [9] 52001653 51138955 Smallest eigenvalues: [1] 0.36775398 0.36635231 0.28628080 0.22434271 0.14659257 0.10947501 [7] 0.07425764 -0.13103102 -0.46137337 -8.81269989 Largest eigenvalues: [1] 65632878 60315777 57704361 56882175 55055499 53485093 52860971 52488291 [9] 52332170 51832382 Smallest eigenvalues: [1] 0.41436564 0.38280502 0.36637619 0.29972288 0.21380625 0.19608325 [7] 0.13019916 0.02778648 -0.26604737 -0.36041729 Largest eigenvalues: [1] 63463811 60308786 56959079 55314477 54933507 53235613 52011915 51545353 [9] 51359442 51117125 Smallest eigenvalues: [1] 0.42499966 0.40481843 0.37754132 0.33857223 0.19431705 0.18293681 [7] -0.08745294 -0.22701228 -0.22901659 -1.85418629 Largest eigenvalues: [1] 64778842 59975199 57334997 56085416 54691803 53210121 52154412 52089627 [9] 51865965 51359928 Smallest eigenvalues: [1] 0.43607020 0.38846239 0.37169210 0.32916283 0.26544295 0.25766863 [7] 0.23214259 0.19554605 -0.01945274 -0.23953616 Largest eigenvalues: [1] 63577978 59508908 57116957 55813181 54230290 52799328 51803495 51498936 [9] 51095340 50431225 Smallest eigenvalues: [1] 0.382521787 0.303025366 0.233012294 0.222400318 0.217929149 [6] 0.146430846 0.003283711 -0.071249471 -0.364714792 -2.076921842 Largest eigenvalues: [1] 63389438 60524476 57270817 55576869 54974677 53437762 52024739 51993810 [9] 51715772 51310069 Smallest eigenvalues: [1] 0.35367247 0.34057294 0.30666115 0.23073180 0.22192793 0.18926718 [7] 0.18611158 0.05033477 -0.67011418 -1.04611634 Largest eigenvalues: [1] 64474348 59593010 57349514 56989253 54446650 52950565 52602283 52560805 [9] 51821221 51089856 Smallest eigenvalues: [1] 0.18523578 0.16596405 0.09903060 0.07801804 0.07507484 0.04546843 [7] 0.01899126 -0.02363648 -0.57226297 -1.83073925 Largest eigenvalues: [1] 66504444 61601941 58788573 57689326 55697108 54093670 53626734 52955438 [9] 52543049 52223916 Smallest eigenvalues: [1] 0.4544503 0.4184977 0.4027554 0.3353646 0.3245670 0.2896932 [7] 0.2108479 0.1587453 0.1257685 -0.1317678 Largest eigenvalues: [1] 65259073 60189300 57816812 56136084 54910889 53332152 52055641 52008840 [9] 51532561 51196078 Smallest eigenvalues: [1] 0.45254930 0.44487126 0.39384401 0.38563752 0.34448654 0.29665333 [7] 0.19905804 0.15241638 0.00551193 -0.03876237 Largest eigenvalues: [1] 65927861 60712931 57938491 56459590 55520595 53970151 52773381 52682583 [9] 52463471 51814417 Smallest eigenvalues: [1] 0.410698714 0.408099959 0.243021489 0.232795109 0.127629407 [6] 0.083217061 0.003270844 -0.155305548 -0.395444815 -2.934279357 Largest eigenvalues: [1] 65876519 60353230 57619607 56827282 55201571 53869789 52895199 52133512 [9] 52105097 51236102 Smallest eigenvalues: [1] 0.181022704 0.174913007 0.150845916 0.042466630 -0.009345051 [6] -0.096044263 -0.183298468 -0.187795549 -0.836485269 -3.559519544 Largest eigenvalues: [1] 62707691 59235668 56963571 54769921 54040168 53213604 51564434 51096805 [9] 50516481 50315509 Smallest eigenvalues: [1] 0.165680136 0.146564132 0.112689155 0.046108623 -0.002610232 [6] -0.023676892 -0.124903852 -0.136475594 -0.232947222 -0.383598663 Largest eigenvalues: [1] 64922418 60290803 57654552 55311559 54784116 53417417 52095025 51496364 [9] 51305503 51217163 Smallest eigenvalues: [1] 0.44105618 0.39454040 0.32722464 0.30564660 0.28974343 0.21912103 [7] 0.12869477 0.02467714 -0.10971108 -2.06292443 Largest eigenvalues: [1] 65484262 59849210 57211460 56312252 54694300 53293779 52426081 51836154 [9] 51818290 51009001 Smallest eigenvalues: [1] 0.32180552 0.18214718 0.13225753 0.10831086 0.03874408 -0.04069816 [7] -0.15856280 -0.24018360 -0.87680988 -1.68601624 Largest eigenvalues: [1] 64515020 59466898 56478765 55719171 54747729 52889345 51884086 51712812 [9] 51281814 50690846 Smallest eigenvalues: [1] 0.47174664 0.47005563 0.34241999 0.33970331 0.28957042 0.19171958 [7] 0.04497320 0.04476324 -0.04559572 -0.31645563 Largest eigenvalues: [1] 64531091 60184811 57181651 56350083 54713090 53098936 52418216 52223430 [9] 51552641 51090515 Smallest eigenvalues: [1] 0.41526513 0.39880820 0.34388130 0.27121541 0.24190545 0.18419011 [7] 0.07437829 -0.16510526 -0.21212665 -4.52041256 Largest eigenvalues: [1] 62207773 59355186 55921699 54675618 54162259 52702627 51450199 50723030 [9] 50231418 49925273 Smallest eigenvalues: [1] 0.37074429 0.34164873 0.30671791 0.27714647 0.22234495 0.19320356 [7] 0.16831436 0.07345757 0.04423442 -1.44009343 Largest eigenvalues: [1] 63990438 59830093 57168527 55672086 55412440 53844115 52520037 51969896 [9] 51625410 51474002 Smallest eigenvalues: [1] 0.30022882 0.27236204 0.22714886 0.19124063 0.11819728 0.07276478 [7] -0.07348596 -0.20636960 -0.21830364 -1.29573249 Largest eigenvalues: [1] 64236562 59801849 56369385 55094268 54736682 52852062 51490881 51162714 [9] 51105142 50595417 Smallest eigenvalues: [1] 0.09820088 0.01650463 -0.07651741 -0.13403839 -0.15289827 -0.22207786 [7] -0.39813064 -0.48560551 -0.91696221 -3.76682158 Largest eigenvalues: [1] 62954386 59115222 56085525 54841022 54356505 52832332 51992030 51445482 [9] 50825124 50507288 Smallest eigenvalues: [1] 0.420085508 0.393832512 0.376946216 0.357338459 0.277455977 [6] 0.207533793 0.080876851 0.008207197 -0.168546993 -0.398576622 Largest eigenvalues: [1] 64370745 60413383 57136266 56321755 55023929 53177864 52610524 52328249 [9] 51732811 51464329 Smallest eigenvalues: [1] 0.4724632 0.4370566 0.4265297 0.4231744 0.3627276 0.3252239 [7] 0.1988408 0.1272765 -0.3075132 -0.9177189 Largest eigenvalues: [1] 63308648 60185682 57366272 55834980 54989849 53201688 51978565 51913818 [9] 51804414 50900120 Smallest eigenvalues: [1] 0.34648664 0.33279024 0.30633631 0.29363954 0.12753658 0.11236166 [7] -0.01674858 -0.06218904 -0.20278956 -1.65584630 Largest eigenvalues: [1] 62864323 60792602 57091288 55771527 55201640 53898426 52213670 51827805 [9] 51245487 50946048 Smallest eigenvalues: [1] 0.35996701 0.34816292 0.30543824 0.28775183 0.24654443 0.22504584 [7] -0.07327008 -0.08201719 -0.92335522 -1.33899399 Largest eigenvalues: [1] 63152375 59536511 56998389 55489336 54728026 53018664 51765333 51693990 [9] 51507978 50776270 Smallest eigenvalues: [1] 0.34145843 0.30525460 0.24207377 0.19609694 0.18092572 0.07296567 [7] 0.04392425 -0.07557654 -0.20843504 -1.00644044 Largest eigenvalues: [1] 64191288 60468457 57349626 55987471 55267367 53752561 52402743 52337988 [9] 51930716 51342907 Smallest eigenvalues: [1] 0.16480505 0.10501115 0.09733584 -0.05264161 -0.11341967 -0.54094444 [7] -0.62447927 -1.04296375 -1.10775942 -1.28413435 Largest eigenvalues: [1] 65721208 59250519 56443440 55962739 54075474 52612083 52042557 51583471 [9] 51297542 50731930 Smallest eigenvalues: [1] 0.4553532 0.4397757 0.4357501 0.2878770 0.2780496 0.2022769 [7] 0.1498324 0.1361284 0.1015900 -0.9212881 Largest eigenvalues: [1] 64679249 60718639 57771459 55864558 55720175 54153124 53002686 52082547 [9] 51922089 51684424
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.531307 | 0.6518278 | 15.35903 | 0.465 | 2.692704 | 1.446231 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + speed + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
speed = speed_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_speed_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 572 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.55050433 0.53256241 0.48654544 0.38000551 0.33202243 0.29621819 [7] 0.16187231 0.14078987 -0.07034003 -0.08904212 Largest eigenvalues: [1] 77833360 72433811 69511016 68086269 66300872 64557563 63233857 62652249 [9] 62479350 61141199 Smallest eigenvalues: [1] 0.5412244 0.5337260 0.4357262 0.4182506 0.3881416 0.3443903 [7] 0.3059660 0.2733733 0.2503802 -1.2558948 Largest eigenvalues: [1] 76757647 73318543 69260738 67114619 67059005 65255124 62702247 62626440 [9] 62182056 61147733 Smallest eigenvalues: [1] 0.5193067 0.4496392 0.3968282 0.3397934 0.3136508 0.2613941 [7] 0.2323116 0.1967921 0.1406068 -0.2743322 Largest eigenvalues: [1] 78468244 72626014 69694125 68449978 66778806 64797285 63930462 63603712 [9] 62850940 62459966 Smallest eigenvalues: [1] 0.34468866 0.32021831 0.31255933 0.30876547 0.22313897 0.20452539 [7] 0.10849901 -0.02678394 -0.24521738 -2.46405812 Largest eigenvalues: [1] 77157694 73870474 69773724 67675367 67247413 65972609 63671250 63335281 [9] 62358348 62240166 Smallest eigenvalues: [1] 0.4896740 0.4732335 0.4701173 0.3629771 0.3490251 0.2594458 [7] 0.1323622 0.1005853 -0.3194762 -0.8731024 Largest eigenvalues: [1] 79282261 73605326 69275792 68900141 67130452 64877079 63826134 63429073 [9] 63143960 62163698 Smallest eigenvalues: [1] 0.39351702 0.32168073 0.29418720 0.15565554 0.14602426 0.13982603 [7] 0.04342068 -0.27676117 -0.34207489 -1.72044392 Largest eigenvalues: [1] 75465392 71566958 68134935 66426086 65997371 64299402 62690276 61646054 [9] 61284674 60797550 Smallest eigenvalues: [1] 0.5853250 0.5295660 0.4590514 0.4474366 0.4301865 0.3775529 [7] 0.3452556 0.2490105 0.2460635 -0.9763349 Largest eigenvalues: [1] 77279787 72166896 68395283 67597868 65696280 63631743 62627451 62437772 [9] 61800440 60756817 Smallest eigenvalues: [1] 0.5936902 0.5721702 0.4994369 0.4402444 0.4320499 0.4255537 [7] 0.4044148 0.3486449 0.1886876 -3.6099993 Largest eigenvalues: [1] 75975802 72899327 68982820 67141956 66127681 64770376 62202316 61953649 [9] 61553745 60864096 Smallest eigenvalues: [1] 0.70127365 0.61435980 0.61046660 0.49482274 0.49357250 0.37027296 [7] 0.31642644 0.27751581 0.08055193 -2.50509719 Largest eigenvalues: [1] 77987238 73823862 69589330 67767612 67102764 65011914 62887331 62830596 [9] 62683486 61500945 Smallest eigenvalues: [1] 0.5748293 0.5487580 0.4717583 0.4461822 0.3779188 0.3253492 [7] 0.3214183 0.2483043 0.1717289 -0.2814774 Largest eigenvalues: [1] 77040482 73344713 69358448 67665073 66661542 64800505 63543228 62803723 [9] 62577633 62151441 Smallest eigenvalues: [1] 0.5771021 0.5649774 0.5511547 0.4714670 0.3947720 0.3835320 [7] 0.2355225 0.1835590 -0.4674059 -0.6436282 Largest eigenvalues: [1] 78368187 73064907 68970571 68580579 66422429 64577415 63480186 63007314 [9] 62456438 61504093 Smallest eigenvalues: [1] 0.6203575 0.5639875 0.4805643 0.4394764 0.3923364 0.3507042 [7] 0.3216985 0.1956973 0.1574092 -0.4715224 Largest eigenvalues: [1] 77985049 72880844 69054724 68574424 65986723 64297307 63466068 62831782 [9] 62558638 61806695 Smallest eigenvalues: [1] 0.44527544 0.42061535 0.38830877 0.38245969 0.32906657 0.20603643 [7] 0.17947217 0.13179447 0.07722245 -0.85837095 Largest eigenvalues: [1] 78119939 72564923 69189920 67586477 66704913 64955492 62945960 62770982 [9] 62640721 61430230 Smallest eigenvalues: [1] 0.5959746 0.5408543 0.5241625 0.5105877 0.5086148 0.4984554 [7] 0.4759609 0.4247122 0.2083826 -0.8058766 Largest eigenvalues: [1] 76214867 72314659 68497350 66450934 66418714 64185016 62076139 61763088 [9] 61701115 60720334 Smallest eigenvalues: [1] 0.52401028 0.49724913 0.48734768 0.45129408 0.43999226 0.40520349 [7] 0.30748820 0.25934623 0.20358497 -0.06406239 Largest eigenvalues: [1] 79426568 73743266 70159137 68764587 67142681 65355790 63970909 63939034 [9] 63302679 62973021 Smallest eigenvalues: [1] 0.6588228 0.5463475 0.5355863 0.4894836 0.4351913 0.3469303 [7] 0.3281641 0.3167582 0.3085053 -0.0465695 Largest eigenvalues: [1] 76606890 72467099 68985091 67941250 65993602 64177961 62826310 62577722 [9] 62163914 61278191 Smallest eigenvalues: [1] 0.44059291 0.37935961 0.33071818 0.32587899 0.29147508 0.28413418 [7] 0.11581144 0.06103834 0.01497845 -1.26512857 Largest eigenvalues: [1] 77381967 71730105 68202847 67104511 66028013 64238671 62286996 62211881 [9] 61183800 60177009 Smallest eigenvalues: [1] 0.5103336 0.4925815 0.4613206 0.4486733 0.3553426 0.2700776 [7] 0.2658374 0.2394336 0.1595794 -0.2364893 Largest eigenvalues: [1] 76688563 72635813 69506089 67062396 66512681 64747988 62971768 62897015 [9] 62290806 61711971 Smallest eigenvalues: [1] 0.66782273 0.58425948 0.55109872 0.54734984 0.45735486 0.42625028 [7] 0.31454942 0.28902263 0.28009124 -0.07082533 Largest eigenvalues: [1] 76496572 72602802 68670322 67309433 66753084 64560926 63186928 62468255 [9] 62257546 61715133 Smallest eigenvalues: [1] 0.5199745 0.4130775 0.4101600 0.3792363 0.3167555 0.2399512 [7] 0.1821167 0.1570986 -0.4443419 -0.4521060 Largest eigenvalues: [1] 75964362 72524464 68472647 67121279 66146361 64380685 62330255 62103026 [9] 62101038 61109529 Smallest eigenvalues: [1] 0.5914923 0.5014930 0.3686788 0.3570254 0.3132893 0.2763499 [7] 0.2492538 0.2061373 0.1413934 -0.6540668 Largest eigenvalues: [1] 76879680 73335645 69733528 67462648 67280318 65397243 63236041 63010438 [9] 62422218 61994426 Smallest eigenvalues: [1] 0.3768560 0.3675516 0.3177338 0.2860588 0.2793688 0.2619481 [7] 0.1743407 0.1728558 0.1706334 -0.6185908 Largest eigenvalues: [1] 79011653 73255900 69574188 68350744 66803205 65060220 63532324 62822332 [9] 62592111 61419237 Smallest eigenvalues: [1] 0.54377271 0.53810294 0.49180748 0.43076881 0.41986959 0.31024692 [7] 0.22004644 0.21379538 0.07893951 -4.94836246 Largest eigenvalues: [1] 76275202 73050970 69362795 67274582 67034827 65193982 62915040 62848413 [9] 62195007 61645705 Smallest eigenvalues: [1] 0.67386427 0.61904324 0.55139825 0.54992412 0.50972916 0.45653835 [7] 0.37376453 0.33818627 -0.07756398 -0.12099685 Largest eigenvalues: [1] 75573170 72494355 68634885 66929348 66235218 64553658 62457016 61631814 [9] 61457280 60808897 Smallest eigenvalues: [1] 0.5852783 0.4424343 0.4060084 0.3986288 0.3782321 0.3419111 [7] 0.3350956 0.2818306 0.1333849 -1.4844796 Largest eigenvalues: [1] 77455001 73409251 69747000 68069587 66934803 65349581 63010848 62950832 [9] 62885780 61916476 Smallest eigenvalues: [1] 0.61067130 0.59564890 0.44528318 0.40287246 0.33257559 0.27736386 [7] 0.25389963 0.24623060 0.17950845 -0.04802855 Largest eigenvalues: [1] 77064087 73854580 69682392 68325183 67648650 66072303 63385077 63356016 [9] 62704506 61869063 Smallest eigenvalues: [1] 0.49998707 0.47878998 0.31904681 0.29153507 0.27464203 0.26828693 [7] 0.15851103 0.11926162 0.05747892 -0.28229002 Largest eigenvalues: [1] 78535214 73035915 69783202 68019307 66459357 64829533 63256695 63156090 [9] 62797589 62322318 Smallest eigenvalues: [1] 0.4723635 0.3912575 0.3851720 0.3414968 0.3232837 0.2842141 [7] 0.2669647 0.1974578 0.1950401 -0.3505106 Largest eigenvalues: [1] 77418887 73755864 69249846 68157358 67142982 65500067 63052892 62941243 [9] 62641739 61670557 Smallest eigenvalues: [1] 0.4828237 0.4817132 0.4446093 0.4317999 0.3067970 0.2624808 [7] 0.2278049 0.2119374 0.1027619 -0.1712094 Largest eigenvalues: [1] 76086378 72846042 68789078 66383887 66327873 64569867 62583088 61842470 [9] 61547881 61012645 Smallest eigenvalues: [1] 0.5271975 0.5063615 0.4562745 0.4227428 0.3839283 0.2926226 [7] 0.2325375 0.2297640 0.2137379 -0.1613282 Largest eigenvalues: [1] 77896849 72825463 69021100 67986920 66591967 64675585 63089559 62982052 [9] 62377297 61886280 Smallest eigenvalues: [1] 0.36566361 0.31865925 0.30146308 0.19483654 0.18097169 0.17424625 [7] 0.06623446 0.02375042 -0.09330488 -1.64920503 Largest eigenvalues: [1] 76602624 73317207 68912482 67423260 66874147 65168007 62877797 62590343 [9] 62052566 61615224 Smallest eigenvalues: [1] 0.48253825 0.38191451 0.35905960 0.28043671 0.27654467 0.25303596 [7] 0.14123438 0.13488854 -0.04432461 -0.76955118 Largest eigenvalues: [1] 78127783 73592781 68678488 68370272 66709882 64535112 63436856 62978503 [9] 62740783 61590343 Smallest eigenvalues: [1] 0.53753274 0.47434338 0.47176779 0.43937919 0.43308854 0.41313197 [7] 0.28829439 0.28217184 0.21198725 -0.07474942 Largest eigenvalues: [1] 78192087 74035284 69361383 68012899 66828118 65041528 63015074 62961809 [9] 62464416 61669655 Smallest eigenvalues: [1] 0.5610421 0.4957297 0.4849538 0.3511187 0.3411522 0.3139303 [7] 0.2565304 0.2457611 0.2058332 -0.4582968 Largest eigenvalues: [1] 80453923 73430251 70355570 69579319 66744585 64821438 64784183 63805645 [9] 62781328 62269842 Smallest eigenvalues: [1] 0.62527641 0.61646997 0.57774377 0.45831939 0.36207668 0.32392068 [7] 0.28420095 0.21344506 0.20367886 -0.02992591 Largest eigenvalues: [1] 78959018 73483317 69975906 68414059 67086570 65178640 63613461 63582354 [9] 63057415 62304113 Smallest eigenvalues: [1] 0.6535490 0.6503341 0.5825893 0.5250772 0.4696757 0.3816589 [7] 0.3400971 0.2693848 0.2282517 -0.1262570 Largest eigenvalues: [1] 76163899 73108038 68634654 66907999 66874588 64746920 62762017 62404244 [9] 62010359 60933468 Smallest eigenvalues: [1] 0.42372041 0.41129005 0.40427971 0.34114189 0.33793438 0.28477815 [7] 0.27140470 0.19954846 0.03101168 -0.21139883 Largest eigenvalues: [1] 78756867 72166584 68657497 67890919 66190124 64312005 63065588 62739670 [9] 62352902 61698804 Smallest eigenvalues: [1] 0.4889110 0.4670574 0.4561989 0.4361883 0.3815398 0.3720569 [7] 0.3652966 0.2183780 -0.1898968 -1.3632109 Largest eigenvalues: [1] 78571154 72905156 69415063 68076651 66440055 64937061 63171997 62771084 [9] 62555153 61740873 Smallest eigenvalues: [1] 0.37861305 0.34623755 0.28731850 0.28293476 0.24525114 0.21145686 [7] 0.20615373 0.18470773 -0.06399567 -1.38734308 Largest eigenvalues: [1] 76382284 73936040 69742068 67651626 67403684 65891156 63642528 62828995 [9] 62609597 61740626 Smallest eigenvalues: [1] 0.504516582 0.481783800 0.417154221 0.392213521 0.366511135 [6] 0.345189650 0.336792801 0.215669830 0.142559533 -0.009007333 Largest eigenvalues: [1] 75121904 73211474 68627346 66716859 66131307 64939846 62697589 61564480 [9] 61104718 60669143 Smallest eigenvalues: [1] 0.47178434 0.46689147 0.42408490 0.29883213 0.27811200 0.20031507 [7] 0.19424887 0.19265454 -0.08498325 -1.72120260 Largest eigenvalues: [1] 79783506 74809641 70922655 69240333 67776974 66176877 64115474 64058387 [9] 63856147 62950062 Smallest eigenvalues: [1] 0.42841051 0.35748851 0.35104235 0.34628557 0.32002307 0.17171505 [7] 0.15674220 0.14793619 0.01362610 -0.08413527 Largest eigenvalues: [1] 76051779 72982798 69002493 66691266 66629998 65132938 62777816 62245981 [9] 61793328 61272084 Smallest eigenvalues: [1] 0.5053269 0.4669195 0.4523051 0.3586205 0.3102549 0.3076255 [7] 0.2639822 0.2432264 0.0444544 -0.6590660 Largest eigenvalues: [1] 77819523 72704247 69467221 67470467 66572792 65030782 62923634 62610545 [9] 62590702 61438334 Smallest eigenvalues: [1] 0.4461113 0.4373170 0.4342049 0.3131738 0.2421742 0.1919153 [7] -0.1656899 -0.1791776 -0.4526655 -1.8921244 Largest eigenvalues: [1] 77971076 72247094 68633237 68589966 65673255 63286538 63274127 62825766 [9] 62024065 61677701 Smallest eigenvalues: [1] 0.60959073 0.56045632 0.54251189 0.52708391 0.48267544 0.32515361 [7] 0.30563307 0.10723032 0.07525862 -0.03075654 Largest eigenvalues: [1] 76881138 72991010 69273163 67252713 67109028 65321977 63116920 62933591 [9] 62108685 61624245 Smallest eigenvalues: [1] 0.5395889 0.4465586 0.4430413 0.3856597 0.3479056 0.3405963 [7] 0.3242266 0.2430054 0.1203213 -0.4976387 Largest eigenvalues: [1] 77596092 73632707 70044309 67475099 66745345 65431474 63047603 62726262 [9] 62454268 61933265 Smallest eigenvalues: [1] 0.5162739 0.4707992 0.4466143 0.4318657 0.3449503 0.3380128 [7] 0.3030409 0.2049623 0.1517631 -1.0239417 Largest eigenvalues: [1] 77911493 72368512 69163137 68378787 66349914 64748610 63384586 62610399 [9] 62402670 61393930 Smallest eigenvalues: [1] 0.6209771 0.5586180 0.5447933 0.4704432 0.4246072 0.3730246 [7] 0.2698720 0.2310374 0.1868026 -0.4445809 Largest eigenvalues: [1] 76802668 72075979 68053775 67895986 65537138 63495467 62667215 62053720 [9] 62016796 60706000 Smallest eigenvalues: [1] 0.53917242 0.52364442 0.50318045 0.49074244 0.39386796 0.25189182 [7] 0.24257973 0.17284128 -0.06541903 -0.11566226 Largest eigenvalues: [1] 78178169 73481684 70147871 68791633 66947936 65308010 63547850 63393160 [9] 63361117 62062268 Smallest eigenvalues: [1] 0.53531316 0.41311835 0.38000035 0.36012147 0.35002906 0.32506645 [7] 0.31025279 0.27805186 0.06468173 -0.21606587 Largest eigenvalues: [1] 78118240 72743653 69513000 67206435 66442566 64810401 62456040 62424790 [9] 62321697 61512553 Smallest eigenvalues: [1] 0.34534472 0.26903293 0.26728483 0.25213307 0.21637402 0.11050141 [7] 0.10522272 0.03568764 -0.04337439 -0.69033036 Largest eigenvalues: [1] 76892843 72361285 68507388 67504949 66351923 64481874 62766663 62730446 [9] 62451337 61728254 Smallest eigenvalues: [1] 0.58121399 0.47110198 0.45271145 0.45004487 0.42270916 0.39485928 [7] 0.32562693 0.02700045 -0.07682017 -1.93117202 Largest eigenvalues: [1] 76310896 71988663 68410729 66565202 66269356 64545937 62297320 62042835 [9] 61405903 60984028 Smallest eigenvalues: [1] 0.45676543 0.44527826 0.39215912 0.35903114 0.34584123 0.22250206 [7] 0.16530757 0.09010545 0.01147663 -1.33018835 Largest eigenvalues: [1] 75095531 71952906 68563142 66122172 65720257 64630884 62709329 61574776 [9] 60847417 60626242 Smallest eigenvalues: [1] 0.5268369 0.5253547 0.4495646 0.4423658 0.4184852 0.3685783 [7] 0.3667439 0.2412914 0.1556810 -0.1227073 Largest eigenvalues: [1] 76100395 72210466 68437501 66964931 65989060 64151053 62502850 62037942 [9] 61930884 61124902 Smallest eigenvalues: [1] 0.40484377 0.39793920 0.34790528 0.31805481 0.24604047 0.22465553 [7] 0.17961903 0.16210385 0.09696991 -0.85821771 Largest eigenvalues: [1] 76507782 73157931 68700539 67384821 66631695 64840047 62518241 62485411 [9] 62243271 61297501 Smallest eigenvalues: [1] 0.5516048 0.5488101 0.4782532 0.4424994 0.4374080 0.4062754 [7] 0.3802243 0.3542188 0.3119516 -0.2950655 Largest eigenvalues: [1] 77146701 72380999 68618636 67233614 66293726 64482192 62551356 62330466 [9] 62149749 61141032 Smallest eigenvalues: [1] 0.47717635 0.41341230 0.37705806 0.29628191 0.25032638 0.24637906 [7] 0.17340250 -0.01253615 -0.20420115 -0.35763236 Largest eigenvalues: [1] 78599037 74052911 70071353 68619373 67013716 65359968 63599203 63425910 [9] 63115799 62286738 Smallest eigenvalues: [1] 0.4698582 0.4584676 0.3625502 0.3533563 0.3204797 0.3173521 [7] 0.3013119 0.2705705 0.2255708 -0.5698507 Largest eigenvalues: [1] 78209693 72756919 68693173 67645069 66337854 64639666 62842837 62716814 [9] 62530664 61762373 Smallest eigenvalues: [1] 0.44779206 0.43566215 0.34168218 0.32916163 0.32586749 0.25358317 [7] 0.09478012 -0.13104861 -0.46889495 -0.77400065 Largest eigenvalues: [1] 80983373 73569976 69927200 69216526 66743145 64753879 64327749 63180453 [9] 63083247 62310527 Smallest eigenvalues: [1] 0.60888615 0.60459091 0.53468755 0.50691583 0.50219473 0.48142919 [7] 0.42987856 0.27504740 0.07144804 -2.05436477 Largest eigenvalues: [1] 77153155 73152370 69017596 67302684 66772292 65301586 62999670 62583448 [9] 62100404 61369623 Smallest eigenvalues: [1] 0.52895510 0.49442599 0.48104675 0.45537924 0.34736516 0.27135971 [7] 0.26967318 0.16084657 0.03217937 -0.81455937 Largest eigenvalues: [1] 77274361 73749314 68980206 67792938 66906199 64987919 62783561 62749710 [9] 62720216 61602799 Smallest eigenvalues: [1] 0.52861223 0.48861124 0.44761914 0.31506121 0.31003877 0.27424240 [7] 0.21370409 0.19839632 0.02218377 -0.12963859 Largest eigenvalues: [1] 76899967 73548428 70205726 67696032 67422512 65680919 63068549 62996275 [9] 62573304 61658094 Smallest eigenvalues: [1] 0.4412637846 0.4021458286 0.3352397799 0.3020136481 0.2595983249 [6] 0.1278242713 0.1114825481 0.0995514685 -0.0007480274 -0.9706437438 Largest eigenvalues: [1] 75305121 72765104 68989948 66677045 66383655 64814612 62856081 62605236 [9] 61759319 61269979 Smallest eigenvalues: [1] 0.46657352 0.37997608 0.37000797 0.25268517 0.19378856 0.16554402 [7] 0.13818003 0.06135697 -0.21252654 -0.48520943 Largest eigenvalues: [1] 78111223 73351079 69642694 68807010 66758053 64730898 63500882 63185421 [9] 63006764 61920670 Smallest eigenvalues: [1] 0.64935658 0.64072863 0.50601624 0.48834324 0.48359208 0.43185791 [7] 0.34494965 0.27843737 0.12514701 -0.06596242 Largest eigenvalues: [1] 77653081 73196163 69244050 67038671 66965760 65027059 63054388 62340578 [9] 62136939 61763364 Smallest eigenvalues: [1] 0.37397266 0.36474379 0.33165730 0.31943787 0.26674836 0.24388061 [7] 0.22712632 0.22567748 0.02903477 -0.12074796 Largest eigenvalues: [1] 77192291 72821900 69320856 67528601 66627303 64950272 62531135 62525489 [9] 62240820 61028107 Smallest eigenvalues: [1] 0.5392415 0.5018866 0.4681729 0.4210981 0.4128392 0.2235284 [7] 0.2005025 0.1542450 0.1411396 -0.4116996 Largest eigenvalues: [1] 76236441 73513879 68753236 67366333 67073354 65157224 63019944 62999863 [9] 62387108 61709371 Smallest eigenvalues: [1] 0.47067317 0.45587766 0.41450008 0.41180087 0.37041416 0.31865170 [7] 0.30156645 0.24869087 0.09840674 -1.45738032 Largest eigenvalues: [1] 78625495 73943120 70053826 67900037 67528669 65723528 63232622 63095219 [9] 63024978 61809164 Smallest eigenvalues: [1] 0.49035567 0.46403231 0.46030065 0.41631453 0.39330579 0.32607545 [7] 0.27186241 0.16009162 0.12545506 -0.03469129 Largest eigenvalues: [1] 75754326 72633080 68543620 66902312 66570848 64579859 62459999 62265668 [9] 61811048 60952404 Smallest eigenvalues: [1] 0.5398690 0.5337990 0.4551504 0.4133656 0.3830911 0.3224970 [7] 0.2961641 0.2927599 0.2107947 -0.4301329 Largest eigenvalues: [1] 76011933 72759279 68805530 67430964 65945013 64178365 62742387 62344299 [9] 62061291 61507686 Smallest eigenvalues: [1] 0.5939107 0.5496027 0.5430406 0.5197949 0.4425005 0.4355064 [7] 0.4294090 0.2908245 0.2724754 -2.2176092 Largest eigenvalues: [1] 77413898 72315803 68538406 67219119 66374923 64622331 62449201 62317798 [9] 61872895 60933781 Smallest eigenvalues: [1] 0.5369338 0.5282296 0.3907041 0.3614953 0.3385366 0.3300459 [7] 0.2953671 0.2750601 -1.4669558 -3.9988135 Largest eigenvalues: [1] 77219137 72343277 68637272 67328812 65963346 64082986 62486022 62316023 [9] 61930033 60880881 Smallest eigenvalues: [1] 0.4142293 0.4035843 0.3052835 0.2849635 0.1726516 0.1083813 [7] -0.1880029 -0.2041266 -0.2573278 -2.5245213 Largest eigenvalues: [1] 77433652 73456762 69012646 67534088 67324165 65224541 63070684 62750628 [9] 62538916 61607362 Smallest eigenvalues: [1] 0.4221675 0.4113480 0.3930594 0.3746244 0.2771734 0.1951779 [7] 0.1224577 0.1107408 -0.4173752 -5.1942842 Largest eigenvalues: [1] 78127798 72408071 68784249 68317234 65645803 63809997 63389613 61746248 [9] 61665710 60511450 Smallest eigenvalues: [1] 0.44308815 0.37342399 0.35375460 0.25680067 0.18955281 0.15217654 [7] 0.08022281 0.07096196 -0.11677683 -2.32595269 Largest eigenvalues: [1] 75469703 73117869 68682190 66832167 66793529 64570801 62548250 62233732 [9] 61884019 61083913 Smallest eigenvalues: [1] 0.56346443 0.55503063 0.49899161 0.48856436 0.47968829 0.47249497 [7] 0.38707996 0.28378114 0.06293197 -1.08068189 Largest eigenvalues: [1] 77917674 72863760 68776013 67666951 65836530 63944199 62708812 62299124 [9] 62141814 61241046 Smallest eigenvalues: [1] 0.49084275 0.39420319 0.30362793 0.28679473 0.25313097 0.23911682 [7] 0.21345937 0.17107179 0.08149994 -0.62999759 Largest eigenvalues: [1] 77288711 72935714 69468388 67443297 66381396 64889352 62801701 62505797 [9] 62315728 61235107 Smallest eigenvalues: [1] 0.5259478 0.4960631 0.4397647 0.3904451 0.3842165 0.3791179 [7] 0.3566501 0.2939234 0.2539997 -0.2633033 Largest eigenvalues: [1] 79269402 73253894 70130360 69228123 66144359 64262989 64226383 62763002 [9] 62681195 61485402 Smallest eigenvalues: [1] 0.5875704 0.5791915 0.5432155 0.4957099 0.4836447 0.3999043 [7] 0.3810816 0.3335534 0.2872577 -4.8400558 Largest eigenvalues: [1] 77799495 72663782 69436910 67941288 66491539 64461592 62947637 62896994 [9] 62811459 61738942 Smallest eigenvalues: [1] 0.5576461 0.4978513 0.4297535 0.3962712 0.3585189 0.3076665 [7] 0.2889435 0.2823608 0.1092095 -0.1328825 Largest eigenvalues: [1] 78758288 73995560 69556351 69023946 67109005 65072259 63889386 63260724 [9] 63113737 61944731 Smallest eigenvalues: [1] 0.46112632 0.44435734 0.42251972 0.29146883 0.29132954 0.24225346 [7] 0.18044426 0.07978961 -0.89466780 -1.56549320 Largest eigenvalues: [1] 78063315 72578398 68681560 67917398 66463991 64665735 63005270 62897881 [9] 62785928 61764655 Smallest eigenvalues: [1] 0.57240816 0.56308732 0.50883246 0.50231902 0.42581645 0.40998954 [7] 0.33292717 0.32940473 0.28866679 -0.04808187 Largest eigenvalues: [1] 77409563 73125107 68973620 67631870 66693053 64613172 62822764 62573552 [9] 62443090 61102096 Smallest eigenvalues: [1] 0.4391791 0.3818668 0.3096826 0.3021444 0.2835909 0.2828333 [7] 0.2625952 0.2236139 0.1998042 -4.7503656 Largest eigenvalues: [1] 78790445 72778588 69023574 68301885 66402769 64670038 63227362 62320534 [9] 61884988 61095223 Smallest eigenvalues: [1] 0.57913374 0.57233952 0.47368403 0.40336224 0.36699524 0.34711919 [7] 0.30289895 0.16496625 0.08726118 -0.04250618 Largest eigenvalues: [1] 76777460 72725437 69307654 67540522 67150182 65402113 63048511 62751375 [9] 62524140 61356749 Smallest eigenvalues: [1] 0.56560520 0.54824738 0.38209648 0.31009612 0.26685413 0.23989876 [7] 0.08325651 -0.07290181 -0.44716777 -3.71661430 Largest eigenvalues: [1] 75815132 72685190 68316372 66621151 66460553 64474652 62346917 62011299 [9] 61709544 60672364 Smallest eigenvalues: [1] 0.5085805 0.4511928 0.3903523 0.3236891 0.3016539 0.2422886 [7] 0.1332402 0.1244244 0.0847495 -0.0216849 Largest eigenvalues: [1] 76996633 73493556 69461115 67539468 67170144 65171259 63122729 62869575 [9] 62695229 61693950 Smallest eigenvalues: [1] 0.44120920 0.39339443 0.37504544 0.28969713 0.28796913 0.20753454 [7] 0.19918180 0.16882218 0.05465016 -0.82452239 Largest eigenvalues: [1] 78163800 72813736 69359576 68001799 66691651 65042677 63146372 63142900 [9] 62827565 61852691 Smallest eigenvalues: [1] 0.617619693 0.607399444 0.585992566 0.584248216 0.570915035 [6] 0.488495903 0.361012994 0.268844625 0.004517985 -0.110975565 Largest eigenvalues: [1] 77765798 72529640 68313254 67574197 65971805 64079464 62560910 62103770 [9] 61985712 60867424 Smallest eigenvalues: [1] 0.49791580 0.42858258 0.41856716 0.34348125 0.34320007 0.29930628 [7] 0.22130627 0.11641306 0.03357146 -0.07973467 Largest eigenvalues: [1] 77071222 73384443 69879048 67128201 66838548 65103819 63095360 62882015 [9] 62472171 62106800 Smallest eigenvalues: [1] 0.56331037 0.48432183 0.44766832 0.35688816 0.31167840 0.29389868 [7] 0.27011621 0.16106373 0.06863595 -0.28255588 Largest eigenvalues: [1] 75160003 71911892 67840389 66365889 65775111 63891334 62482308 61333487 [9] 61179947 60216015 Smallest eigenvalues: [1] 0.5900622 0.5458285 0.5292158 0.4826307 0.4531926 0.2855408 [7] 0.2518647 0.2512229 0.1130998 -2.1437523 Largest eigenvalues: [1] 78780594 72607505 68342437 67795706 66117146 63961777 62946644 62115656 [9] 62026870 61063362 Smallest eigenvalues: [1] 0.58861946 0.49640218 0.43775227 0.42612548 0.39857828 0.30424909 [7] 0.28018261 0.10328813 0.03197308 -0.25670430 Largest eigenvalues: [1] 77427337 71816789 68831165 66818233 65837571 64172204 62740240 62334261 [9] 62047765 61263721 Smallest eigenvalues: [1] 0.56689404 0.48850955 0.46939879 0.34963593 0.33034713 0.29036723 [7] 0.26425258 0.17036773 0.06080502 -0.97775593 Largest eigenvalues: [1] 77534749 73612076 69884162 67921779 67367274 65658338 63126119 63065810 [9] 62797875 61977944 Smallest eigenvalues: [1] 0.6019600 0.5864450 0.5741068 0.5360648 0.4351847 0.4127963 [7] 0.4102074 0.3936848 0.1670804 -0.2264092 Largest eigenvalues: [1] 76260796 73009611 68736599 66711711 66412668 64823934 62175142 61750840 [9] 61405641 60366456 Smallest eigenvalues: [1] 0.4409786 0.4111338 0.3186108 0.3071264 0.2950198 0.2814946 [7] 0.1922572 0.1591420 -0.1500812 -1.1966799 Largest eigenvalues: [1] 76265530 72209777 68865885 66217759 66172428 64507541 62504952 61820144 [9] 61502691 60943276 Smallest eigenvalues: [1] 0.5642905 0.5095889 0.4971675 0.4878429 0.4122527 0.3813373 [7] 0.3761242 0.2741862 0.1263883 -1.1254294 Largest eigenvalues: [1] 80569601 73498846 69629049 69609463 66611171 64780602 64678186 63054462 [9] 62351974 61795270 Smallest eigenvalues: [1] 0.4165391 0.4061869 0.3801803 0.3758458 0.3492932 0.3094795 [7] 0.2949535 0.2807042 -0.0446970 -1.1192370 Largest eigenvalues: [1] 77753404 71851585 68407970 67847595 65548043 63902492 62890705 61850894 [9] 61827038 60803865 Smallest eigenvalues: [1] 0.23580639 0.18449458 0.04556393 -0.07006873 -0.11100463 -0.12889717 [7] -0.30172450 -0.78758416 -1.91594761 -2.27607093 Largest eigenvalues: [1] 77463285 72682369 68455940 66715950 66508523 64493809 62148304 62083714 [9] 61509947 60480488 Smallest eigenvalues: [1] 0.42480957 0.38230947 0.36170997 0.34639133 0.28592913 0.26116859 [7] 0.23132756 0.15846357 0.03461095 -1.02061837 Largest eigenvalues: [1] 78972912 73753321 69913122 69324787 66804428 64928578 64055176 63003238 [9] 62852595 61379146 Smallest eigenvalues: [1] 0.5188156 0.4869317 0.4624479 0.4432447 0.4414182 0.3905045 [7] 0.3713981 0.2250883 0.2144155 -0.2394167 Largest eigenvalues: [1] 79279739 73093688 69066838 67842352 66316280 64535821 63032728 62541785 [9] 62086213 61388374 Smallest eigenvalues: [1] 0.5805323 0.3862634 0.3670794 0.3152899 0.2883731 0.2795393 [7] 0.2485552 0.2365054 -0.0322109 -0.2993613 Largest eigenvalues: [1] 77880808 72725815 69544808 67528551 66549866 64842371 62599739 62575413 [9] 62484803 61641779 Smallest eigenvalues: [1] 0.42296303 0.39789931 0.35138867 0.31732080 0.30924156 0.25076722 [7] 0.25069625 0.19087366 -0.03506752 -0.07986408 Largest eigenvalues: [1] 77658976 73205022 69691871 67960144 66421848 64935479 63127203 62678803 [9] 62625332 61612506 Smallest eigenvalues: [1] 0.5231114 0.4885183 0.4756620 0.4338424 0.4213640 0.3910881 [7] 0.3731172 0.3541567 0.3254599 -0.1442809 Largest eigenvalues: [1] 77634579 74569619 69517185 68228571 67805852 65733503 63649713 63283406 [9] 62887977 61914440 Smallest eigenvalues: [1] 0.46825758 0.41001124 0.39826089 0.35338986 0.19811679 0.19510919 [7] 0.17650116 0.07220242 -0.08088277 -1.17307476 Largest eigenvalues: [1] 76756107 73605860 69925933 67745143 67166340 65653043 63274565 63191222 [9] 62606971 62189851 Smallest eigenvalues: [1] 0.61404251 0.59563550 0.54559627 0.53695696 0.48206830 0.43228333 [7] 0.31985793 0.13353889 -0.02976476 -0.09610230 Largest eigenvalues: [1] 76436547 73364426 68851775 67485648 67153334 65063053 63063983 62791114 [9] 62387669 61586475 Smallest eigenvalues: [1] 0.6368985 0.5992832 0.5298476 0.5252220 0.4081237 0.3937257 [7] 0.3368829 0.3278955 0.2221071 -0.1225472 Largest eigenvalues: [1] 78786428 73228843 69764036 67829182 66631214 64828976 63187796 62833134 [9] 62752870 62031575 Smallest eigenvalues: [1] 0.6034882 0.5622188 0.5527781 0.4696642 0.4495244 0.3468501 [7] 0.2752957 0.2652741 0.2441000 -0.9947116 Largest eigenvalues: [1] 76136307 73385784 69679216 67816752 66291656 65776054 63042418 62801364 [9] 61608940 61392461 Smallest eigenvalues: [1] 0.6614102 0.5622234 0.4988345 0.4871921 0.4594174 0.3883313 [7] 0.3646422 0.3596251 0.2796611 -0.5140386 Largest eigenvalues: [1] 77287175 73210031 69393766 67633693 66760161 65149125 62715912 62660124 [9] 62546000 61202066 Smallest eigenvalues: [1] 0.45113533 0.31167135 0.23957183 0.22823710 0.21656046 0.19917037 [7] 0.19746384 0.17195608 0.01762304 -3.66413946 Largest eigenvalues: [1] 78153112 74250472 69579670 67958038 67934422 65686324 64010624 63238870 [9] 62997561 62307720 Smallest eigenvalues: [1] 0.4428171 0.3386460 0.3271099 0.3078645 0.2770213 0.2396184 [7] 0.2125655 0.2103045 0.0510398 -0.1143580 Largest eigenvalues: [1] 75962506 73574452 69204811 67123065 67096864 65373454 62951476 62666350 [9] 61991785 61382775 Smallest eigenvalues: [1] 0.4788231 0.3958568 0.3691574 0.3422451 0.3113427 0.3099296 [7] 0.2567396 0.2322446 0.2243544 -1.5490367 Largest eigenvalues: [1] 76294750 72606221 69194034 66852446 66146795 64790943 62623308 62113617 [9] 61906546 60894250 Smallest eigenvalues: [1] 0.3932003 0.3822624 0.2838283 0.2732697 0.2700669 0.2583313 [7] 0.2225064 0.1801301 0.1490531 -0.8078267 Largest eigenvalues: [1] 75909093 72717956 69219321 67262170 66110932 65089804 62689428 62120018 [9] 61366950 61208515 Smallest eigenvalues: [1] 0.653822298 0.547785579 0.544422903 0.482389915 0.416249122 [6] 0.388129221 0.320381895 0.296084028 -0.002701621 -0.202626325 Largest eigenvalues: [1] 77175254 72619515 68697195 66656285 66551738 64701016 62405511 62378784 [9] 61790609 61339649 Smallest eigenvalues: [1] 0.53805211 0.52310086 0.51480711 0.44434781 0.34135233 0.32900681 [7] 0.31333002 0.05509160 0.05057911 -0.13531371 Largest eigenvalues: [1] 79290068 72489841 69135627 68867761 65843308 64028619 63970212 62425821 [9] 62073776 61213946 Smallest eigenvalues: [1] 0.5731632 0.5621653 0.4422420 0.3415889 0.2869506 0.2798386 [7] 0.2171453 0.1695872 -0.3088695 -2.6463412 Largest eigenvalues: [1] 77002304 73169061 69333926 67669040 67494706 65392622 63242620 63068306 [9] 62664227 61755188 Smallest eigenvalues: [1] 0.4866866 0.4732881 0.4692815 0.3272880 0.3114048 0.2442588 [7] 0.2112379 0.1919694 0.1912410 -0.2096386 Largest eigenvalues: [1] 76802814 72995127 68904226 66913591 66888311 64892519 63338202 62334215 [9] 62169367 62012067 Smallest eigenvalues: [1] 0.54168339 0.51492056 0.49215215 0.48313743 0.40801997 0.34566312 [7] 0.25437909 0.08720135 0.01184963 -0.40672102 Largest eigenvalues: [1] 76738709 72492713 68304976 66459158 66139108 64304907 62481815 61849896 [9] 61541475 60715281 Smallest eigenvalues: [1] 0.59422875 0.54765128 0.43647906 0.42889650 0.34781227 0.34371081 [7] 0.33752622 0.19671603 0.17768952 -0.06990113 Largest eigenvalues: [1] 79515958 72959497 70224055 67890661 66785833 64899071 63358694 63111499 [9] 62870705 62002546 Smallest eigenvalues: [1] 0.379250925 0.352382197 0.291887880 0.226144928 0.180574337 [6] 0.167773321 0.081935654 -0.008258228 -1.603749107 -3.951294003 Largest eigenvalues: [1] 77605872 73646713 69116494 67640191 67117824 65249860 62817406 62709710 [9] 62672017 61116528 Smallest eigenvalues: [1] 0.5439338 0.5086563 0.5040921 0.3478505 0.3075325 0.2226177 [7] 0.1989941 0.1726739 0.1107143 -3.4974201 Largest eigenvalues: [1] 77850545 73165436 69702503 67760699 66741289 65091200 63316654 62985319 [9] 62833767 61872835 Smallest eigenvalues: [1] 0.3872133 0.3687104 0.3294288 0.3177236 0.1733053 0.1713076 [7] 0.1547694 0.0922867 -0.2280324 -1.3032510 Largest eigenvalues: [1] 75366867 71380151 67943990 66148025 65807121 64374438 62716088 61301821 [9] 61001013 60514629 Smallest eigenvalues: [1] 0.3905634 0.3704986 0.3524538 0.3509479 0.2984183 0.2698907 [7] 0.1789072 0.1175717 -0.5745736 -1.0216216 Largest eigenvalues: [1] 77138439 72574859 68912307 67106992 66802229 65057912 62838001 62137101 [9] 62099146 61336521 Smallest eigenvalues: [1] 0.512608489 0.463687837 0.390407122 0.385917345 0.379095724 [6] 0.375592065 0.331197253 0.321957394 0.244113622 -0.003397504 Largest eigenvalues: [1] 77442569 73103416 69048494 67955201 66682735 64982715 62718646 62500266 [9] 62097532 61009960 Smallest eigenvalues: [1] 0.64807655 0.59362882 0.57008654 0.56957219 0.49588229 0.41817972 [7] 0.41464411 0.32462628 0.26399870 -0.05003109 Largest eigenvalues: [1] 78883203 73460068 69560661 68546682 66822170 64723024 63613382 63473926 [9] 62474684 61711092 Smallest eigenvalues: [1] 0.54558508 0.50753203 0.40975616 0.39230917 0.36221065 0.32815604 [7] 0.27085496 0.25340695 0.07968162 -0.02581307 Largest eigenvalues: [1] 78258221 73888749 70199984 68292358 66794885 65290275 63389264 63221732 [9] 62684859 61893222 Smallest eigenvalues: [1] 0.5946218 0.5020848 0.4803186 0.4758547 0.4383129 0.4248227 [7] 0.3893174 0.3137578 0.1961756 -0.1769507 Largest eigenvalues: [1] 78157728 73293276 69113388 68449311 66757270 64661385 63409632 62660965 [9] 62546629 61362084 Smallest eigenvalues: [1] 0.51784275 0.47465287 0.39471867 0.37467349 0.36192549 0.27385162 [7] 0.23877685 0.22242167 0.08843524 -0.11657658 Largest eigenvalues: [1] 76137846 72530144 68826374 66463363 66431514 64812217 62443842 62207630 [9] 61748431 60997144 Smallest eigenvalues: [1] 0.6335119 0.4482552 0.4443160 0.4352408 0.4347628 0.4338516 [7] 0.2572862 0.1995757 0.1645509 -0.7597067 Largest eigenvalues: [1] 79100255 73650071 69822202 68676300 66968180 65175732 63811355 63207373 [9] 62746681 62102726 Smallest eigenvalues: [1] 0.424242081 0.381771450 0.369927507 0.318038870 0.302561677 [6] 0.252094052 0.204688963 0.160558092 -0.007016862 -0.425280753 Largest eigenvalues: [1] 75475984 72260806 68587102 66254981 66092394 64482786 62390454 61887300 [9] 61030723 60756095 Smallest eigenvalues: [1] 0.60732390 0.47654025 0.39272312 0.36503256 0.32383390 0.21054712 [7] 0.18168489 0.17763563 0.04821269 -0.89859070 Largest eigenvalues: [1] 77444673 73180115 69612109 67503067 67111461 65294823 63503125 63287374 [9] 62533953 62293359 Smallest eigenvalues: [1] 0.63537171 0.58361521 0.50900256 0.45650631 0.41422482 0.31998696 [7] 0.31354813 0.29442810 0.23267037 -0.02179254 Largest eigenvalues: [1] 78348604 73400596 70109961 67809934 67430546 65892228 63524756 63228926 [9] 62979895 62207051 Smallest eigenvalues: [1] 0.71403417 0.63169834 0.52851899 0.51838754 0.48714279 0.45832461 [7] 0.37180565 0.34834287 0.08639388 -0.02537194 Largest eigenvalues: [1] 77089287 72517406 68560387 67490415 66194984 64226423 62557354 62370431 [9] 61889377 60708265 Smallest eigenvalues: [1] 0.5561950 0.4940294 0.4197982 0.3556398 0.3081623 0.2629303 [7] 0.2209056 0.2207962 0.1061034 -0.6377883 Largest eigenvalues: [1] 77711272 73733625 70065973 67646860 67512603 66210261 63709492 63218166 [9] 62664969 62163537 Smallest eigenvalues: [1] 0.3860705 0.3017566 0.2264116 0.1501360 0.1384508 0.1251060 [7] 0.1070625 0.0268163 -0.1506807 -0.2326486 Largest eigenvalues: [1] 74829898 72046528 68652648 67405727 65403028 65205342 63436229 61924215 [9] 61169553 61070315 Smallest eigenvalues: [1] 0.6222086 0.5692506 0.5194139 0.4304063 0.3843781 0.3639545 [7] 0.2800696 0.2344509 0.2278835 -1.4740686 Largest eigenvalues: [1] 76978447 73023212 69646903 67402839 67087318 65203727 63080172 63067332 [9] 62530120 61761270 Smallest eigenvalues: [1] 0.56005307 0.49448898 0.42479411 0.41008631 0.33622247 0.32297986 [7] 0.18350642 0.09914597 -0.03587974 -3.62056726 Largest eigenvalues: [1] 78883296 74197628 69790020 68553894 67385265 65274494 63933112 63666201 [9] 62871260 62342541 Smallest eigenvalues: [1] 0.53400353 0.46389788 0.42076565 0.37511738 0.34801570 0.26929821 [7] 0.26035183 0.24019392 0.22532802 -0.04512077 Largest eigenvalues: [1] 78343413 73505308 69894118 68126356 67282577 65597415 64063539 63224748 [9] 63212522 62655273 Smallest eigenvalues: [1] 0.5937502 0.5404256 0.4705270 0.4627922 0.4072046 0.3297166 [7] 0.3123015 0.1937314 0.1492728 -0.1010974 Largest eigenvalues: [1] 77065069 73563738 70032609 67310861 67033510 65406908 63383889 63139497 [9] 62606798 62130782 Smallest eigenvalues: [1] 0.4828148 0.3907461 0.3639922 0.3611642 0.3496244 0.3289970 [7] 0.2980622 0.2353663 0.2211265 -0.5727577 Largest eigenvalues: [1] 78257025 73164929 69561379 68334250 66368222 65027147 63273473 62687783 [9] 62368170 61427819 Smallest eigenvalues: [1] 0.4728710 0.4586556 0.4149114 0.4029525 0.3346516 0.3011435 [7] 0.1800176 0.1387795 0.0118461 -0.8114178 Largest eigenvalues: [1] 77628906 73405687 69510169 67913743 67202519 65472942 63612263 63168614 [9] 62703582 62075609 Smallest eigenvalues: [1] 0.6101223 0.5680907 0.5276110 0.4674018 0.4574974 0.3935130 [7] 0.3873984 0.2507839 0.1910051 -0.3275738 Largest eigenvalues: [1] 78041992 73244927 69371595 68039403 67216725 65055741 63386192 63203365 [9] 62800800 62104435 Smallest eigenvalues: [1] 0.63580334 0.57989306 0.47218193 0.46540855 0.40600048 0.34239513 [7] 0.33955572 0.18737824 0.06358133 -0.17945200 Largest eigenvalues: [1] 77859725 73575235 69405833 68078511 66760414 64932989 62940994 62738567 [9] 62575689 61472237 Smallest eigenvalues: [1] 0.4484417 0.3736445 0.3588141 0.3487862 0.3230052 0.3159369 [7] 0.2344544 0.1331244 -0.2035580 -2.0140574 Largest eigenvalues: [1] 78700511 73592656 69533151 67975934 66804175 64988935 63061251 62874714 [9] 62307879 61696484 Smallest eigenvalues: [1] 0.42969097 0.37649904 0.32953453 0.26879063 0.26206248 0.15468292 [7] 0.15113522 0.08440772 -0.06491986 -0.35192571 Largest eigenvalues: [1] 75692201 73448299 69590133 68351001 66219662 66055551 63610227 62822700 [9] 61639198 61344042 Smallest eigenvalues: [1] 0.5042810 0.4236652 0.4065005 0.3964352 0.3739095 0.3444603 [7] 0.2693778 0.2653005 0.2297315 -0.3884519 Largest eigenvalues: [1] 77155261 72539793 69250173 67926819 66329224 64424568 62915333 62635906 [9] 62481406 61531767 Smallest eigenvalues: [1] 0.49168582 0.44511370 0.44113008 0.42213586 0.35589466 0.32327593 [7] 0.25261458 0.22836430 -0.03718705 -0.32728381 Largest eigenvalues: [1] 75632067 72783182 68743555 67575557 66314284 65541295 63360283 61907494 [9] 61346053 61154631 Smallest eigenvalues: [1] 0.5754385 0.5284635 0.5122090 0.4266025 0.3964567 0.3258635 [7] 0.3229003 0.2932079 0.2706647 -0.3307973 Largest eigenvalues: [1] 76273297 73188051 68835157 66577962 66160661 64817159 62394719 62226057 [9] 61418985 60972459 Smallest eigenvalues: [1] 0.4316791 0.4301878 0.4294169 0.4209674 0.3489428 0.3017923 [7] 0.2438169 0.1551130 0.1524928 -0.1097878 Largest eigenvalues: [1] 76796472 73058723 69081596 66801540 66754274 64839715 63134292 62528694 [9] 62082844 61914747 Smallest eigenvalues: [1] 0.52693423 0.42705024 0.38814423 0.33278257 0.22822342 0.20926477 [7] 0.19002762 -0.09751184 -0.15372031 -0.85328667 Largest eigenvalues: [1] 78206428 73818672 70015033 67645889 67365166 65319066 63773753 63312352 [9] 62957854 62486697 Smallest eigenvalues: [1] 0.5346416 0.5065598 0.4619060 0.3966006 0.3412903 0.2634656 [7] 0.2554226 0.2450997 -0.3910511 -0.4462226 Largest eigenvalues: [1] 74811730 72075892 68380355 66495942 65952974 64216149 62561081 62312758 [9] 61240852 61166290 Smallest eigenvalues: [1] 0.6764752 0.5722619 0.5525329 0.5152314 0.4612097 0.2178576 [7] 0.2056087 0.2001281 0.0693849 -0.2792403 Largest eigenvalues: [1] 75411431 73468368 69206157 67795269 66390033 65740601 63375192 63141253 [9] 61792418 61554280 Smallest eigenvalues: [1] 0.61958873 0.47505559 0.45934819 0.43075196 0.40352850 0.36104174 [7] 0.34576566 0.26638340 0.24576449 -0.04670816 Largest eigenvalues: [1] 76385710 73635296 68949514 67278367 67100741 65181825 62886132 62620811 [9] 62169196 61566930 Smallest eigenvalues: [1] 0.43851264 0.43052135 0.40936852 0.34033719 0.23375146 0.17150987 [7] 0.03583367 -0.01091468 -1.58063976 -5.34231098 Largest eigenvalues: [1] 76367503 72071484 67956823 66047230 66045958 64214099 62211047 62041353 [9] 61214424 61082679 Smallest eigenvalues: [1] 0.5379096 0.5047268 0.3660185 0.3403853 0.2793852 0.2646597 [7] 0.2399460 0.2164335 0.1727535 -0.1641470 Largest eigenvalues: [1] 74407904 72311339 68923313 66291952 66205309 64455215 62471934 62332369 [9] 61322164 61148691 Smallest eigenvalues: [1] 0.6329424 0.6321771 0.6111984 0.5425904 0.5185075 0.4791763 [7] 0.4058807 0.2314654 0.1938446 -0.1626324 Largest eigenvalues: [1] 75395840 72177689 68087365 66497674 66326170 64194774 62292133 62172689 [9] 61332746 60786486 Smallest eigenvalues: [1] 0.52140079 0.47864039 0.47176709 0.40635498 0.36266667 0.26839433 [7] 0.24524689 0.14545060 0.04393903 -0.19839482 Largest eigenvalues: [1] 76315724 73052585 68704411 67785933 66714240 64583243 62709020 62624962 [9] 62558368 61173891 Smallest eigenvalues: [1] 0.37495057 0.34634444 0.33256559 0.30153222 0.28124835 0.23766733 [7] 0.23112482 0.22683800 0.20653937 -0.05645087 Largest eigenvalues: [1] 78322768 72043838 68954446 67750771 66055037 64330911 62791647 62310125 [9] 62184150 61406664 Smallest eigenvalues: [1] 0.46671237 0.44859994 0.44787846 0.39241518 0.30106268 0.26946639 [7] 0.16228008 0.15265390 -0.03588098 -0.86799539 Largest eigenvalues: [1] 77811691 72687101 68643073 68057620 66488840 64202955 63335451 62663561 [9] 62588523 61486338 Smallest eigenvalues: [1] 0.5738878 0.5212360 0.5026136 0.4937408 0.4736657 0.3469288 [7] 0.3262566 0.2486761 0.1451266 -1.3156564 Largest eigenvalues: [1] 76823527 71984241 68405254 66851240 65815352 63922274 62160381 61951557 [9] 61186924 60412151 Smallest eigenvalues: [1] 0.56686551 0.51874500 0.50717794 0.39833543 0.34924779 0.34638839 [7] 0.33816218 0.30676061 0.06802969 -0.28199406 Largest eigenvalues: [1] 76694909 72760935 68669257 67173003 66158832 64467593 62413275 62019350 [9] 61540983 60484878 Smallest eigenvalues: [1] 0.60699465 0.49105293 0.45285170 0.43007205 0.40741436 0.37120272 [7] 0.30887573 0.25304342 0.22924822 -0.02335191 Largest eigenvalues: [1] 75630329 72039281 68460823 66440300 66342896 64577474 62533060 61872744 [9] 61537119 60921486 Smallest eigenvalues: [1] 0.47430805 0.42336787 0.37840012 0.37463387 0.25035398 0.23057415 [7] 0.16635048 0.11260586 0.07523869 -0.11008967 Largest eigenvalues: [1] 76811195 72636970 69644068 67371222 66856558 65161956 62894580 62664372 [9] 62385395 61542000 Smallest eigenvalues: [1] 0.56192331 0.52523709 0.47296856 0.44851631 0.42596966 0.38270716 [7] 0.33885588 0.26087053 -0.03636955 -0.12855814 Largest eigenvalues: [1] 79316301 72270075 69483623 68262428 65986177 63947730 63495571 62697827 [9] 61949502 61577226 Smallest eigenvalues: [1] 0.5214146 0.4373091 0.4238392 0.4169651 0.3998511 0.3966686 [7] 0.3821218 0.3608148 0.0233280 -2.1786051 Largest eigenvalues: [1] 79051855 72459514 69001420 68565304 65829869 64081239 63605455 62321077 [9] 61778802 60965545 Smallest eigenvalues: [1] 0.4238450 0.3850903 0.3806719 0.3628110 0.3259736 0.3090765 [7] 0.2435713 0.2337977 0.1739058 -0.8904169 Largest eigenvalues: [1] 79534900 72920690 69579358 68982976 66146969 64307659 64114858 62624933 [9] 62103010 61323642 Smallest eigenvalues: [1] 0.4417435 0.4086389 0.4033034 0.2792020 0.2675175 0.2356599 [7] 0.2091957 0.1563795 0.1335076 -0.2107113 Largest eigenvalues: [1] 77184360 72696971 69159634 67501565 66896864 64890073 63539650 62803729 [9] 62572832 62017221 Smallest eigenvalues: [1] 0.6624453 0.6303578 0.6196134 0.5564708 0.5177692 0.4249571 [7] 0.3867329 0.1604138 0.1172345 -0.3902365 Largest eigenvalues: [1] 77040916 72650381 68943252 66814516 66741803 64929454 62693032 62587944 [9] 62011911 61268522 Smallest eigenvalues: [1] 0.45798793 0.45633148 0.37774876 0.37496777 0.37379365 0.30929490 [7] 0.28899159 0.24799622 0.08377336 -1.11258283 Largest eigenvalues: [1] 78900277 73629670 69700503 68582907 66982432 65361294 63576306 62950253 [9] 62664983 61636778 Smallest eigenvalues: [1] 0.6305051 0.4387054 0.4292747 0.4200145 0.3931072 0.2590602 [7] 0.2176671 0.2016262 -1.0875164 -1.0981275 Largest eigenvalues: [1] 79705027 74033302 70491431 69229768 67045618 64924497 64247923 64116563 [9] 62920660 62655285 Smallest eigenvalues: [1] 0.48787339 0.44564366 0.37283063 0.34702816 0.28345017 0.19014642 [7] 0.11991021 0.10696743 0.07180644 -0.55819769 Largest eigenvalues: [1] 78053710 73620655 70112814 67536802 67209654 65754262 63633056 63034544 [9] 62891633 62083419 Smallest eigenvalues: [1] 0.5082068 0.4633876 0.4389805 0.4332896 0.3487568 0.3288734 [7] 0.3228620 0.2322629 0.1382711 -0.3830972 Largest eigenvalues: [1] 77648812 73413537 69064868 67527692 66770882 64888663 63106793 62497552 [9] 62287741 61387221 Smallest eigenvalues: [1] 0.47420501 0.47380065 0.44095983 0.36480024 0.21259658 0.20787040 [7] 0.17738861 0.15967101 0.01472700 -0.02465229 Largest eigenvalues: [1] 75704414 73851577 69597385 67979518 66366150 65747858 63231503 63199302 [9] 61770625 61616543 Smallest eigenvalues: [1] 0.53666510 0.53570212 0.50662900 0.43048219 0.35490832 0.32411047 [7] 0.27259041 0.17336792 0.13486057 -0.04425019 Largest eigenvalues: [1] 76495627 72438441 69061634 66776847 66702609 64915012 63071417 62293055 [9] 62002643 61154225 Smallest eigenvalues: [1] 0.60835550 0.54886199 0.54013265 0.49849366 0.46269301 0.42102675 [7] 0.38400003 0.25060351 0.11637300 -0.08452492 Largest eigenvalues: [1] 76732649 73587269 68994652 67363126 67252504 65238214 62985757 62814645 [9] 62194421 61700367
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.229381 | 0.846894 | 16.34333 | 0 | 2.066983 | 4.269703 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + steps + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
steps = steps_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_steps_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 596 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.55687112 0.53569714 0.50426534 0.45079293 0.45007921 0.44912612 [7] 0.37583368 0.11103673 -0.01388968 -0.18580991 Largest eigenvalues: [1] 65128131 60301836 57485971 56558063 54933725 53240486 52519780 51979198 [9] 51733698 50890918 Smallest eigenvalues: [1] 0.414116763 0.387579473 0.378678563 0.371295928 0.338374686 [6] 0.313321104 0.309448258 0.141811756 -0.009306981 -0.171816604 Largest eigenvalues: [1] 65341506 59947236 56968613 56278473 54917796 52984859 52496682 52442448 [9] 51434141 51384566 Smallest eigenvalues: [1] 0.60644245 0.56121131 0.46256413 0.44032827 0.40697927 0.39444046 [7] 0.34290363 0.26409122 -0.04566527 -0.05932885 Largest eigenvalues: [1] 64108753 60186149 57621320 55732571 55114963 53453615 52195941 51772330 [9] 51733262 51207729 Smallest eigenvalues: [1] 0.48783042 0.42729969 0.38378504 0.37758830 0.25824490 0.23982461 [7] 0.18355483 0.12728013 -0.03011679 -1.07840210 Largest eigenvalues: [1] 63422861 61109891 57765317 55934410 55395763 53999215 52790295 52485817 [9] 51927114 51676842 Smallest eigenvalues: [1] 0.504267900 0.492722818 0.380579481 0.280285809 0.271283633 [6] 0.245279758 0.195201247 0.003416523 -4.279198071 -21.485173449 Largest eigenvalues: [1] 63416652 59658973 56681350 55377681 54971927 53668047 51955144 51631036 [9] 51085226 50712610 Smallest eigenvalues: [1] 0.34925108 0.23008916 0.16079795 0.10828240 0.05681264 [6] -0.40148557 -0.69321495 -1.33484111 -3.94585907 -11.27616806 Largest eigenvalues: [1] 65232586 59878722 57362752 56087718 54785082 53209734 52179158 52031762 [9] 51479028 51186894 Smallest eigenvalues: [1] 0.440997342 0.412429781 0.342110671 0.304887786 0.296257523 [6] 0.228656580 0.085959578 0.043035705 0.007661383 -1.736909097 Largest eigenvalues: [1] 64426087 60693580 57322693 56107975 55716697 53909241 52800435 52075424 [9] 51767150 51484123 Smallest eigenvalues: [1] 0.4501320 0.4365989 0.3779659 0.3536999 0.3382276 0.3345129 [7] 0.2565055 0.1977048 0.1957531 -0.2255753 Largest eigenvalues: [1] 65080896 61056860 57712812 56213345 55545358 53927770 53021143 52197053 [9] 52103791 51815280 Smallest eigenvalues: [1] 0.47344605 0.36370195 0.33513862 0.32476445 0.32233421 0.31500958 [7] 0.22047040 -0.09114835 -0.29602937 -1.21915111 Largest eigenvalues: [1] 65352723 60563253 58131699 56782109 55181753 53954780 52680551 52488068 [9] 52252395 51853720 Smallest eigenvalues: [1] 0.4894155 0.4355029 0.4241096 0.3421384 0.3161329 0.2843101 [7] 0.2772782 0.2072198 0.1968273 -1.9607034 Largest eigenvalues: [1] 65224104 60201985 57300745 56341612 55372381 53829466 52422928 52384924 [9] 52252523 51382684 Smallest eigenvalues: [1] 0.40695360 0.36038905 0.29562369 0.29225967 0.24687806 0.18989229 [7] -0.09093593 -1.11431836 -1.59614066 -3.75925425 Largest eigenvalues: [1] 64938209 59906516 56584057 56532929 54557191 52752711 52532100 52226467 [9] 51736859 51295520 Smallest eigenvalues: [1] 0.4959405 0.4659263 0.3764014 0.3534696 0.2896080 0.2246971 [7] 0.2135307 0.2127684 -0.3342576 -0.4500901 Largest eigenvalues: [1] 63963617 59864066 57282662 55877880 54742138 53232050 52281182 51838132 [9] 51710608 51106206 Smallest eigenvalues: [1] 0.38111495 0.31020414 0.29966429 0.23838408 0.21337859 0.20601348 [7] 0.08933640 0.07373036 -0.13328462 -4.00107803 Largest eigenvalues: [1] 64574769 60469970 58072464 55696716 55386346 54136136 52779784 52164945 [9] 51936786 51768649 Smallest eigenvalues: [1] 0.55800055 0.53222857 0.47901164 0.45327221 0.40111130 0.29574129 [7] 0.28865336 0.21698533 -0.01837324 -0.08723218 Largest eigenvalues: [1] 64763631 60091526 57289727 55859550 55257864 53031663 52245414 52011088 [9] 51747918 51298262 Smallest eigenvalues: [1] 0.44555950 0.35855589 0.34644380 0.34254610 0.31386154 [6] 0.30381877 0.16489995 -0.02806064 -0.62321588 -10.73542989 Largest eigenvalues: [1] 65098445 60496720 57916559 56530651 55892263 54401973 52598333 52311894 [9] 52193945 51413150 Smallest eigenvalues: [1] 0.42884363 0.41326134 0.35288602 0.31155545 0.30340781 0.28770810 [7] 0.19576906 0.14889819 0.05327519 -0.39449121 Largest eigenvalues: [1] 64308146 61317997 57541652 56335300 56265408 54379653 53956661 52376686 [9] 52147255 52016770 Smallest eigenvalues: [1] 0.4977455 0.4652190 0.3768249 0.3524583 0.2692991 0.2287106 [7] 0.2221596 0.1675569 0.1574845 -5.5116755 Largest eigenvalues: [1] 63381151 59922187 57170124 55257217 54884088 53663842 52200231 52078116 [9] 51400733 51059013 Smallest eigenvalues: [1] 0.4074224 0.3968622 0.3530963 0.2555267 0.2474881 0.2263166 [7] 0.2006830 0.1595939 -1.6013676 -5.5512470 Largest eigenvalues: [1] 64932740 59777837 57214617 56597890 54838139 53365041 52598440 52224892 [9] 51547044 50832763 Smallest eigenvalues: [1] 0.5220158 0.4689755 0.4232338 0.2780233 0.2505749 0.2480184 [7] 0.2270590 0.1189813 -0.6327994 -2.5670336 Largest eigenvalues: [1] 65084496 59542378 56827508 56021559 54950602 53297069 52200860 52005525 [9] 51899353 51268144 Smallest eigenvalues: [1] 0.2373609 0.2035308 0.1836030 0.1749543 -0.7485899 -1.2278123 [7] -3.4175991 -4.4915799 -4.5950425 -29.3420945 Largest eigenvalues: [1] 66361761 59369288 57301796 56711763 54099806 53316077 52608739 51390608 [9] 51170823 50586295 Smallest eigenvalues: [1] 0.50033964 0.45222152 0.40967222 0.32697790 0.10749068 [6] 0.08785149 -0.80741622 -1.44425650 -1.64350508 -10.49660788 Largest eigenvalues: [1] 63411882 60145516 56848071 55306598 55038747 53516827 52047792 51431854 [9] 50892719 50584103 Smallest eigenvalues: [1] 0.31150923 0.24619425 -0.03639436 -0.13244920 -0.14563683 -0.34485592 [7] -0.82018803 -0.96012485 -1.31702944 -2.22271195 Largest eigenvalues: [1] 66582209 60594525 57924544 57325979 55106941 53443545 53250426 52996640 [9] 51720950 51555079 Smallest eigenvalues: [1] 0.42886063 0.31631996 0.23713970 0.17590678 0.17500220 0.05010624 [7] 0.04544901 -0.01995707 -0.02289414 -3.01281466 Largest eigenvalues: [1] 65822252 60558361 57030909 56817179 55176836 53528394 52780736 52295592 [9] 52069992 51326101 Smallest eigenvalues: [1] 0.447146989 0.324025542 0.230563255 0.184923170 0.143353772 [6] 0.022862673 0.008039507 -2.121552625 -4.611530489 -6.806283202 Largest eigenvalues: [1] 63486616 59936176 57126829 55413115 54947221 53841226 52468866 51859666 [9] 51046936 50944832 Smallest eigenvalues: [1] 0.5142570 0.4758353 0.4264181 0.3762573 0.3063389 0.2692648 [7] 0.2392225 0.2137642 0.1945631 -0.6363635 Largest eigenvalues: [1] 64350185 61545702 58157471 56681847 55718662 54089246 52847029 52583822 [9] 52530699 51844875 Smallest eigenvalues: [1] 0.4374744 0.3992590 0.3849865 0.3492341 0.3307163 0.2983505 [7] 0.2186151 0.2003982 0.1124304 -0.7832771 Largest eigenvalues: [1] 64890640 61154660 58079071 56477370 56474882 54768964 53110028 52649256 [9] 52373044 51770007 Smallest eigenvalues: [1] 0.56421538 0.55752709 0.55664422 0.52688970 0.47180185 0.45960272 [7] 0.42816317 0.24870440 0.09815254 -0.19587481 Largest eigenvalues: [1] 65254606 60332741 57564846 56789798 54984187 53174178 52694222 51836743 [9] 51564777 50801067 Smallest eigenvalues: [1] 0.4205212 0.3674697 0.3267711 0.3218011 0.2654311 0.2497190 [7] 0.2466122 0.1998852 -0.7425969 -0.7772123 Largest eigenvalues: [1] 64812466 60273890 57064084 55990185 54948271 53392165 52032082 51987480 [9] 51623529 50953563 Smallest eigenvalues: [1] 0.35707207 0.32921013 0.27030210 0.26479053 -0.01234182 [6] -0.34181885 -3.10642187 -3.94843410 -9.80614986 -20.53973229 Largest eigenvalues: [1] 63297274 60393515 57209411 55756904 54896577 53166682 51970749 51817363 [9] 51740014 50828502 Smallest eigenvalues: [1] 0.5175133 0.4495037 0.4493913 0.4063343 0.3834703 0.3451151 [7] 0.2864278 0.2171597 0.2043953 -0.9392579 Largest eigenvalues: [1] 63962432 59816902 57302680 55249458 54486613 53023524 51980301 51414788 [9] 51170903 51131405 Smallest eigenvalues: [1] 0.50530142 0.41933493 0.40986760 0.27762105 0.25989676 0.24079429 [7] 0.15032521 0.02589387 -0.56884545 -4.70105351 Largest eigenvalues: [1] 65182516 59415329 56789268 55701408 54775762 53196347 51916299 51662484 [9] 51476359 50698181 Smallest eigenvalues: [1] 0.32356859 0.27967519 0.24517137 0.14298235 0.12618440 [6] -0.04201492 -4.11753473 -7.15476213 -14.51420748 -23.34458119 Largest eigenvalues: [1] 65820940 60471866 57911199 56791327 55161976 53472017 53040179 52805807 [9] 52048815 51956339 Smallest eigenvalues: [1] 0.37316140 0.36300033 0.25392025 0.25376290 0.25240567 0.20462237 [7] 0.03507761 -0.73317526 -1.04810045 -1.89526955 Largest eigenvalues: [1] 63260942 60530009 57808460 55825974 55100184 54463211 52809452 52497301 [9] 51469800 51179138 Smallest eigenvalues: [1] 0.29226497 0.25172135 0.22835484 0.17392128 0.07286766 -0.28217109 [7] -0.41373482 -0.83910045 -0.85686019 -1.20358330 Largest eigenvalues: [1] 65044269 59895276 57226892 56088957 55088512 53265286 52149720 52113740 [9] 51545297 51205620 Smallest eigenvalues: [1] 0.4478490 0.4189495 0.3725930 0.3474046 0.3211359 0.2678841 [7] 0.2567332 0.1185031 0.1022033 -0.6812989 Largest eigenvalues: [1] 63606247 59186747 57049402 55599175 54504143 52953180 51656158 51552367 [9] 51481831 50633547 Smallest eigenvalues: [1] 0.366817117 0.308699385 0.302670629 0.103656940 -0.008364085 [6] -0.054458435 -0.241645060 -1.013964921 -27.473403519 -53.823053513 Largest eigenvalues: [1] 61191986 59094498 56176233 54883639 54187020 52970589 51843654 50897582 [9] 50181656 49987469 Smallest eigenvalues: [1] 0.37929030 0.28229472 0.27060161 0.23332496 0.13353378 0.01769273 [7] -0.04359874 -0.52088314 -3.14103586 -3.45004325 Largest eigenvalues: [1] 64928846 61126488 58270512 55700657 55616981 54281038 52518675 52031029 [9] 51731769 51485685 Smallest eigenvalues: [1] 0.44207729 0.39741612 0.39478884 0.31490376 0.27290942 0.18846113 [7] 0.03118364 -0.37961401 -0.62435106 -7.57848891 Largest eigenvalues: [1] 63037909 60635596 57433418 55560252 55485423 54186659 52550081 52127120 [9] 51418896 51024559 Smallest eigenvalues: [1] 0.3757570 0.3734703 0.3075687 0.2105842 0.1971154 0.1915167 [7] 0.1705802 0.1499399 0.1365020 -0.3246430 Largest eigenvalues: [1] 63090313 60402108 57302651 55505550 55259369 53643226 52820723 51995209 [9] 51644508 51427010 Smallest eigenvalues: [1] 0.5004582363 0.4677769404 0.4175565730 0.3934018498 0.3446933755 [6] 0.3339203213 0.3123174852 0.1966392916 -0.0006498299 -0.1149381748 Largest eigenvalues: [1] 64910078 61114409 57800651 56693335 55662039 54066405 52832887 52658092 [9] 52430728 51864759 Smallest eigenvalues: [1] 0.42893636 0.42508809 0.28301472 0.26806698 0.26663556 0.15846928 [7] 0.04607751 -0.17602037 -0.61911520 -0.69753981 Largest eigenvalues: [1] 62456339 59522829 56222054 55441612 54462673 52726942 51877080 51563276 [9] 51051773 50272218 Smallest eigenvalues: [1] 0.4894173 0.4633274 0.4321226 0.3420420 0.3268126 0.3031480 [7] 0.2112384 0.1694344 0.1211073 -0.4119919 Largest eigenvalues: [1] 64663687 60013593 57632066 56035560 55360168 53925969 52236725 52167398 [9] 51994886 51504129 Smallest eigenvalues: [1] 0.5727118 0.4790871 0.4767965 0.3858702 0.3735021 0.3611180 [7] 0.3558342 0.3087649 0.2924612 -0.7861576 Largest eigenvalues: [1] 64583895 60680502 57781192 56258924 55770917 54208541 52430470 52244122 [9] 52232199 51350791 Smallest eigenvalues: [1] 0.29338469 0.27420392 0.13254373 0.09721057 0.04793512 0.02019989 [7] -0.02937095 -0.81876192 -1.06515388 -3.32199415 Largest eigenvalues: [1] 64571381 60191796 56704498 56329417 55352128 53351106 52584919 52297363 [9] 52247966 51266410 Smallest eigenvalues: [1] 0.38422846 0.29566629 0.29526793 0.21934122 0.17661412 0.15617584 [7] 0.11950021 -0.02736394 -1.21608458 -6.66204627 Largest eigenvalues: [1] 64096711 58864039 56525972 55883897 54040246 52311477 51805215 51308204 [9] 51082181 50019992 Smallest eigenvalues: [1] 0.4306284 0.4281921 0.4254483 0.4215927 0.3606504 0.2962655 [7] 0.2712279 0.2479106 0.2145853 -0.1993490 Largest eigenvalues: [1] 61898313 59884704 56945231 55130839 54731281 53531303 52169263 51525367 [9] 50789389 50582759 Smallest eigenvalues: [1] 0.4200911 0.4082382 0.3926899 0.3717099 0.2662142 0.2190207 [7] 0.1680343 0.1418466 -0.9401058 -3.7003649 Largest eigenvalues: [1] 66559080 60630818 57455306 56486817 55395057 53745658 52602166 52477638 [9] 51847353 51721052 Smallest eigenvalues: [1] 0.3885635 0.3335561 0.3165416 0.3067927 0.2583692 0.2180735 [7] 0.1945838 0.1756398 -0.5093009 -0.5216461 Largest eigenvalues: [1] 64637448 60799634 58274546 55843795 55666532 54296734 52808288 52501305 [9] 51839164 51584826 Smallest eigenvalues: [1] 0.62921028 0.61213362 0.55685992 0.55663502 0.48811402 0.42769164 [7] 0.37711107 0.24052497 0.08135995 -0.30148987 Largest eigenvalues: [1] 65307649 60424549 57535552 56476860 54908540 53127783 52600814 52184804 [9] 51353414 50953242 Smallest eigenvalues: [1] 0.4940349 0.4148464 0.4017195 0.3607420 0.3544056 0.3437997 [7] 0.3300890 0.2178246 0.1822510 -0.7168477 Largest eigenvalues: [1] 63237064 59881546 57025049 55212974 55055675 53431689 51760286 51728149 [9] 51207105 50956947 Smallest eigenvalues: [1] 0.4339095 0.3762701 0.3644910 0.3296540 0.3066297 0.2596743 [7] 0.2540064 0.2046422 -3.5255256 -6.1202354 Largest eigenvalues: [1] 65307576 60002497 57237961 57194643 54581906 53149487 52914004 52078957 [9] 51958575 51138392 Smallest eigenvalues: [1] 0.5409622 0.4566514 0.4437517 0.4334861 0.4111928 0.2600885 [7] 0.2229195 0.1329756 0.0141318 -1.2802341 Largest eigenvalues: [1] 65138502 61041128 58122737 56844557 55408092 53466789 53063749 52713232 [9] 51888007 51770388 Smallest eigenvalues: [1] 0.529785916 0.523294080 0.512311540 0.448145987 0.386795870 [6] 0.352477961 0.333146952 0.263928439 0.253707046 -0.008032498 Largest eigenvalues: [1] 64300050 60671379 57693389 56130887 55818194 54529858 52926283 52112752 [9] 52003261 51453048 Smallest eigenvalues: [1] 0.43807672 0.36899806 0.34642450 0.26440199 0.24571534 0.12937061 [7] 0.01600913 -0.35984653 -0.82246332 -1.44659688 Largest eigenvalues: [1] 64922702 60638583 58137692 56473698 55134241 53563983 52770642 52529513 [9] 52142465 51851146 Smallest eigenvalues: [1] 0.5464070 0.5408620 0.4847972 0.4526939 0.3574238 0.3560562 [7] 0.3387780 0.2565086 0.1040409 -0.4622915 Largest eigenvalues: [1] 65285620 59864009 56941939 56453727 54809409 52833551 52428444 52106885 [9] 51591950 51179410 Smallest eigenvalues: [1] 0.5795934 0.5231061 0.4924282 0.4198396 0.3977189 0.3756215 [7] 0.3230170 0.3163818 0.2793956 -0.1175031 Largest eigenvalues: [1] 64237753 60497364 57646620 55903064 55433126 53721747 51793706 51755625 [9] 51620744 50719989 Smallest eigenvalues: [1] 0.4442047 0.4383072 0.3958422 0.3793990 0.3267505 0.2727223 [7] 0.2713087 0.1411989 -0.7821975 -2.1247937 Largest eigenvalues: [1] 62786351 60124673 56979890 55306766 54960093 53261006 51987015 51973627 [9] 51098465 50979871 Smallest eigenvalues: [1] 0.52077886 0.49876598 0.48560069 0.41178838 0.37660218 0.33909050 [7] 0.25761768 0.18956798 0.09143721 -0.12658351 Largest eigenvalues: [1] 62200625 59586788 56697758 55295604 54399359 53454450 51729831 51645731 [9] 50513054 50345127 Smallest eigenvalues: [1] 0.4833877 0.4487874 0.3642969 0.3582604 0.3234725 0.2850042 [7] 0.2837291 0.1549455 0.1166377 -1.6427620 Largest eigenvalues: [1] 63570500 59615578 56824923 55350516 55104913 53428982 52434907 51888519 [9] 51501994 51273157 Smallest eigenvalues: [1] 0.4610588 0.4476073 0.4152041 0.2880318 0.2828920 0.2346105 [7] 0.2121308 -0.2061981 -0.8369581 -5.1849205 Largest eigenvalues: [1] 65592710 60421501 57753963 56935015 54685234 53285151 53002233 52118460 [9] 51496817 51157625 Smallest eigenvalues: [1] 0.4749086 0.4583713 0.4416734 0.4012094 0.2871016 0.2540906 [7] 0.2431543 0.2330525 0.2182223 -1.0845595 Largest eigenvalues: [1] 64313503 60130081 57156629 56088696 55145242 53619070 52484156 52017336 [9] 51992416 51510113 Smallest eigenvalues: [1] 0.40661740 0.39977450 0.35001365 0.28207737 0.26227096 0.23448724 [7] 0.21981857 0.21588404 0.08300476 -5.32097231 Largest eigenvalues: [1] 64882170 61110112 58412171 56173023 55855630 54455208 52515092 52370432 [9] 52076450 51603479 Smallest eigenvalues: [1] 0.4028769 0.3611067 0.3268382 0.2607294 0.2589110 0.1960836 [7] 0.1926653 0.1755897 0.1153372 -2.1516945 Largest eigenvalues: [1] 65543612 60537830 57751143 56637878 55279459 53752519 52545734 52220830 [9] 52047836 51312755 Smallest eigenvalues: [1] 0.496872340 0.314472066 0.303361469 0.299760573 0.223741512 [6] 0.180105937 -0.009718017 -0.233019380 -1.574875006 -1.806591585 Largest eigenvalues: [1] 62791170 59691242 56940123 55314304 54901898 53682569 52143773 52116159 [9] 51077011 50897653 Smallest eigenvalues: [1] 0.40291080 0.40079374 0.34784687 0.29734893 0.20029571 [6] 0.13859035 0.08521309 -0.02655003 -1.10552199 -17.82229237 Largest eigenvalues: [1] 64991724 59869275 56727952 56509970 55008326 53378814 52416319 51948472 [9] 51719625 51019982 Smallest eigenvalues: [1] 0.47215332 0.43549486 0.42841373 0.34674341 0.32663521 0.31044831 [7] 0.29070554 0.26323988 0.15073677 -0.02575701 Largest eigenvalues: [1] 64615516 60407232 57838657 56351142 55284822 53969586 52292664 52224104 [9] 52047168 51225406 Smallest eigenvalues: [1] 0.5690613 0.5205353 0.4330237 0.3823208 0.3110412 0.2667287 [7] 0.2504866 0.2403642 0.2242317 -1.5732473 Largest eigenvalues: [1] 65510103 60931571 58035151 56486548 55663633 54159916 52696003 52589097 [9] 52078788 51592138 Smallest eigenvalues: [1] 0.3825955193 0.3465771545 0.3266057443 0.2917143789 0.2804264278 [6] 0.2161354287 0.1955692611 0.1806341677 0.0001922657 -1.9903300286 Largest eigenvalues: [1] 65877671 59820381 57162904 56583631 54712230 53427067 52631425 51977859 [9] 51857543 51158048 Smallest eigenvalues: [1] 0.4631269 0.4420274 0.4352148 0.4124177 0.3447332 0.2811365 [7] 0.2540594 0.2386270 0.2346326 -0.3102671 Largest eigenvalues: [1] 65459730 60789418 58025229 56682454 56094863 54497776 52666601 52422671 [9] 52350156 51419882 Smallest eigenvalues: [1] 0.55595527 0.42255741 0.38889732 0.37790478 0.36312972 0.33262057 [7] 0.29156613 0.22392322 -0.08571046 -1.89131944 Largest eigenvalues: [1] 66402625 60769644 58049245 57203154 55161122 53588053 53333340 52393701 [9] 51952523 51588469 Smallest eigenvalues: [1] 0.32334565 0.31470741 0.30558009 0.25747671 0.22075442 [6] 0.16445292 0.10399909 0.08779512 -2.68437498 -12.41718633 Largest eigenvalues: [1] 63950819 60559943 57214921 55841486 55799538 54107813 52962771 52257269 [9] 52009351 51747433 Smallest eigenvalues: [1] 0.4627924 0.4515449 0.3483190 0.3441082 0.3022074 0.1902092 [7] 0.1689880 0.1487121 -0.3972390 -1.0250360 Largest eigenvalues: [1] 64986232 59629971 57078285 56515258 54264181 52742541 52502388 51462965 [9] 51240974 50412621 Smallest eigenvalues: [1] 0.47440064 0.45541880 0.36783967 0.32543219 0.28070597 0.25383126 [7] 0.03064683 -0.10842933 -0.21209974 -0.61047971 Largest eigenvalues: [1] 64645633 60839636 58195016 56341965 55508687 54048645 53003425 52335633 [9] 52271694 52153192 Smallest eigenvalues: [1] 0.52860711 0.50602432 0.44910439 0.38096836 0.36973862 0.36913605 [7] 0.33458888 0.25560171 0.03730179 -0.17843664 Largest eigenvalues: [1] 65333169 60250177 57689418 56398985 55541478 53517456 52659321 52163232 [9] 51793067 51127497 Smallest eigenvalues: [1] 0.4684539 0.3580603 0.3500467 0.3371653 0.2599890 0.2316874 [7] 0.1971039 0.1581134 0.1546257 -0.3412086 Largest eigenvalues: [1] 63708269 61347639 57775485 56367958 55296870 53851974 52846802 52281484 [9] 52256330 51908839 Smallest eigenvalues: [1] 0.4085848 0.3696719 0.3610226 0.3368879 0.3106543 0.3027610 [7] 0.2210889 0.1492056 -1.0504551 -5.6213128 Largest eigenvalues: [1] 66336823 60904467 57303363 57290213 55683677 53842934 53303311 52475593 [9] 52271664 51532338 Smallest eigenvalues: [1] 0.4341795 0.4288170 0.3465456 0.3351632 0.2858962 0.2819554 [7] -0.3915791 -1.4953083 -2.0059460 -3.1763198 Largest eigenvalues: [1] 64445338 59740033 56749525 56383904 54603763 52822963 52156069 52119598 [9] 51610916 51150374 Smallest eigenvalues: [1] 0.47414499 0.39191008 0.31645965 0.30515301 0.22465847 0.20404176 [7] 0.15944242 0.15356296 -0.06557322 -0.57799704 Largest eigenvalues: [1] 66287677 60150487 57975260 55944272 54914106 53113036 52403025 51771474 [9] 51334794 51009736 Smallest eigenvalues: [1] 0.52262947 0.49456098 0.45228167 0.36379259 0.26541493 0.18972028 [7] 0.17823375 0.16369692 0.06868716 -1.46927422 Largest eigenvalues: [1] 65567238 61305572 58126318 56905750 55951857 54340055 53532821 52898953 [9] 52433060 52141495 Smallest eigenvalues: [1] 0.359491317 0.316725401 0.303188397 0.087395327 0.084915891 [6] 0.073125534 -0.009058002 -0.090305707 -3.404361370 -23.124767119 Largest eigenvalues: [1] 63575839 59845969 57026909 55610680 54863587 53258768 52019940 51796018 [9] 51581616 51018487 Smallest eigenvalues: [1] 0.58847563 0.58439112 0.48304140 0.43891327 0.34503924 0.32082815 [7] 0.28543576 0.21930659 0.19753695 -0.01494624 Largest eigenvalues: [1] 63410234 60651897 57238111 55887118 54964182 53962264 52007807 51828169 [9] 51076926 50786357 Smallest eigenvalues: [1] 0.4829039 0.4411541 0.4402740 0.3638287 0.2803197 0.2758135 [7] -0.2509864 -3.2133647 -4.5349836 -9.8932472 Largest eigenvalues: [1] 65517617 60219811 57731374 56602001 54950426 53345087 52431123 52367019 [9] 52007936 51595635 Smallest eigenvalues: [1] 0.49022287 0.44842297 0.42023439 0.41845079 0.33591054 0.26391905 [7] 0.19665207 -0.06565401 -0.16904697 -0.64212192 Largest eigenvalues: [1] 65936136 61016526 58335240 56706049 55716509 54046302 53107029 52657558 [9] 52526708 52260459 Smallest eigenvalues: [1] 0.5091731 0.4988933 0.4635476 0.3837046 0.3553260 0.2483208 [7] 0.1870440 0.1504206 -0.8252498 -6.4720725 Largest eigenvalues: [1] 64682522 59691224 56578733 56293903 54501255 52768861 52348300 51584484 [9] 51134778 50474530 Smallest eigenvalues: [1] 0.45716376 0.44675999 0.44032831 0.33661926 0.28228493 0.26023967 [7] 0.22095369 0.21544754 0.09446898 -0.55000765 Largest eigenvalues: [1] 62852535 59611108 56719973 54907857 54704344 53225484 51894505 51286076 [9] 50867526 50479107 Smallest eigenvalues: [1] 0.5566516 0.5497998 0.5371614 0.3926779 0.3920331 0.3496225 [7] 0.2891229 0.2354058 0.2290273 -0.1327787 Largest eigenvalues: [1] 64026025 60334355 57531186 55892878 55403885 53637280 52173797 52113138 [9] 52020071 51169166 Smallest eigenvalues: [1] 0.208202378 0.182164133 0.144571504 0.142474170 0.005658326 [6] -0.169415653 -0.271356775 -1.580269859 -13.101889962 -78.872866181 Largest eigenvalues: [1] 66394273 60468445 57821383 56866718 55128835 53975427 52694053 52554097 [9] 52415603 51878196 Smallest eigenvalues: [1] 0.47092887 0.39673917 0.37374886 0.30459197 0.30057850 0.20609619 [7] 0.16883538 0.05347199 -0.18556661 -0.52515644 Largest eigenvalues: [1] 66267447 60012662 57440091 56934727 54716480 53102366 52919398 52519317 [9] 51716136 51642043 Smallest eigenvalues: [1] 0.4870925 0.4201529 0.3524366 0.2707847 0.2662001 0.2362070 [7] 0.1981400 0.1886403 -0.2972681 -0.8451265 Largest eigenvalues: [1] 64679471 60412348 57557884 56391465 55367023 53888970 52440969 52436978 [9] 52241598 51370126 Smallest eigenvalues: [1] 0.47265321 0.43905638 0.40816087 0.37583259 0.35613690 0.30507054 [7] 0.29656979 0.26183338 0.07229652 -8.55325326 Largest eigenvalues: [1] 64839410 59716434 57199934 55814648 54969113 53564409 51983255 51906474 [9] 51384200 50492619 Smallest eigenvalues: [1] 0.36979219 0.34686253 0.34555022 0.32810270 0.24652984 0.23777955 [7] 0.21258142 0.18888686 0.09415171 -0.12239939 Largest eigenvalues: [1] 64259980 60668607 57842826 56267074 55672748 54229906 52488012 52195034 [9] 52095942 51540803 Smallest eigenvalues: [1] 0.39907536 0.31226478 0.30257437 0.26679892 0.24798533 0.17270903 [7] 0.15577954 0.06888145 0.05246053 -4.82363239 Largest eigenvalues: [1] 64351251 60520554 57336334 55747545 55538185 53856151 52942348 52023513 [9] 51955174 51699811 Smallest eigenvalues: [1] 0.3474004 0.2910447 0.2809725 0.2579128 0.2362527 0.2082751 [7] 0.1354125 -0.4076301 -3.9098781 -31.9134298 Largest eigenvalues: [1] 62694985 60815276 57242799 55497258 55429043 53740710 52322965 52236456 [9] 51405304 51218747 Smallest eigenvalues: [1] 0.5364960 0.4951196 0.3947891 0.3669663 0.2562212 0.2537648 [7] 0.2444996 0.2042522 -0.6174763 -3.8959178 Largest eigenvalues: [1] 62875462 60230210 57137033 55834864 54868885 54173293 52496332 52259350 [9] 51130352 50899563 Smallest eigenvalues: [1] 0.4465246 0.4187393 0.4138390 0.3424988 0.3028660 0.2348833 [7] 0.2290926 0.1843967 -0.4643544 -1.2229795 Largest eigenvalues: [1] 64878431 60316363 57878499 56217490 55196172 53368590 52499838 52204281 [9] 52132144 51655414 Smallest eigenvalues: [1] 0.5550184 0.4925687 0.4398451 0.3675941 0.3393733 0.3300166 [7] 0.3124096 0.2532578 0.2167142 -1.4547489 Largest eigenvalues: [1] 65295323 61190271 58376214 56778936 56205796 54762466 53112358 52765226 [9] 52708031 52165363 Smallest eigenvalues: [1] 0.5487436 0.4834131 0.3658915 0.3560428 0.2742899 0.2410628 [7] 0.2080247 0.1824926 0.1688730 -0.3472891 Largest eigenvalues: [1] 65570937 60577458 57523745 56275345 55179465 53432642 52427320 52371246 [9] 51966847 51391441 Smallest eigenvalues: [1] 0.36263043 0.26285390 0.21467178 0.20066332 0.17755906 0.11234721 [7] -0.03433613 -0.24992273 -0.76688587 -1.93874694 Largest eigenvalues: [1] 63100795 59980154 57178604 55229096 54794367 53171186 52243574 51402622 [9] 51215979 50989546 Smallest eigenvalues: [1] 0.5854559 0.5338526 0.4780691 0.4113695 0.3800489 0.3351957 [7] 0.3149091 0.2626591 0.1262375 -0.2925665 Largest eigenvalues: [1] 65093749 60060161 57003507 56282110 54911051 53245152 52235738 51565875 [9] 51484388 50738895 Smallest eigenvalues: [1] 0.54856036 0.44652671 0.42205664 0.40911038 0.39664975 0.35873767 [7] 0.24180036 0.18233704 -0.01858205 -0.03243652 Largest eigenvalues: [1] 61789060 59195945 56835602 54908764 54372150 53144543 51495767 51149699 [9] 50454339 50143290 Smallest eigenvalues: [1] 0.5048170 0.4690351 0.3860628 0.3852930 0.3769440 0.3563368 [7] 0.3276463 0.2590424 0.1667146 -0.3130165 Largest eigenvalues: [1] 63581401 59735741 57253250 55046782 54981326 53467902 51899533 51604730 [9] 51176779 51034629 Smallest eigenvalues: [1] 0.3991672 0.2842230 0.2575741 0.2406207 0.1655588 0.1486110 [7] -0.3444484 -1.9012484 -2.3645298 -2.9585352 Largest eigenvalues: [1] 65373108 60326961 58421759 55649203 55572464 54483705 52924234 52749572 [9] 51907739 51611065 Smallest eigenvalues: [1] 0.4044360 0.3700122 0.3380100 0.2570864 0.2236595 0.2106244 [7] 0.1774052 0.1771675 -0.1182595 -1.3200906 Largest eigenvalues: [1] 63751087 59379090 57384541 55940798 54228980 52896185 51845470 51772902 [9] 51440966 50758635 Smallest eigenvalues: [1] 0.4240648 0.4154436 0.3843697 0.3617769 0.3047146 0.3037085 [7] 0.2413956 -0.2370802 -0.9400032 -16.8047873 Largest eigenvalues: [1] 63141117 59976841 57069004 55410494 55046130 53513199 51849498 51615723 [9] 51341837 50760183 Smallest eigenvalues: [1] 0.41079383 0.40004016 0.39186619 0.23227558 0.21161560 0.19731791 [7] 0.16821605 0.04787791 -0.68951299 -1.15706176 Largest eigenvalues: [1] 64113510 59758975 57134690 56030406 54769663 53263617 52140142 51878629 [9] 51855517 50988740 Smallest eigenvalues: [1] 0.51208175 0.46359693 0.42486102 0.37572087 0.30933654 0.28308623 [7] 0.27534646 0.25562913 -0.01522618 -0.13450978 Largest eigenvalues: [1] 63243761 59677873 57194006 54835868 54688477 53195996 51913301 51409588 [9] 50953990 50600816 Smallest eigenvalues: [1] 0.45935445 0.34154354 0.29565289 0.25858665 0.24081906 0.14932325 [7] 0.08765192 -0.71586374 -0.78576505 -3.58276166 Largest eigenvalues: [1] 61512218 59879142 57012750 56100549 54153126 54005372 52779347 51680797 [9] 50796224 50727733 Smallest eigenvalues: [1] 0.4774591 0.4001589 0.3821787 0.3495943 0.3159623 0.2980202 [7] 0.2680286 0.1940331 -0.1651045 -0.9206551 Largest eigenvalues: [1] 62829746 59858801 57030816 55370418 54883636 53248419 51976502 51767486 [9] 51215671 50834441 Smallest eigenvalues: [1] 0.5364089 0.4862082 0.4772586 0.4040991 0.3261372 0.2856991 [7] 0.2835674 0.1768774 0.1304353 -0.3145844 Largest eigenvalues: [1] 65017426 60620211 57428741 55756017 55643786 53825153 52595311 52134562 [9] 51975601 51520368 Smallest eigenvalues: [1] 0.4434064 0.4395518 0.3525506 0.3152943 0.2793821 0.2435580 [7] 0.2241346 0.1813491 -0.1195115 -15.8819635 Largest eigenvalues: [1] 63780023 60756843 57376258 55969683 55884591 54167061 52593769 52061899 [9] 51930395 51541088 Smallest eigenvalues: [1] 0.49775391 0.45683374 0.42963565 0.42254716 0.39353727 0.36640863 [7] 0.26354221 0.23603533 0.03156872 -0.04335921 Largest eigenvalues: [1] 61901980 60916646 57579560 55714668 55083593 53938743 52196613 52184141 [9] 51310338 51048254 Smallest eigenvalues: [1] 0.56159057 0.53913405 0.51424397 0.44650607 0.35016410 0.27937198 [7] 0.24378028 0.20893485 0.16579020 -0.06604083 Largest eigenvalues: [1] 65844376 60113973 57449022 56172186 54977998 53108764 52469601 51776433 [9] 51695232 50984391 Smallest eigenvalues: [1] 0.329482750 0.299406788 0.292092786 0.276973612 0.272808284 [6] 0.270974185 0.115381683 0.009487049 -0.549922516 -0.705155022 Largest eigenvalues: [1] 64685045 61441070 58361160 56656261 55906751 54067509 53827662 52889651 [9] 52301327 52142906 Smallest eigenvalues: [1] 0.4926276 0.4252582 0.3247247 0.3203620 0.2782666 0.2696032 [7] 0.2059279 -0.4013662 -1.6710334 -1.9346226 Largest eigenvalues: [1] 67351440 60233791 57926855 57545911 55044970 53955029 53417343 52441801 [9] 51689901 51393581 Smallest eigenvalues: [1] 0.5028066 0.4598284 0.3406696 0.3371947 0.2921826 0.2635888 [7] 0.1489174 -0.2291181 -0.6490476 -2.8156941 Largest eigenvalues: [1] 64957544 59830827 56993061 55519536 54713315 53056823 52019789 51701506 [9] 51350618 51186215 Smallest eigenvalues: [1] 0.43220810 0.38636236 0.36793845 0.29676587 0.24093444 0.17698063 [7] 0.17273032 0.08978660 -0.05412637 -0.74001572 Largest eigenvalues: [1] 61429446 59978796 57185861 54760050 54529848 53254737 51503812 51435700 [9] 50664543 50507936 Smallest eigenvalues: [1] 0.5244092 0.5058885 0.4621850 0.3854107 0.2503368 0.2023883 [7] 0.1925894 0.1883249 0.1255680 -0.1032316 Largest eigenvalues: [1] 66179908 60869187 58040440 57176096 55447147 53294012 53278424 52891039 [9] 52145034 52021875 Smallest eigenvalues: [1] 0.5202558 0.4570686 0.4249764 0.4122457 0.4006000 0.2844237 [7] 0.1264753 0.1146851 -0.6090154 -2.8584040 Largest eigenvalues: [1] 65358649 60845581 57503041 57189387 55305721 53715620 52926826 52717604 [9] 52390730 51473703 Smallest eigenvalues: [1] 0.40069336 0.36172398 0.29709438 0.24853261 0.23074548 0.13644957 [7] -0.02623012 -0.03430969 -1.50780229 -4.77644863 Largest eigenvalues: [1] 65383779 61081726 57456667 56280965 56067542 54173237 53113389 52592965 [9] 52261687 51724421 Smallest eigenvalues: [1] 0.5783467 0.5492639 0.4903990 0.4173796 0.3279668 0.3085591 [7] 0.2959652 0.2462573 0.1167170 -2.4047407 Largest eigenvalues: [1] 64185674 60268420 57399950 56091047 55435454 53568602 52119494 52017087 [9] 51834072 50856751 Smallest eigenvalues: [1] 0.404408027 0.361504118 0.322585431 0.316639368 0.256264481 [6] 0.241559245 0.233504892 0.001168221 -0.218110778 -2.958904329 Largest eigenvalues: [1] 63701866 59692499 57263466 55558321 55446519 53794299 51962390 51444093 [9] 51404963 50602460 Smallest eigenvalues: [1] 0.14141059 0.13883528 -0.01223263 -0.06992098 -0.27988867 [6] -0.36051405 -1.96096052 -2.46839828 -11.83413634 -43.81338733 Largest eigenvalues: [1] 62199161 58971650 56477483 54873447 54773226 53060590 52022000 51548419 [9] 50768286 50530362 Smallest eigenvalues: [1] 0.5596169 0.5129533 0.4517147 0.4178378 0.4166618 0.3759475 [7] 0.2478439 0.1605925 0.1566739 -0.8638321 Largest eigenvalues: [1] 64035523 60093898 56724116 55475089 55351109 53642206 52267672 51508171 [9] 51468208 50642928 Smallest eigenvalues: [1] 0.3672976 0.3582742 0.3268389 0.3168456 0.2481369 0.1948450 [7] 0.1798662 0.1540865 -0.1478091 -1.9687731 Largest eigenvalues: [1] 64993133 59232486 56750690 56435837 54647901 53084906 52473206 51657555 [9] 50827152 50247334 Smallest eigenvalues: [1] 0.53147116 0.47976895 0.43886625 0.42846584 0.34837400 0.26593943 [7] 0.23471560 0.11366452 -0.04505713 -0.44611046 Largest eigenvalues: [1] 65526284 60435370 57556909 56102453 55558251 54012274 52720020 52218051 [9] 52025995 51845651 Smallest eigenvalues: [1] 0.42034369 0.40364548 0.39459076 0.33490726 0.31175138 0.22955885 [7] 0.19247885 0.05876411 -0.55990331 -1.69576473 Largest eigenvalues: [1] 62959051 60401462 57502049 55426037 55080809 53725410 52027710 51837241 [9] 51221604 50859656 Smallest eigenvalues: [1] 0.5025006 0.4720202 0.3527511 0.3397403 0.3050973 0.2037698 [7] 0.1891805 0.1258058 -0.1187030 -0.2852127 Largest eigenvalues: [1] 62515607 59677899 56844393 55429824 54515527 53506642 52132085 51852826 [9] 51097314 50737816 Smallest eigenvalues: [1] 0.51926145 0.51170863 0.46626228 0.38989217 0.35517676 0.30743454 [7] 0.28717816 0.25170314 0.20959253 -0.07195489 Largest eigenvalues: [1] 64242436 60696544 57806979 56507526 55320795 53738012 52824229 52588714 [9] 51989520 51672614 Smallest eigenvalues: [1] 0.4874746 0.4851699 0.4691206 0.4548387 0.3604664 0.2629032 [7] -0.6340852 -2.3046159 -6.1862649 -7.0992374 Largest eigenvalues: [1] 65753681 60174252 57398785 56975387 55001455 53806839 52848116 52223651 [9] 52066150 51212054 Smallest eigenvalues: [1] 0.58012936 0.49962223 0.48867993 0.47137868 0.30818961 0.24196721 [7] 0.11875628 -0.01764024 -0.43213145 -0.92839728 Largest eigenvalues: [1] 65178972 60608807 57775887 56451767 55418327 53924886 52511814 52460861 [9] 52074861 51417317 Smallest eigenvalues: [1] 0.5713031 0.4893699 0.4629765 0.4359207 0.2937939 0.2641157 [7] 0.2264419 0.2149273 -0.3567650 -2.5545332 Largest eigenvalues: [1] 64498337 60927996 57499315 55846139 55820113 54147413 52423565 52318910 [9] 51948004 51389174 Smallest eigenvalues: [1] 0.47055351 0.42229862 0.36186616 0.30449530 0.28785649 0.19015364 [7] 0.16544825 0.09250296 -1.63350141 -2.51834416 Largest eigenvalues: [1] 63199872 60542384 56927855 55889197 55012968 53321381 52226294 51762524 [9] 51589463 50796383 Smallest eigenvalues: [1] 0.45144524 0.41527873 0.39254774 0.34714667 0.29839453 0.28619885 [7] 0.22725457 -0.01124519 -0.26446983 -4.62512366 Largest eigenvalues: [1] 64994297 59885540 57501212 56111916 54768116 53144052 52247329 51908584 [9] 51810107 51072469 Smallest eigenvalues: [1] 0.5221984 0.5153910 0.3986418 0.3637976 0.3511665 0.3133694 [7] 0.3092224 0.1069729 -0.1353626 -0.2273444 Largest eigenvalues: [1] 63632313 60301474 57504686 55646723 55232314 53699852 52222529 51971896 [9] 51734877 51110215 Smallest eigenvalues: [1] 0.36893990 0.34833040 0.26851125 0.19541971 0.18012315 0.15154066 [7] 0.01548687 -0.14529901 -1.44733600 -5.27980262 Largest eigenvalues: [1] 64584752 59265620 56794742 54904093 54896497 53177404 52194779 51346174 [9] 51268553 50655812 Smallest eigenvalues: [1] 0.5005562 0.4350601 0.3985985 0.3589825 0.3191489 0.3152433 [7] 0.2819248 0.2816232 -1.1744147 -2.2487883 Largest eigenvalues: [1] 63258390 60136150 57391915 55932966 54774178 53418205 52233535 51767703 [9] 51708706 51262995 Smallest eigenvalues: [1] 0.4161857 0.3794335 0.2949921 0.2812370 0.2765253 0.2330728 [7] 0.1867400 -0.1271999 -0.2500482 -1.1780693 Largest eigenvalues: [1] 65012206 59858645 57710051 55985226 54691974 53519670 52272835 51753941 [9] 51546467 50862011 Smallest eigenvalues: [1] 0.28340625 0.26473059 0.22640351 0.19818052 0.18209428 0.16626746 [7] 0.13875135 0.06621314 0.02917200 -6.90873899 Largest eigenvalues: [1] 62533692 60307250 57342346 55705124 55118293 53550309 52350443 52240598 [9] 51511171 50876336 Smallest eigenvalues: [1] 0.34789506 0.33183102 0.32530547 0.29281073 0.28577904 0.24550149 [7] 0.17013453 0.12269745 0.06637537 -1.14009785 Largest eigenvalues: [1] 63673436 59531840 57031669 54877711 54758367 53278347 51649247 51184499 [9] 51044313 50506501 Smallest eigenvalues: [1] 0.4584325 0.4333225 0.3582918 0.3074576 0.2577924 0.2047237 [7] 0.1277437 -0.2867576 -1.5064289 -1.7980924 Largest eigenvalues: [1] 65047246 59765000 56987611 56364494 54935287 53213247 52519439 52317855 [9] 51811202 51326559 Smallest eigenvalues: [1] 0.42436130 0.33880340 0.32668277 0.32224075 0.25386499 0.13132488 [7] -0.08021959 -0.11743139 -0.50124035 -2.50257072 Largest eigenvalues: [1] 65956435 59844002 57127156 56680734 54633526 53119369 52722814 52249303 [9] 51474506 51449975 Smallest eigenvalues: [1] 0.5408122 0.5328957 0.4685447 0.4518159 0.4113033 0.3076544 [7] 0.2852938 0.2345276 0.1819165 -0.3397039 Largest eigenvalues: [1] 63885006 59473290 56404851 55146894 54695714 52995278 51761836 51342906 [9] 51188054 50433517 Smallest eigenvalues: [1] 0.466261262 0.437427203 0.425656048 0.362187336 0.317853143 [6] 0.262597809 0.226635319 0.207970545 -0.007786358 -0.036772981 Largest eigenvalues: [1] 63426416 59490417 56816766 54854058 54581901 53068476 51742847 51305115 [9] 51131445 50706530 Smallest eigenvalues: [1] 0.2415813945 0.2273253978 0.1937465863 0.0949346837 0.0007970694 [6] -0.2193448813 -0.2357611043 -0.4773698490 -3.0020953399 -3.6143458221 Largest eigenvalues: [1] 65962942 59593381 56912351 56315480 54465763 53061088 52371886 51813708 [9] 51414935 51009642 Smallest eigenvalues: [1] 0.4208521 0.4114712 0.4094289 0.3875344 0.3570711 0.2894118 [7] 0.2382051 -0.1251349 -0.2998943 -10.1987027 Largest eigenvalues: [1] 66525941 60483172 58522230 57011494 55203439 53257600 52947900 52283763 [9] 51852717 51548519 Smallest eigenvalues: [1] 0.434444305 0.426163973 0.363162587 0.238188011 0.207862423 [6] 0.177847395 0.152227120 0.147449057 0.059952267 -0.004589747 Largest eigenvalues: [1] 64596809 60786319 58214509 55878681 55757262 54436362 52489528 52123289 [9] 51981637 51254343 Smallest eigenvalues: [1] 0.40398985 0.28993059 0.28549567 0.24028940 0.13266274 0.09990907 [7] 0.06953243 -0.06564481 -0.63784257 -1.53078405 Largest eigenvalues: [1] 66224622 60461811 58040077 57317653 54917187 53433720 53173527 52862275 [9] 51955190 51575189 Smallest eigenvalues: [1] 0.5591208 0.5545035 0.4925871 0.4320349 0.4013075 0.3762457 [7] 0.3267191 0.2626546 0.2324088 -0.2916859 Largest eigenvalues: [1] 63720377 60116309 56886227 55638981 55201961 53382512 51634090 51620390 [9] 51556789 50679307 Smallest eigenvalues: [1] 0.38386540 0.37805452 0.34003551 0.30947581 0.29734050 [6] 0.28207337 0.18907370 0.04500703 -2.65313247 -14.95351402 Largest eigenvalues: [1] 63704824 60337250 57466047 56339276 55076040 53401728 52578461 52120606 [9] 51882475 51396763 Smallest eigenvalues: [1] 0.4322080 0.3281810 0.3183111 0.3109831 0.2714275 0.2617141 [7] 0.1612092 0.1309599 -0.2709503 -0.6854954 Largest eigenvalues: [1] 66329832 60112264 57838001 57157511 54927072 53635504 53252536 51998843 [9] 51804282 51054854 Smallest eigenvalues: [1] 0.35093574 0.30243586 0.28726189 0.25670133 0.15429107 0.14498640 [7] 0.09098483 -0.63385053 -1.29929390 -2.17960787 Largest eigenvalues: [1] 65016029 60177187 57095141 56634755 54961632 53364063 52603558 52547768 [9] 52031266 51598556 Smallest eigenvalues: [1] 0.49988845 0.47529707 0.46638092 0.27996576 0.23874053 0.22102476 [7] -0.01512170 -0.05025554 -0.44761128 -6.03208135 Largest eigenvalues: [1] 65890820 59874780 57192564 56264223 54589980 53014725 52485182 51567248 [9] 51520916 50563826 Smallest eigenvalues: [1] 0.46332744 0.38686915 0.38112818 0.32362992 0.24769322 0.24263068 [7] 0.06749610 0.06551303 -0.07890308 -0.13695690 Largest eigenvalues: [1] 65364059 60360038 57765094 56575277 54829272 53495650 52703738 52224807 [9] 51675941 51418518 Smallest eigenvalues: [1] 0.5305591 0.5075246 0.5062072 0.4537682 0.3536183 0.3294674 [7] 0.1676961 -0.2420098 -0.2697666 -14.8295587 Largest eigenvalues: [1] 64271153 59318899 56661006 55621899 54412221 52350677 51672772 51175722 [9] 51151279 50334644 Smallest eigenvalues: [1] 0.5743931 0.5493130 0.4858762 0.3989672 0.3351589 0.3212625 [7] 0.1091344 -0.1554295 -0.3136636 -1.4933195 Largest eigenvalues: [1] 65554236 59878330 56893590 56499604 54610444 52608177 52313604 51531469 [9] 51469158 50703526 Smallest eigenvalues: [1] 0.4495952 0.4399953 0.3982052 0.2379758 0.2186152 0.2003421 [7] 0.1730716 -0.2911618 -0.9133189 -1.9214797 Largest eigenvalues: [1] 66399867 60468573 57442417 57251624 55058784 53334485 53188891 52883126 [9] 51909840 51866537 Smallest eigenvalues: [1] 0.57176123 0.48574687 0.45428844 0.44243157 0.34061053 0.24904783 [7] 0.24869553 0.00457662 -0.04234539 -0.54184527 Largest eigenvalues: [1] 64195376 59920448 56952940 55197531 54745090 53153994 51827438 51711555 [9] 51345781 51106600 Smallest eigenvalues: [1] 0.4890101 0.4517800 0.3682552 0.2948088 0.2907152 0.1775843 [7] 0.1414866 -0.1117288 -0.1457795 -0.3714791 Largest eigenvalues: [1] 64154087 59832977 57256539 55768918 54677701 53306797 52063670 51851831 [9] 51729582 50827569 Smallest eigenvalues: [1] 0.4776109 0.4771060 0.4559435 0.4341539 0.3583790 0.2678629 [7] 0.2404454 0.1621592 -0.8983148 -3.1907707 Largest eigenvalues: [1] 64683767 60382793 56924640 56101382 55465793 53699398 51965701 51836344 [9] 51777165 50937773 Smallest eigenvalues: [1] 0.5306352 0.5296879 0.4059932 0.3156602 0.2887626 0.2886394 [7] 0.1939669 0.1453778 0.0907439 -0.4474634 Largest eigenvalues: [1] 66219979 60822738 58241203 56418207 55323593 53828261 52644160 52339004 [9] 51967982 51508198 Smallest eigenvalues: [1] 0.5450274 0.5271497 0.4839840 0.4417641 0.3843889 0.3784636 [7] 0.3370521 0.1922719 -0.6498761 -1.5077960 Largest eigenvalues: [1] 65381905 60151309 57165539 56532344 55271170 53777933 52439671 52199484 [9] 52016625 51332287 Smallest eigenvalues: [1] 0.4491205 0.3961330 0.3606945 0.3201626 0.2609917 0.2525351 [7] 0.2443581 0.2352861 0.1882568 -0.7495873 Largest eigenvalues: [1] 64515620 59885305 56611753 55923642 54765470 53171315 51971075 51924063 [9] 51505105 50861641 Smallest eigenvalues: [1] 0.53308618 0.51744240 0.47585514 0.44785083 0.27852202 0.26670976 [7] 0.01367621 -0.01091271 -0.05497936 -2.89193457 Largest eigenvalues: [1] 65559979 60824817 57468016 55944090 55426795 53507889 52062479 51953165 [9] 51683793 51213346 Smallest eigenvalues: [1] 0.4309154 0.4216400 0.3656186 0.3599604 0.2927533 0.1678212 [7] -0.2632419 -0.7448668 -5.6835426 -13.8155333 Largest eigenvalues: [1] 66631900 60485496 58202582 57637510 54838726 53680894 53559720 52182750 [9] 51808686 51304561 Smallest eigenvalues: [1] 0.4398044 0.4323594 0.4234483 0.4209823 0.3904476 0.3623953 [7] 0.3205402 0.2543731 0.2331397 -26.3787623 Largest eigenvalues: [1] 64380217 59436844 56951791 56370705 54485346 52395617 52324390 52072265 [9] 51112143 50749537 Smallest eigenvalues: [1] 0.4769435 0.4730963 0.4114147 0.4008876 0.3778841 0.3272200 [7] 0.3162803 0.2118835 0.1100390 -1.8263022 Largest eigenvalues: [1] 64237505 60185987 57341417 55507893 55476112 53835862 51955261 51623677 [9] 51390341 50493087 Smallest eigenvalues: [1] 0.39625962 0.38157149 0.35342311 0.32583066 0.27074997 0.20847047 [7] -0.02167151 -0.17127891 -1.64305769 -2.80552804 Largest eigenvalues: [1] 65800277 60402343 57493645 56499415 55430630 53998070 52533358 52042311 [9] 51899116 50678653 Smallest eigenvalues: [1] 0.4832357 0.4332341 0.3803877 0.3701274 0.2927207 0.2530939 [7] 0.2465986 0.1726147 0.1341766 -0.4302989 Largest eigenvalues: [1] 64348332 60346133 57329240 56131624 55304682 53606162 52421312 52094844 [9] 51891369 51391340 Smallest eigenvalues: [1] 0.3689468 0.3574100 0.2452902 0.2289294 0.2216702 0.1257119 [7] -0.2730172 -0.6618811 -11.2429554 -16.1895911 Largest eigenvalues: [1] 65383593 59876893 57708685 55999810 55068015 53790423 52592117 52070824 [9] 52061073 51712467 Smallest eigenvalues: [1] 0.5406926 0.4697975 0.4517916 0.3750419 0.3056596 0.2682609 [7] 0.2283717 0.0210087 -0.1077770 -0.7328168 Largest eigenvalues: [1] 65498816 60246536 57965849 56772044 54864376 53246998 52784297 52048504 [9] 51842346 51274974 Smallest eigenvalues: [1] 0.54072058 0.52944273 0.43453421 0.39734882 0.33277288 0.16204473 [7] 0.15650868 0.07111315 -0.05915046 -6.19028250 Largest eigenvalues: [1] 64265374 59415228 56794181 55292918 54604631 53005091 51530621 51449540 [9] 51352219 50541916 Smallest eigenvalues: [1] 0.58651710 0.50571635 0.42750083 0.40600214 0.34097664 0.21093217 [7] 0.16199785 0.07832537 0.05664466 -0.59843557 Largest eigenvalues: [1] 63659433 60535382 57840866 55187611 55045144 53812851 51995940 51942472 [9] 51226687 51010547 Smallest eigenvalues: [1] 0.49021341 0.42461715 0.38762597 0.38303786 0.33617703 0.29306333 [7] 0.20388292 0.09266713 -0.08945048 -1.83237952 Largest eigenvalues: [1] 65186530 60356009 58081255 55798651 55443708 53714582 52488709 52134078 [9] 52006769 51546137 Smallest eigenvalues: [1] 0.36056382 0.34021378 0.29258483 0.28240462 0.24689612 0.17544780 [7] 0.09905085 0.08256006 -1.30397905 -1.98239575 Largest eigenvalues: [1] 66244544 60615705 58023050 56666242 55053661 53661261 52728561 52672522 [9] 51980704 51824708 Smallest eigenvalues: [1] 0.4778597 0.4435899 0.4068742 0.4062279 0.3787896 0.3586641 [7] 0.3158504 0.1870563 0.1222329 -0.1793295 Largest eigenvalues: [1] 61909813 59834985 56839004 54916578 54615913 53405222 51970260 51209453 [9] 50670842 50430270 Smallest eigenvalues: [1] 0.45195193 0.41115985 0.33329924 0.31201618 0.31015451 0.19867034 [7] 0.18886407 0.08014479 -2.82524194 -3.31910731 Largest eigenvalues: [1] 66621614 61073822 57943279 57338792 56115200 54422012 53369645 53278776 [9] 52460712 52065854 Smallest eigenvalues: [1] 0.4660936 0.3685865 0.3603954 0.3578815 0.3484880 0.3378645 [7] 0.3246350 0.2219678 0.1820377 -0.4078484 Largest eigenvalues: [1] 64726710 60973669 57886930 56046089 55943532 54226049 52512248 52166820 [9] 52057019 51553353 Smallest eigenvalues: [1] 0.3764079 0.3480869 0.3441127 0.3310985 0.2568513 0.2216378 [7] 0.1127019 -0.2594567 -0.8621922 -1.4643204 Largest eigenvalues: [1] 65549750 59600336 57341334 56851883 54670519 53390008 52790668 51931754 [9] 51537623 51054069 Smallest eigenvalues: [1] 0.5060991 0.4870456 0.4610628 0.4553131 0.3943436 0.3348051 [7] 0.2695934 0.2224787 0.1437522 -0.8872853 Largest eigenvalues: [1] 63861132 60694511 57968395 56085826 55761381 54465041 52764048 52714974 [9] 51945764 51642869 Smallest eigenvalues: [1] 0.4263046 0.4003046 0.3723493 0.3383564 0.2936327 0.2406578 [7] 0.1796888 0.1486866 -4.2383471 -19.2118721 Largest eigenvalues: [1] 64289374 60376723 57775001 55686070 55593431 54219178 52596074 52346362 [9] 51676903 51171061 Smallest eigenvalues: [1] 0.5548711 0.4931591 0.4575653 0.4320617 0.3139352 0.2886235 [7] 0.2763743 0.2569307 0.1211830 -19.1282041 Largest eigenvalues: [1] 63072247 60119423 57001363 55424894 54712440 53675173 51838142 51738903 [9] 50978677 50878156 Smallest eigenvalues: [1] 0.4846561 0.4607000 0.3844532 0.3098568 0.2715368 0.2377455 [7] 0.1077077 -0.1850138 -0.8344726 -1.4884489 Largest eigenvalues: [1] 65243394 61339602 57731511 56649661 56354961 54624259 53492563 52629288 [9] 52334143 51883163 Smallest eigenvalues: [1] 0.41566287 0.40642435 0.32463694 0.30233169 0.27980582 0.24816331 [7] 0.21782159 0.19045934 0.06856897 -2.13150705 Largest eigenvalues: [1] 63873119 59830778 57199124 55455712 54820795 53415017 51826371 51591862 [9] 51546287 50813437 Smallest eigenvalues: [1] 0.45826277 0.37661712 0.37518788 0.26561324 0.19295784 0.16999554 [7] 0.12859338 -0.04130816 -0.79620896 -3.69373523 Largest eigenvalues: [1] 65937546 59865360 57822638 56167997 55018247 53852151 52539872 52355663 [9] 52060609 51499046 Smallest eigenvalues: [1] 0.4139886 0.3641170 0.3464064 0.3293694 0.3244529 0.3093846 [7] 0.1291062 0.0249714 -5.6929043 -9.3069458 Largest eigenvalues: [1] 64008928 60408479 57746086 55719560 55324554 54071320 51911299 51876264 [9] 51423796 50885048 Smallest eigenvalues: [1] 0.6403346 0.5855630 0.5592453 0.3966013 0.3757541 0.3739998 [7] 0.3017524 0.2542082 -0.2473475 -0.3472239 Largest eigenvalues: [1] 65821871 60477506 57718384 56972401 54911748 52960939 52905841 52494687 [9] 51779747 51596833 Smallest eigenvalues: [1] 0.5795766 0.3888811 0.3595193 0.3188216 0.2690237 0.2510893 [7] 0.2201783 0.0801908 -0.4393881 -0.4694700 Largest eigenvalues: [1] 65565381 60801012 57737444 56707756 55540550 53802333 52838172 52661072 [9] 52008593 51465674 Smallest eigenvalues: [1] 0.38472066 0.35331810 0.32975636 0.31088146 0.25222224 0.19079225 [7] 0.06460247 -0.25671302 -0.44770621 -1.40856262 Largest eigenvalues: [1] 65212187 60296345 57754453 56430604 55160844 53529062 53275694 52625681 [9] 51916021 51661593 Smallest eigenvalues: [1] 0.42237180 0.42032528 0.31233382 0.16524639 0.05787527 [6] 0.01202229 -0.63636918 -1.68376650 -14.93204405 -16.16891740 Largest eigenvalues: [1] 64552038 60472445 57342727 55983733 55185087 53460466 51956421 51881523 [9] 51853834 50961401 Smallest eigenvalues: [1] 0.4286482 0.3473948 0.3297445 0.3159395 0.2949013 0.2788363 [7] 0.2747424 0.2642496 -0.1466519 -1.1626724 Largest eigenvalues: [1] 65700000 60796125 58178536 56760625 55445271 53968170 52714220 52367880 [9] 52325203 51485866 Smallest eigenvalues: [1] 0.3286857 0.3194254 0.3132222 0.2723912 0.2676347 0.2431626 [7] 0.2395744 0.1641341 0.0429887 -2.4088361 Largest eigenvalues: [1] 65068798 60052382 57560834 56030043 54736076 53404028 52147713 51920559 [9] 51624305 51253356 Smallest eigenvalues: [1] 0.6614362 0.6403125 0.5126743 0.4071050 0.3952139 0.3674139 [7] 0.3460903 0.2670907 0.2648928 -0.7606246 Largest eigenvalues: [1] 64600665 59900758 57115765 55762293 55089866 53649784 52203205 51892990 [9] 51692900 50862597 Smallest eigenvalues: [1] 0.34926447 0.30013149 0.29411579 0.18386155 0.17518293 0.03194533 [7] -0.11371876 -0.66660138 -2.20708859 -2.40010136 Largest eigenvalues: [1] 65867518 60715944 58399371 56423239 55533358 53963358 52633517 52469002 [9] 52386662 51856974 Smallest eigenvalues: [1] 0.4062109 0.3548507 0.2620249 0.2274064 0.1787668 0.1624238 [7] 0.1595502 0.1217733 -0.0695975 -0.3605582 Largest eigenvalues: [1] 63416808 61049453 56959543 55899649 55281965 54022118 51999001 51856170 [9] 51392778 50637348 Smallest eigenvalues: [1] 0.4767220 0.4514406 0.4259908 0.4115469 0.2173005 0.1676919 [7] -0.5425180 -1.6655514 -7.1278341 -9.9574590 Largest eigenvalues: [1] 65497881 59884294 57176821 56820661 54909157 52902306 52701398 52483434 [9] 51888812 51542175 Smallest eigenvalues: [1] 0.4060931 0.3150107 0.2145123 0.2082711 0.1386461 0.1279345 [7] -0.1606087 -1.8452163 -2.5555222 -10.6843925 Largest eigenvalues: [1] 62046911 59537646 56211139 54871859 54865287 53119149 52012013 52006173 [9] 50932514 50735064 Smallest eigenvalues: [1] 0.198303712 0.155067222 0.097439951 0.027048659 0.011378508 [6] 0.005265852 -0.281215271 -0.493394858 -0.884524960 -1.862326452 Largest eigenvalues: [1] 65351690 61514551 58327310 57309372 55428947 53737179 53442117 52740637 [9] 52343485 51506782 Smallest eigenvalues: [1] 0.46450843 0.46054168 0.45284442 0.41450965 0.37355043 0.27335440 [7] 0.20753410 0.19570522 0.16160896 -0.01449703 Largest eigenvalues: [1] 62976642 59457855 56950107 54880378 54772066 53294796 51970638 51260449 [9] 50905360 50530197 Smallest eigenvalues: [1] 0.55305861 0.54941815 0.54413921 0.50327213 0.44790488 0.44528093 [7] 0.38393194 0.22429424 0.07960443 -0.08169211 Largest eigenvalues: [1] 63483000 60556650 57658353 55429371 55381283 53886898 52126457 51854446 [9] 51436065 50882670 Smallest eigenvalues: [1] 0.44223909 0.44120642 0.38524675 0.37500863 0.31265581 [6] 0.25437073 0.06182566 0.05031048 -0.28850931 -11.67986817 Largest eigenvalues: [1] 65248968 60746361 57638220 57029907 55038544 53253835 53069990 52039874 [9] 51944501 51181638 Smallest eigenvalues: [1] 0.4360076 0.4202398 0.3889183 0.3880379 0.3236710 0.3046222 [7] 0.2550710 -0.1149168 -0.5660980 -1.5233874 Largest eigenvalues: [1] 64147105 60019420 57599055 55797462 54904387 53625591 51848097 51825624 [9] 51767888 50890702 Smallest eigenvalues: [1] 0.5085601 0.5059506 0.4490781 0.4049120 0.3501748 0.2672402 [7] 0.2226407 0.2133033 0.1708226 -1.3584313 Largest eigenvalues: [1] 63702979 60239126 57092081 55698385 55443170 53895907 52250143 51820241 [9] 51307070 50933972 Smallest eigenvalues: [1] 0.6933409 0.5524056 0.5121185 0.3767376 0.3618350 0.3338048 [7] 0.3005060 0.2620378 0.1317146 -0.1480377 Largest eigenvalues: [1] 63892461 60325373 57481052 55669956 55559986 53822663 52686715 51871872 [9] 51791487 51347378 Smallest eigenvalues: [1] 0.17902819 0.13735683 0.13413892 0.09712550 0.08150493 [6] -0.06849755 -0.11427658 -0.41936993 -2.49260382 -11.27649523 Largest eigenvalues: [1] 63661147 59378065 56441556 55595307 54846100 53145422 51822430 51550666 [9] 50893874 50263697 Smallest eigenvalues: [1] 0.486330705 0.401310625 0.361569251 0.291178136 0.288211599 [6] 0.274139766 0.192191030 -0.007872327 -0.531349612 -2.865874205 Largest eigenvalues: [1] 64602378 60810156 57849329 56003413 55418830 53819263 52851527 52225698 [9] 52159588 51942990 Smallest eigenvalues: [1] 0.4297659 0.2969011 0.2879350 0.2405863 0.2353714 0.2013860 [7] 0.1412234 0.1290179 -1.4790095 -15.5185224 Largest eigenvalues: [1] 64664764 59624506 56944092 56048611 54706838 53098375 52299283 52050540 [9] 51654430 51088358 Smallest eigenvalues: [1] 0.4690986 0.4671841 0.4160146 0.3865764 0.3245286 0.3200399 [7] 0.2716805 -0.6287659 -7.1402322 -28.1024389 Largest eigenvalues: [1] 64507080 60615817 57274571 56322253 55661814 54022942 52281343 52145345 [9] 51995816 51115181 Smallest eigenvalues: [1] 0.42515764 0.38707386 0.38168610 0.25775125 0.22365832 0.19184253 [7] 0.18927772 0.11209596 0.02461388 -0.88692641 Largest eigenvalues: [1] 65463396 61192026 58655962 56557350 55656957 54238820 52758294 52632723 [9] 52468398 51848997 Smallest eigenvalues: [1] 0.4807497 0.3589228 0.3012715 0.2997176 0.2974495 0.2919229 [7] 0.2827454 0.2601469 0.1770138 -0.6608962 Largest eigenvalues: [1] 64329002 59862198 56879615 55686579 54787696 53127926 51915843 51826370 [9] 51345560 51025563 Smallest eigenvalues: [1] 0.4383523 0.4287468 0.4243869 0.3264658 0.3031195 0.2817753 [7] 0.2279140 0.2142666 0.1657544 -1.1273006 Largest eigenvalues: [1] 65062571 60488852 57441608 56610897 54915390 53613978 52545262 52471781 [9] 51842764 51709671 Smallest eigenvalues: [1] 0.3440562 0.2972671 0.2789140 0.2334340 0.2285750 -0.1489077 [7] -0.6235325 -0.6600562 -1.6493303 -6.1141973 Largest eigenvalues: [1] 64188076 59297122 57089277 55529979 54328238 53232339 51905846 51695037 [9] 51520910 51004256 Smallest eigenvalues: [1] 0.3679006 0.3589779 0.3323990 0.3097555 0.2737755 0.2658786 [7] 0.2091142 0.1310916 -0.4877401 -4.5705615 Largest eigenvalues: [1] 62030613 59288621 56405619 54602514 54389954 53003010 51733344 51277357 [9] 50599073 50472286 Smallest eigenvalues: [1] 0.3711072 0.3515920 0.3241428 0.3214037 0.2901418 0.1984046 [7] 0.1846894 0.1846851 0.1410481 -4.0522866 Largest eigenvalues: [1] 64872565 60884767 57819973 56136849 55728928 54385399 52731393 52663380 [9] 52077315 51889963 Smallest eigenvalues: [1] 0.5427293 0.4457126 0.3975445 0.3885092 0.3600539 0.3346986 [7] 0.3194983 0.1537804 -0.1775802 -9.3676397 Largest eigenvalues: [1] 64004823 60083941 57351803 55459867 55451526 53972452 52340519 52187071 [9] 51565397 51214728 Smallest eigenvalues: [1] 0.5659330 0.5125104 0.4268804 0.4120106 0.3154069 0.2870757 [7] 0.2809774 0.2719967 0.1644634 -0.9117688 Largest eigenvalues: [1] 62386470 59924937 56853106 55060536 54763992 53368543 51747769 51650931 [9] 50723234 50552338 Smallest eigenvalues: [1] 0.5214853 0.5078764 0.4104156 0.3182400 0.3139806 0.2605687 [7] 0.2545131 0.1311899 0.1181188 -0.1641932 Largest eigenvalues: [1] 64706046 60883901 57989507 56019024 55774126 54277521 52630187 52302357 [9] 52158812 51398535 Smallest eigenvalues: [1] 0.50662068 0.50098790 0.43533707 0.38707777 0.34083586 0.31003635 [7] 0.07233502 0.05012036 -0.02410819 -7.14065752 Largest eigenvalues: [1] 63928280 59891202 57214322 55518332 55117478 53627896 52228955 51963762 [9] 51541175 51045167 Smallest eigenvalues: [1] 0.2989950 0.2550337 0.1502615 0.1291306 0.1279780 0.1256411 [7] -0.6146667 -0.8459516 -1.4656638 -3.2379288 Largest eigenvalues: [1] 62754731 60102345 57163953 55517682 55162538 53372643 52487571 52304303 [9] 51362555 51140771 Smallest eigenvalues: [1] 0.3485707 0.3380235 0.2695217 0.2148699 0.1657066 0.1174540 [7] 0.1068433 -0.7518550 -5.0166651 -30.9693160 Largest eigenvalues: [1] 65552034 60167825 57144656 56726714 55247771 53688975 52631441 52420851 [9] 52058507 51649182 Smallest eigenvalues: [1] 0.54103680 0.52987206 0.45859309 0.31873353 0.26511036 0.23010307 [7] 0.22161534 0.06543372 -0.02668467 -0.05773266 Largest eigenvalues: [1] 63012792 60856183 57701532 56327576 54945243 54463426 52866543 52569567 [9] 51629791 51126495 Smallest eigenvalues: [1] 0.51394867 0.48694573 0.34642951 0.33550289 0.32814874 0.20139485 [7] 0.17144900 0.10751981 -0.02051304 -1.09090557 Largest eigenvalues: [1] 63066018 61100929 57903420 56527610 55186528 54695862 52933778 52845990 [9] 51932618 51268881 Smallest eigenvalues: [1] 0.35682451 0.24193373 0.22294541 0.21559344 0.20550307 0.19011960 [7] 0.16205078 0.04673723 -1.89516848 -6.01773199 Largest eigenvalues: [1] 65252231 59877344 57402895 56239435 54697675 53400471 52332243 52039031 [9] 51766494 51260483 Smallest eigenvalues: [1] 0.47023212 0.43494665 0.40907428 0.37657835 0.37523447 0.29405689 [7] 0.15445700 0.14943049 -0.03897097 -0.06423467 Largest eigenvalues: [1] 64236936 60818448 58145114 56233424 55314495 53790260 52066118 52001542 [9] 51899200 50999333 Smallest eigenvalues: [1] 0.32756505 0.32626878 0.20643357 0.20242644 0.01903709 [6] -1.39830508 -2.68564863 -9.47163581 -10.36819970 -11.68292471 Largest eigenvalues: [1] 65072573 59910117 57647424 56544694 55210904 53983881 53003440 52386733 [9] 52330172 51956962 Smallest eigenvalues: [1] 0.3096654 0.3090025 0.2804232 0.2802372 0.2728030 0.2104141 [7] 0.1670914 -1.3165414 -2.2910843 -16.9555180 Largest eigenvalues: [1] 64638089 60318555 57158846 56351941 54788890 53212547 52482490 52336762 [9] 51833797 51675028 Smallest eigenvalues: [1] 0.5990672 0.5753152 0.5088953 0.4419816 0.4380498 0.4013660 [7] 0.2768234 0.2386689 0.1065587 -0.2715800 Largest eigenvalues: [1] 65643142 59796376 56791181 56350979 54435819 52680183 52366000 51451129 [9] 51186549 50700039 Smallest eigenvalues: [1] 0.36895721 0.34396163 0.31410840 0.28298139 0.25909227 0.21975918 [7] 0.05981791 0.01201510 -0.28140585 -0.66953327 Largest eigenvalues: [1] 64797505 59868026 57490639 55445021 55359860 53871038 51769984 51652509 [9] 51544514 50789831 Smallest eigenvalues: [1] 0.42470322 0.41055890 0.27497065 0.21800859 0.21152169 0.09437311 [7] 0.03334797 -0.35497369 -0.82023264 -2.80679120 Largest eigenvalues: [1] 64349347 60225770 57365724 55938268 55768186 54190848 52436484 52363377 [9] 51865357 51769467 Smallest eigenvalues: [1] 0.5237585 0.4634357 0.4386310 0.4374384 0.2856463 0.2246010 [7] 0.2228062 0.1838654 0.1734203 -11.3668351 Largest eigenvalues: [1] 63439325 60194733 57670206 55434559 55110543 53772095 52639540 51815082 [9] 51270688 51018156 Smallest eigenvalues: [1] 0.4913837 0.3941252 0.3486019 0.2890221 0.2782221 0.2726352 [7] 0.2538432 0.2389814 -1.6265157 -4.4181662 Largest eigenvalues: [1] 65820029 59765195 57302032 56801695 54677183 53159629 52693893 52191980 [9] 51660452 51195984 Smallest eigenvalues: [1] 0.50489358 0.50365432 0.49193032 0.43581565 0.34947623 [6] 0.22595731 0.20026470 0.14911770 0.03814112 -15.73330755 Largest eigenvalues: [1] 64389014 60073505 56823247 56037478 54993227 53160060 52026139 51968122 [9] 51738982 50929732 Smallest eigenvalues: [1] 0.5211476 0.4309044 0.4262893 0.3359452 0.2760792 0.2639118 [7] 0.2572332 0.1870684 -0.1463880 -0.3596316 Largest eigenvalues: [1] 64646156 60256438 57585373 55503915 55292578 53857069 52540883 52187185 [9] 51627267 51404687 Smallest eigenvalues: [1] 0.498045951 0.446217558 0.372592248 0.333866438 0.284588928 [6] 0.270684177 0.085222644 -0.008961274 -1.378552731 -8.874650204 Largest eigenvalues: [1] 64527615 59793747 56889091 56142488 55021822 53439635 52223899 52169400 [9] 51674675 51107127 Smallest eigenvalues: [1] 0.48233708 0.36992749 0.36207737 0.35415485 0.23478621 0.23062738 [7] 0.18878878 -0.05536206 -0.39166060 -1.40072389 Largest eigenvalues: [1] 63519575 59640641 57367400 55344104 54802799 53592206 52265371 51892833 [9] 51506713 51094671 Smallest eigenvalues: [1] 0.50979273 0.44799375 0.39664625 0.37864999 0.34871614 0.33743973 [7] 0.33171887 0.31597474 0.31462146 -0.06652291 Largest eigenvalues: [1] 62888454 59727528 57120586 55635237 54921626 53261246 51669744 51569105 [9] 51490267 50478484 Smallest eigenvalues: [1] 0.4910824 0.3972007 0.3154717 0.2861554 0.2733556 0.2211642 [7] 0.1811651 0.1288606 -0.3257948 -0.7971756 Largest eigenvalues: [1] 64110555 60512999 57369419 55975025 55724813 54004942 52735302 52373465 [9] 52134294 51544277 Smallest eigenvalues: [1] 4.943753e-01 4.644037e-01 4.099888e-01 3.556866e-01 3.222602e-01 [6] 5.637430e-02 8.488341e-04 -2.689939e+00 -4.092281e+00 -1.093544e+01 Largest eigenvalues: [1] 63845342 60123164 56903036 55819898 55171739 53496958 51827463 51651492 [9] 51632371 50635157 Smallest eigenvalues: [1] 0.511902826 0.391811157 0.355104186 0.338616642 0.224828174 [6] 0.195832998 0.147541926 0.008617541 -0.435038316 -1.274842798 Largest eigenvalues: [1] 63703858 59492645 56677602 55419044 54761169 52948938 52523007 51448248 [9] 51244392 50849026 Smallest eigenvalues: [1] 0.4037483 0.3448537 0.2283588 0.1234852 0.0243138 -1.0464683 [7] -1.0969872 -1.4954078 -16.9805327 -26.6206378 Largest eigenvalues: [1] 65925359 59772096 57408318 56116769 54804511 53272863 52296392 52008850 [9] 51908258 50826511 Smallest eigenvalues: [1] 0.36182890 0.30900435 0.29322075 0.21342664 0.18976960 0.13990826 [7] 0.05191947 -1.90202254 -6.21153044 -8.57171392 Largest eigenvalues: [1] 64789453 59837587 57122325 55972095 55264381 53634971 52016771 51733060 [9] 51247360 50187423 Smallest eigenvalues: [1] 0.44947592 0.43765086 0.41989136 0.33485956 0.26842534 0.25984820 [7] 0.17658225 0.09902333 -0.06692555 -2.98197615 Largest eigenvalues: [1] 62907013 59173045 56711266 54626259 54594023 52988384 51385151 51112734 [9] 50794823 50437308 Smallest eigenvalues: [1] 0.49043409 0.47585817 0.40458216 0.39927649 0.36304888 0.26643871 [7] 0.13765931 0.06804248 0.03264467 -2.39048668 Largest eigenvalues: [1] 62273270 59499321 56320411 54835306 54669833 53004833 52010331 51359682 [9] 50797037 50629046 Smallest eigenvalues: [1] 0.5232948 0.4804485 0.4329797 0.4202325 0.4164453 0.3675846 [7] 0.2900074 0.2028474 -0.1084662 -1.6457422 Largest eigenvalues: [1] 65565493 59745979 56976391 56855160 54734853 52892560 52861791 51664491 [9] 51268744 50620728 Smallest eigenvalues: [1] 0.5178064 0.4179244 0.4030907 0.3577429 0.3257148 0.2918364 [7] 0.2267856 -0.1917349 -1.4290024 -1.5326092 Largest eigenvalues: [1] 65620870 60074169 57526222 56810956 54667560 52865144 52649759 52050366 [9] 51629791 51181589 Smallest eigenvalues: [1] 0.39260410 0.34953644 0.31170280 0.26112896 0.12487434 0.09307156 [7] 0.02481046 0.01645569 -4.74246393 -5.85633424 Largest eigenvalues: [1] 65139334 61321232 57618347 57066327 56074727 54095637 53681841 52637686 [9] 52592386 52083911 Smallest eigenvalues: [1] 0.36571956 0.33700234 0.33322130 0.32827244 0.29718526 0.26899324 [7] 0.20399366 0.17770055 0.09028794 -0.96468343 Largest eigenvalues: [1] 66152809 59670620 57008219 56690274 54315354 52836945 52820326 51995762 [9] 51231714 51187809 Smallest eigenvalues: [1] 0.4344119 0.3866784 0.3545301 0.3312515 0.2167982 0.2162476 [7] 0.1794588 0.1360532 -1.0033746 -2.4314693 Largest eigenvalues: [1] 64344965 59233572 56672244 55420241 54575984 52968008 51756274 51371445 [9] 51050317 50390125 Smallest eigenvalues: [1] 0.58735794 0.58439897 0.55705517 0.45004977 0.40355399 0.37806130 [7] 0.36149598 0.16865441 -0.03656117 -0.25703712 Largest eigenvalues: [1] 63909803 59468496 56639740 55616033 54331479 52774705 51637263 51438670 [9] 50903888 50032762 Smallest eigenvalues: [1] 0.3317985 0.2829668 0.2701496 0.2534508 0.2304108 0.1637035 [7] -0.1366548 -0.1699129 -3.1024367 -22.0833133 Largest eigenvalues: [1] 65562918 60745086 58354216 56859163 55306949 54106764 52796623 52465027 [9] 52232344 51368995 Smallest eigenvalues: [1] 0.45199364 0.45142586 0.37355628 0.35873771 0.30615962 0.28058194 [7] 0.17715282 0.03441338 -0.28165633 -1.77421589 Largest eigenvalues: [1] 62970373 60255539 57449498 55719557 55318768 54119362 52295189 52219458 [9] 51329566 51125936 Smallest eigenvalues: [1] 0.37214233 0.33843039 0.28558953 0.22058754 0.01874993 [6] -0.13182764 -0.87666441 -1.92890787 -4.17955045 -31.49485577 Largest eigenvalues: [1] 65151931 59723014 56858919 55364936 54604880 53053399 51846055 51474343 [9] 51338154 50991641 Smallest eigenvalues: [1] 0.4095651 0.4023405 0.3976419 0.3295473 0.3027252 0.2535563 [7] 0.1851376 0.1461018 -0.3584446 -0.5377062 Largest eigenvalues: [1] 63941470 59899283 57231504 55652351 55206554 53410827 52580042 51586551 [9] 51520506 51297029 Smallest eigenvalues: [1] 0.52770824 0.51318534 0.45686886 0.42542908 0.41305383 0.27805446 [7] 0.26843279 0.26483839 -0.03980633 -0.23471707 Largest eigenvalues: [1] 64511101 59750617 56674057 55365101 54665551 53142965 51614166 51450739 [9] 51143714 50393605 Smallest eigenvalues: [1] 0.3094944 0.2909495 0.2782641 0.2573035 0.1300734 -0.6695198 [7] -1.1145329 -2.0404946 -2.6458127 -2.6554158 Largest eigenvalues: [1] 65235231 60452407 57834573 55612622 55249439 53700569 52283082 51770623 [9] 51620031 51568499 Smallest eigenvalues: [1] 0.4800631 0.4585918 0.4483562 0.4119571 0.4049369 0.4048675 [7] 0.3801985 0.2341481 0.1921845 -0.3389320 Largest eigenvalues: [1] 64247433 60081791 57486908 55861861 55324579 53753431 52067930 51927612 [9] 51708346 50968941 Smallest eigenvalues: [1] 0.45799798 0.37013537 0.35011968 0.31336693 0.31006175 0.24372401 [7] 0.21297489 0.17176743 -0.02461585 -0.69865875 Largest eigenvalues: [1] 63382578 60457092 56989019 55556444 55193983 53505991 52586150 51604084 [9] 51549199 51370289 Smallest eigenvalues: [1] 0.4293221 0.4054114 0.2970813 0.2816352 0.1962420 0.1787878 [7] 0.1646537 0.1629980 -1.3821071 -1.8896098 Largest eigenvalues: [1] 63806469 60123208 57006236 55430143 55298102 53756710 52329487 52170220 [9] 51545726 51244078 Smallest eigenvalues: [1] 0.52543925 0.47528417 0.42826691 0.37678783 0.37473071 0.35180748 [7] 0.30405575 0.27209099 -0.00451787 -0.64916346 Largest eigenvalues: [1] 65665319 60422227 57684417 56436265 55038987 53622329 52590517 51940032 [9] 51739034 51128415 Smallest eigenvalues: [1] 0.6050815 0.4540769 0.4159589 0.3916320 0.3191691 0.2875455 [7] 0.2775322 0.2313483 0.2265472 -1.2249425 Largest eigenvalues: [1] 66147800 60495421 57914147 56554371 55294724 53945929 52667259 52468596 [9] 51939389 51508193 Smallest eigenvalues: [1] 0.44092375 0.37704863 0.37614067 0.36630488 0.17029349 0.14374279 [7] 0.04201448 -0.48832531 -1.55736974 -2.47170599 Largest eigenvalues: [1] 65190724 60841645 58140224 56574760 55338689 54051223 52483682 52342578 [9] 52119098 51210054 Smallest eigenvalues: [1] 0.39501378 0.39034721 0.38672347 0.29609991 0.09380120 [6] 0.07522996 -0.64518221 -1.94474786 -2.15186961 -15.22652123 Largest eigenvalues: [1] 64974230 59631272 56635984 56458013 54459930 52999864 52273082 51789803 [9] 51509588 50533324 Smallest eigenvalues: [1] 0.55100071 0.47030707 0.44955272 0.42784270 0.22999470 0.17706786 [7] 0.15442987 -0.04238832 -0.88612253 -1.97862781 Largest eigenvalues: [1] 63874236 60261060 57057849 55415575 55347800 53806837 52348497 52060619 [9] 51507414 51329895 Smallest eigenvalues: [1] 0.32664073 0.31620186 0.29239656 0.18099823 0.14323823 0.12115699 [7] 0.11847783 0.09850989 -0.48055052 -9.08741087 Largest eigenvalues: [1] 62097229 60397236 57484512 56003076 55079187 54228388 52702656 52403581 [9] 51568554 51068446 Smallest eigenvalues: [1] 0.52870699 0.49924345 0.42511647 0.39849348 0.25205413 0.21436063 [7] 0.09580388 0.03257360 -1.23034655 -1.96314667 Largest eigenvalues: [1] 64204835 60719614 57094034 55739680 55662182 54038637 52393168 52227470 [9] 51586799 51131383 Smallest eigenvalues: [1] 0.4253974 0.4218092 0.3156482 0.2842590 0.2811186 0.2441448 [7] 0.2099048 0.1925365 -1.0390803 -1.2280968 Largest eigenvalues: [1] 65987487 60139376 57589420 57291364 54922370 53515124 53263022 52132776 [9] 52056488 51204587 Smallest eigenvalues: [1] 0.5286978 0.4811105 0.4627575 0.4175315 0.3879989 0.3701321 [7] 0.2383504 0.1616359 -0.0625703 -0.8114657 Largest eigenvalues: [1] 63531253 60363673 57025081 55377033 54997084 53297403 52068976 51597092 [9] 51417828 51178776 Smallest eigenvalues: [1] 0.5173593 0.4241830 0.4168549 0.4036091 0.3727598 0.3368390 [7] 0.3363504 0.2868963 0.2113646 -0.6128432 Largest eigenvalues: [1] 65333403 60580212 58013965 56430980 55296437 53911289 52518356 52282295 [9] 52217627 51534071 Smallest eigenvalues: [1] 0.5516432 0.4793307 0.4626052 0.3586353 0.3109301 0.1953726 [7] -0.2754357 -0.3103752 -0.3835025 -1.7941468 Largest eigenvalues: [1] 64845273 60031034 57401692 56147614 54753417 53270533 52212877 52146042 [9] 51917847 51424277 Smallest eigenvalues: [1] 0.5127143 0.4282646 0.3082915 0.3004294 0.2768270 0.2753660 [7] 0.2750297 0.2100153 0.1925527 -0.3526256 Largest eigenvalues: [1] 63647176 59571371 57182015 55876939 54297241 52863618 51861190 51560535 [9] 51149371 50496776 Smallest eigenvalues: [1] 0.5926437 0.5227920 0.4321543 0.4059330 0.3634937 0.3253431 [7] 0.2439899 0.1578668 0.1077979 -1.6558530 Largest eigenvalues: [1] 63713602 59849890 57082136 55542713 54818015 53309189 51677624 51579808 [9] 51523474 50723955 Smallest eigenvalues: [1] 0.51159759 0.51023638 0.46651832 0.35157554 0.33044883 0.25126617 [7] 0.20925133 -0.01139049 -0.24336957 -2.40125854 Largest eigenvalues: [1] 65452650 59537760 57179640 56419018 54535451 52724970 52483652 51911319 [9] 51349658 51039505 Smallest eigenvalues: [1] 0.5468221 0.5206742 0.5017553 0.4939106 0.4584472 0.4165003 [7] 0.2748860 0.2451470 0.1930362 -1.2702561 Largest eigenvalues: [1] 64429339 60145463 57168661 56209265 54565969 53104887 52078193 51804935 [9] 51419981 50876500 Smallest eigenvalues: [1] 0.5268249 0.4517559 0.4136712 0.3245934 0.2966428 0.2628115 [7] 0.2274559 0.2102162 0.1068605 -0.4655085 Largest eigenvalues: [1] 63456236 60575416 57333946 55639196 55037543 53498121 52075872 52049983 [9] 51773999 51369596 Smallest eigenvalues: [1] 0.27430203 0.26186675 0.24327558 0.17264445 0.04632937 [6] -0.12428402 -0.24562340 -0.53274021 -7.43571511 -24.47684151 Largest eigenvalues: [1] 64542538 59654738 57419203 57052963 54510624 53013153 52660754 52619683 [9] 51874946 51154474 Smallest eigenvalues: [1] 0.38551201 0.36709385 0.30890115 0.29238059 0.24566885 0.21693885 [7] 0.19537717 -0.08615009 -0.69799262 -0.95670799 Largest eigenvalues: [1] 66574474 61656428 58858014 57754230 55760225 54157496 53685093 53018637 [9] 52598739 52290158 Smallest eigenvalues: [1] 0.38330265 0.33983169 0.31088425 0.29385943 0.21864243 0.20352898 [7] 0.09052186 -0.13745425 -0.24621362 -1.95626287 Largest eigenvalues: [1] 64887439 60174941 57556176 56049647 54452651 53387063 52142076 51973781 [9] 51739898 51463037 Smallest eigenvalues: [1] 0.56027791 0.52995718 0.45405906 0.40876858 0.40172535 0.31803179 [7] 0.30463395 0.25097989 0.19497654 -0.02943948 Largest eigenvalues: [1] 62855840 59622719 56940411 55264515 55001858 53364579 51869545 51544546 [9] 51115441 50697550 Smallest eigenvalues: [1] 0.4414426 0.4250377 0.3865849 0.3048058 0.2862079 0.2246387 [7] 0.2211863 -0.3229429 -1.7776075 -3.7721216 Largest eigenvalues: [1] 65329647 60249736 57889025 56201399 54975888 53399942 52118259 52066470 [9] 51588964 51264106 Smallest eigenvalues: [1] 0.4840260 0.4094132 0.3396146 0.2616245 0.2448007 0.2012485 [7] -0.1039864 -1.2452201 -1.5216364 -3.1470824 Largest eigenvalues: [1] 65994082 60766595 58007289 56520872 55580839 54030819 52833709 52737658 [9] 52516318 51876698 Smallest eigenvalues: [1] 0.5515044 0.5327682 0.4172179 0.3731582 0.3111289 0.3097984 [7] 0.2922014 0.2581040 0.2566385 -1.1498372 Largest eigenvalues: [1] 65944974 60412596 57685059 56890772 55266755 53932457 52952915 52196180 [9] 52159915 51302298 Smallest eigenvalues: [1] 0.41814456 0.39314189 0.34541985 0.26939281 0.23489792 0.20951774 [7] 0.17057690 0.01315328 -0.29688561 -0.37089323 Largest eigenvalues: [1] 62773651 59294909 57020914 54835388 54101565 53274560 51614297 51158836 [9] 50579001 50372914 Smallest eigenvalues: [1] 0.39621089 0.35446720 0.32385079 0.29143220 0.26155909 0.21787816 [7] -0.07438769 -0.18326823 -0.78118679 -1.81490836 Largest eigenvalues: [1] 64990477 60353503 57716952 55375271 54851460 53480116 52156701 51556627 [9] 51370760 51274415 Smallest eigenvalues: [1] 0.5556954 0.5419353 0.4194125 0.3984480 0.3524597 0.3399399 [7] 0.2993663 0.2752001 0.1469461 -0.4885378 Largest eigenvalues: [1] 65553019 59908222 57279562 56375462 54758511 53357263 52483808 51897466 [9] 51872609 51074221 Smallest eigenvalues: [1] 0.5072311 0.5011225 0.4381494 0.3204689 0.3144934 0.1876537 [7] 0.1588890 -0.1159627 -0.1477688 -2.6359257 Largest eigenvalues: [1] 62271960 59411371 55978215 54735408 54223269 52760371 51496625 50779556 [9] 50285884 49984810 Smallest eigenvalues: [1] 0.4540579016 0.4310665511 0.3277427272 0.2825839286 -0.0002956543 [6] -0.5075927693 -0.6863605835 -1.0263465535 -1.1192722922 -8.0652487815 Largest eigenvalues: [1] 64055192 59889378 57234696 55732339 55476351 53903096 52576875 52021694 [9] 51682074 51537125 Smallest eigenvalues: [1] 0.48493020 0.47788870 0.45982691 0.40050190 0.29110657 0.25780536 [7] 0.13460961 -0.06933544 -0.25325773 -2.42433678 Largest eigenvalues: [1] 64302617 59861610 56428838 55156477 54799235 52912201 51550916 51217698 [9] 51155130 50658275 Smallest eigenvalues: [1] 0.05244473 0.01147945 -0.08758079 -0.09317591 -0.11736709 [6] -0.81174103 -3.94934272 -14.73925193 -18.21714085 -25.77473237 Largest eigenvalues: [1] 63020097 59168880 56149827 54902395 54418028 52888214 52040182 51501380 [9] 50879959 50568464 Smallest eigenvalues: [1] 0.61633834 0.57728836 0.51973719 0.44701169 0.38636337 0.31265732 [7] 0.31012775 0.27994223 -0.02494265 -0.26963271 Largest eigenvalues: [1] 64439396 60471002 57201895 56385935 55087244 53241989 52670164 52385631 [9] 51784672 51526406 Smallest eigenvalues: [1] 0.46706762 0.41605830 0.39442802 0.35862910 0.33549837 0.29207152 [7] 0.09859399 -0.10332923 -0.28941812 -0.70817400 Largest eigenvalues: [1] 63375971 60243014 57425385 55898428 55052299 53264420 52036736 51971406 [9] 51857585 50962234 Smallest eigenvalues: [1] 0.47980785 0.44710076 0.44657018 0.39527325 0.36174831 [6] 0.20674897 0.18598973 0.13748697 0.03140506 -10.08939872 Largest eigenvalues: [1] 62931633 60848425 57151671 55835808 55264252 53958788 52262966 51886904 [9] 51302185 51007436 Smallest eigenvalues: [1] 0.383898325 0.376777826 0.365144325 0.300214407 0.275211468 [6] 0.215242439 0.213603201 -0.009588923 -1.265726516 -1.803717930 Largest eigenvalues: [1] 65042280 60016698 57715039 56721182 54889431 53638990 52532446 52331708 [9] 51888005 51552777 Smallest eigenvalues: [1] 0.36867587 0.36506960 0.34734056 0.34235227 0.26131910 [6] 0.23512634 0.23244818 -0.09985559 -1.31761321 -39.12820069 Largest eigenvalues: [1] 64259633 60524063 57413247 56051294 55332096 53815639 52452895 52399566 [9] 51988948 51406286 Smallest eigenvalues: [1] 0.30669706 0.18206619 0.13001425 0.06654499 0.06311839 -0.49289964 [7] -0.89830542 -2.18911448 -3.23607252 -4.00674612 Largest eigenvalues: [1] 65789223 59309050 56508649 56025280 54138677 52673872 52099719 51643971 [9] 51347791 50796745 Smallest eigenvalues: [1] 0.4487168 0.4400651 0.4365738 0.3434058 0.3397972 0.2950390 [7] 0.2297574 0.1445853 -0.9420785 -9.4822939 Largest eigenvalues: [1] 64747170 60779273 57840377 55927244 55785957 54215574 53061880 52136729 [9] 51979816 51748446 Smallest eigenvalues: [1] 0.45622207 0.42307033 0.37501464 0.34258708 0.29661265 0.24997378 [7] 0.17721858 0.13745818 -0.04494189 -0.40437979 Largest eigenvalues: [1] 64987615 60773986 58098685 56235799 55601425 53830389 52815305 52205880 [9] 52107678 51733891 Smallest eigenvalues: [1] 0.5434395 0.5239444 0.4883744 0.3643272 0.3398252 0.2901428 [7] 0.2515719 0.2110094 0.1774434 -0.2383405 Largest eigenvalues: [1] 61659011 59790069 56949753 55144223 54301434 53291700 52276265 51319946 [9] 50968891 50430067 Smallest eigenvalues: [1] 0.22953610 0.19748145 0.18878846 0.15493491 0.12423313 [6] 0.09859973 -0.03579610 -1.73033894 -2.86712317 -15.97736133 Largest eigenvalues: [1] 66311871 60185495 57615424 57421343 55051094 53787984 53061173 52240735 [9] 52077910 51520646 Smallest eigenvalues: [1] 0.4893959 0.4633498 0.4134872 0.3476526 0.3026531 0.2836557 [7] 0.2625640 0.1580110 0.1114099 -0.9127022 Largest eigenvalues: [1] 64267698 61024114 57932219 56347031 56265742 54542587 52976559 52504179 [9] 52318400 51717176 Smallest eigenvalues: [1] 0.36876946 0.36660799 0.27994515 0.27293021 0.21620436 [6] 0.17670845 0.13189257 0.08950989 -1.34918703 -22.48984732 Largest eigenvalues: [1] 64147320 59647604 56858858 55086985 54872494 53351468 51719081 51485611 [9] 51145580 50956039 Smallest eigenvalues: [1] 0.55597881 0.50011038 0.44034585 0.41639828 0.25749607 0.25156686 [7] 0.24949020 0.22544044 0.11176994 -0.02952555 Largest eigenvalues: [1] 64136848 60369642 57837191 55706692 54899367 54180583 52861791 51906424 [9] 51649890 51179798 Smallest eigenvalues: [1] 0.52624047 0.48316042 0.45713392 0.41224744 0.34693880 0.25484233 [7] 0.18280351 0.17924019 0.05478638 -0.02695582 Largest eigenvalues: [1] 65165304 59979734 57837644 55881372 54924788 53357714 52157225 52148538 [9] 51891329 51305529 Smallest eigenvalues: [1] 0.52255831 0.46641143 0.39745544 0.36297084 0.29715088 0.17275600 [7] 0.16883544 0.02204042 -0.10780769 -1.25536952 Largest eigenvalues: [1] 63270216 60632117 57063569 55742424 55579661 53484212 52366672 51824517 [9] 51361399 50862664 Smallest eigenvalues: [1] 0.35326989 0.30794250 0.24389959 0.22674539 0.15009024 [6] 0.11914683 0.03556131 -0.52730149 -4.85948714 -24.05417678 Largest eigenvalues: [1] 64101748 59888006 57144308 55310849 55278939 53308216 52475716 51832087 [9] 51597346 51513396 Smallest eigenvalues: [1] 0.48694943 0.48290118 0.45219524 0.42489809 0.30586551 0.20240792 [7] 0.19600969 0.16692336 0.07440068 -0.54406467 Largest eigenvalues: [1] 64636419 60172021 56964311 55819633 55098549 53467999 52394112 51897803 [9] 51701765 51108802 Smallest eigenvalues: [1] 0.50415756 0.47391765 0.36608868 0.32366657 0.31798859 0.26188897 [7] 0.20026326 -0.06817588 -1.41899616 -2.16789904 Largest eigenvalues: [1] 63702727 60091511 57600699 56022933 55301747 54372158 52787674 52031265 [9] 51435423 51103610 Smallest eigenvalues: [1] 0.54851205 0.50106283 0.41192100 0.40394495 0.37838009 0.37276818 [7] 0.33625466 0.29592259 0.27756369 -0.03711557 Largest eigenvalues: [1] 64820616 60247076 57140986 56105106 55398404 53454936 52582613 52238798 [9] 51641006 51464116 Smallest eigenvalues: [1] 0.5833595 0.4488149 0.4001408 0.3703876 0.3006038 0.2817226 [7] 0.2701746 0.2034730 -0.1537544 -0.3188478 Largest eigenvalues: [1] 62209166 59481037 57065929 55129037 54528572 53381072 51750165 51382137 [9] 50620135 50471273 Smallest eigenvalues: [1] 0.45350775 0.36410385 0.29198560 0.28835189 0.23472534 0.22611414 [7] 0.14337925 0.06857251 -0.53092901 -0.88713100 Largest eigenvalues: [1] 64604005 60314805 57618620 55481360 55339076 53830271 52374846 52135757 [9] 51703320 51326505 Smallest eigenvalues: [1] 0.56381361 0.51331384 0.47362914 0.44724254 0.35469392 0.24324481 [7] -0.08084322 -0.13984993 -0.57924724 -1.30626116 Largest eigenvalues: [1] 63551399 59597631 56482930 55274790 54309343 52655397 51433084 51289137 [9] 51247174 50426864 Smallest eigenvalues: [1] 0.51632690 0.47304526 0.41726490 0.37837206 0.37036446 0.34850952 [7] 0.31367232 0.23430750 0.06151551 -0.11362747 Largest eigenvalues: [1] 62593545 59086250 56207656 54967606 54334202 52640591 51525232 51258116 [9] 50942187 50439364 Smallest eigenvalues: [1] 0.4301214 0.3915651 0.2330392 0.2166153 0.1520424 0.1116029 [7] 0.1065242 -1.1516490 -10.9656849 -14.0333327 Largest eigenvalues: [1] 62680260 60744588 56895459 55816573 55296863 54173593 52474333 52408347 [9] 51250665 51175614 Smallest eigenvalues: [1] 0.4885155 0.4749414 0.4643886 0.4094536 0.3792688 0.3678651 [7] 0.3199618 0.3008881 0.2692542 -2.6180365 Largest eigenvalues: [1] 64591762 59798747 57114844 56735733 54540568 53156395 52565746 51715713 [9] 51616294 50861736 Smallest eigenvalues: [1] 0.4922706 0.4168315 0.3659510 0.3141811 0.2814506 0.2631293 [7] 0.2271075 0.1717822 -2.8144733 -4.2711065 Largest eigenvalues: [1] 65076343 60151562 57545828 55692804 55290595 53858003 52373980 51749940 [9] 51730283 51562485 Smallest eigenvalues: [1] 0.41423009 0.40797371 0.40429173 0.27367731 0.25817378 0.23670355 [7] 0.20788047 0.02670546 -0.16663186 -0.89294617 Largest eigenvalues: [1] 65540211 60066933 57548371 56149164 55211026 53795514 52296852 52226940 [9] 52129404 51247392 Smallest eigenvalues: [1] 0.3954087 0.3204928 0.3169391 0.3026497 0.2731129 0.2722381 [7] 0.2424215 0.2183580 0.2158269 -2.2519128 Largest eigenvalues: [1] 64888489 60513250 57309873 56462839 55041998 53550771 52519860 52167031 [9] 51940595 51061923 Smallest eigenvalues: [1] 0.53671602 0.51763776 0.44863186 0.34084719 0.28206260 0.27268519 [7] 0.23721966 0.14159899 0.07225824 -0.22693872 Largest eigenvalues: [1] 63581936 60494901 58151493 55860274 55101232 54589208 52769930 52338351 [9] 51547990 51362970 Smallest eigenvalues: [1] 0.52501304 0.49803192 0.45372017 0.32331354 0.32000200 0.30433109 [7] 0.09690191 -0.17463927 -0.31365473 -4.16352422 Largest eigenvalues: [1] 65282955 60869471 57823509 55799485 55774965 54282961 52182670 52145989 [9] 51986505 51396203 Smallest eigenvalues: [1] 0.41450056 0.40700190 0.37991430 0.27652375 0.14512729 0.04712675 [7] 0.03715285 0.02444949 -0.29606994 -1.05614948 Largest eigenvalues: [1] 64100890 59472564 56526493 55292362 54594372 53066232 51700571 51456839 [9] 51384307 50598979 Smallest eigenvalues: [1] 0.4466548 0.4212523 0.3634084 0.3449585 0.2236894 0.2120392 [7] 0.1981229 0.1819816 -0.3570136 -0.7909789 Largest eigenvalues: [1] 64705746 60221863 57031411 55683456 55604017 53920192 52232050 52178107 [9] 51679196 51255432 Smallest eigenvalues: [1] 0.43215835 0.39903997 0.31312094 0.20121132 0.18272829 0.15362316 [7] -0.05137536 -0.29879330 -0.33981888 -1.04978910 Largest eigenvalues: [1] 63479401 60165044 57119621 55465674 54873310 53396961 52339479 51727713 [9] 51661483 51424494 Smallest eigenvalues: [1] 0.3383743 0.3253573 0.3022169 0.2933104 0.2615272 0.2109413 [7] 0.2088187 -0.3266090 -1.8309206 -3.8078591 Largest eigenvalues: [1] 65293378 60632251 57819269 56839513 55019116 53088501 52620818 52498445 [9] 51843331 51403317 Smallest eigenvalues: [1] 0.5204391 0.5046829 0.4329070 0.3829721 0.3484199 0.3258325 [7] 0.2419167 0.2044632 0.1212280 -0.1912412 Largest eigenvalues: [1] 65164295 60378136 57656977 56022274 55474334 53812720 52296574 52270925 [9] 52234881 51216244 Smallest eigenvalues: [1] 0.5333894 0.4869640 0.4775101 0.4585743 0.3064971 0.2922270 [7] 0.2795078 0.2207584 0.1397938 -3.0483263 Largest eigenvalues: [1] 65553675 60294348 57285893 57127400 55424384 53733052 53015457 52811973 [9] 52074460 51557435 Smallest eigenvalues: [1] 0.47864687 0.41613528 0.37893291 0.36861429 0.33733748 0.31211842 [7] 0.23396834 0.09058538 -0.00906576 -1.80968394 Largest eigenvalues: [1] 63954265 59374372 56809316 55590799 54726130 53173100 51718021 51664485 [9] 51310437 50399880 Smallest eigenvalues: [1] 0.45310925 0.33654891 0.30349949 0.25381391 0.24817438 0.23131659 [7] 0.10211583 0.05524651 -0.17795393 -4.72547798 Largest eigenvalues: [1] 62805494 59750444 56916141 55128171 54951538 53243741 51868750 51513934 [9] 51033933 50566058 Smallest eigenvalues: [1] 0.3972587 0.3202435 0.3090080 0.2104679 0.1592468 0.1198572 [7] -0.3846592 -1.4215613 -3.3367006 -8.4682147 Largest eigenvalues: [1] 65743858 60283940 57758542 56230526 55223652 53800541 52639613 52426424 [9] 52222864 51354042 Smallest eigenvalues: [1] 0.52258009 0.41781290 0.40511864 0.40425046 0.39020029 0.30903487 [7] 0.26640414 0.23421111 0.02104919 -0.65343221 Largest eigenvalues: [1] 63718046 59792084 56982917 55695338 54595026 53066466 51959387 51824049 [9] 51633883 50915598 Smallest eigenvalues: [1] 0.5724934 0.5482017 0.3785101 0.3720853 0.3233181 0.3102313 [7] 0.2829779 0.2777779 0.2234471 -1.7910019 Largest eigenvalues: [1] 65709402 60901956 57912672 56900245 55401431 53949375 52827558 52431175 [9] 51995446 51443226 Smallest eigenvalues: [1] 0.38454898 0.38298573 0.33463964 0.28159869 0.23504111 -0.05824037 [7] -0.23550332 -0.52195435 -4.08058108 -6.28385702 Largest eigenvalues: [1] 65744834 60729694 57684510 56785826 55400842 54017221 52739971 52209527 [9] 51899878 51527616 Smallest eigenvalues: [1] 0.52624610 0.47731871 0.46561698 0.38174030 0.34652898 0.33682022 [7] 0.31969031 0.31716565 0.26711378 -0.04875817 Largest eigenvalues: [1] 63437678 60028142 57203485 55733735 54936103 53467301 51800957 51772752 [9] 51712463 50789674 Smallest eigenvalues: [1] 0.3927441 0.3770245 0.3301044 0.3270530 0.2264842 0.2096890 [7] 0.1907412 0.1325536 -0.7517308 -0.9367566 Largest eigenvalues: [1] 65264781 59720896 57133935 56159589 54948044 53444519 52273242 52133447 [9] 51396596 50524994 Smallest eigenvalues: [1] 0.18366850 0.14723774 0.05224793 -0.05280047 -0.76159670 [6] -3.24075590 -3.74096086 -6.47079522 -10.62836355 -10.79773562 Largest eigenvalues: [1] 62985059 59277661 56739752 54912864 54598707 53043782 51866513 51333484 [9] 50912342 50469386 Smallest eigenvalues: [1] 0.3949822 0.3568214 0.3435166 0.3319766 0.3038300 0.1930858 [7] 0.1068591 -0.3541584 -0.4123566 -19.1044936 Largest eigenvalues: [1] 65633265 60350118 56947177 56688288 55017829 53275758 52686983 52181234 [9] 51985663 51560981 Smallest eigenvalues: [1] 0.5798457 0.4574402 0.3907756 0.3490754 0.3072805 0.3050042 [7] 0.2684418 0.2166533 0.1736339 -1.1111754 Largest eigenvalues: [1] 64916082 60049120 57596556 55817355 54746942 53472608 51981497 51866323 [9] 51857661 51169494 Smallest eigenvalues: [1] 0.3868718 0.3667433 0.3375549 0.3123727 0.2013986 0.1668878 [7] 0.1354314 -0.1297068 -0.7951714 -7.9008512 Largest eigenvalues: [1] 64950407 59600447 56995097 55767914 54654235 53286705 51903472 51795154 [9] 51733033 51032028 Smallest eigenvalues: [1] 0.3905614 0.3583204 0.3238455 0.2257750 0.2072003 0.1856659 [7] 0.1746135 -0.0379976 -1.2735689 -2.0499019 Largest eigenvalues: [1] 62814378 60072902 56759466 55632161 55336689 53827009 52162906 52084403 [9] 51211447 50942002 Smallest eigenvalues: [1] 0.4174676 0.4036819 0.3979266 0.3799572 0.3780303 0.3133215 [7] 0.2637527 0.2188645 0.1828826 -1.4909045 Largest eigenvalues: [1] 65632006 60028786 57395232 56324373 55009085 53657204 52384662 52198105 [9] 52001570 51240226 Smallest eigenvalues: [1] 0.5055472 0.4488932 0.4247336 0.4224994 0.3730829 0.2293993 [7] 0.2057087 0.1551695 0.1187892 -0.6950585 Largest eigenvalues: [1] 63714349 60338878 56654189 55408319 55192868 53521757 52304978 51658230 [9] 51364444 51197831 Smallest eigenvalues: [1] 0.56355750 0.50469395 0.42543564 0.42367403 0.42187728 0.40356172 [7] 0.19391563 0.16171233 0.09900345 -0.02989223 Largest eigenvalues: [1] 63629082 60848618 57991038 55469468 55366127 53943275 52064775 51977202 [9] 51462830 51045018 Smallest eigenvalues: [1] 0.4999547 0.4242853 0.4070582 0.4011577 0.3378600 0.2541987 [7] 0.2360872 0.1779882 0.1633674 -1.3838193 Largest eigenvalues: [1] 64886841 60717635 58056520 56606923 55440684 53960038 52544578 52397829 [9] 51966702 51254325 Smallest eigenvalues: [1] 0.0195167 -0.0521489 -0.1039803 -1.0326219 -1.0885018 -1.3258018 [7] -1.8535346 -4.9984163 -29.5039805 -95.1446875 Largest eigenvalues: [1] 64815048 60786927 57652890 57105412 55797379 53913438 53279986 52901442 [9] 52161899 52139591 Smallest eigenvalues: [1] 0.40121044 0.32139279 0.26891911 0.24002220 0.16900970 [6] 0.10233386 -0.02403391 -5.48446574 -5.53955665 -22.86751397 Largest eigenvalues: [1] 64445348 60488436 56794722 55851457 55212474 53391065 52349730 51833073 [9] 51265376 51239324 Smallest eigenvalues: [1] 0.44631156 0.43880811 0.42475382 0.36816294 0.34666918 0.28838825 [7] 0.18060447 0.09358551 -0.25291456 -0.43651977 Largest eigenvalues: [1] 64190545 60120469 57091801 55817894 54982105 53082812 51877330 51785098 [9] 51648556 50790621 Smallest eigenvalues: [1] 0.5726905 0.5528845 0.4603301 0.4097984 0.3961458 0.3390871 [7] 0.3076692 0.2914478 0.2877053 -0.9898604 Largest eigenvalues: [1] 64728489 60500390 57851835 55824191 55780306 54271312 52466438 52431263 [9] 51890742 51575871 Smallest eigenvalues: [1] 0.3680929 0.3578169 0.3336184 0.3235404 0.2861786 0.2490393 [7] 0.2459757 0.2417218 -0.6295317 -1.3839640 Largest eigenvalues: [1] 63313376 60182047 57106055 55780369 55474600 53607215 51761671 51676248 [9] 51595507 50711870 Smallest eigenvalues: [1] 0.41658068 0.32506938 0.29691236 0.27005510 0.24228045 [6] 0.22626037 0.14949912 0.03770387 -1.70114147 -25.39538527 Largest eigenvalues: [1] 66600471 60446575 57781217 57096461 54819047 53430499 53141025 52090897 [9] 51860703 51400576 Smallest eigenvalues: [1] 0.5189127 0.4620726 0.4247554 0.3576267 0.3325198 0.3246832 [7] 0.2247279 0.2229573 0.2157122 -6.5047637 Largest eigenvalues: [1] 63699845 60173421 57549723 55515491 54789339 53356881 51725045 51711814 [9] 51653637 50863668 Smallest eigenvalues: [1] 0.4178070 0.3367404 0.2688692 0.2590147 0.2465043 0.2311974 [7] 0.1790864 0.1733880 0.1417462 -2.9555011 Largest eigenvalues: [1] 64387703 60457158 57625016 55943517 55385492 53834958 52500240 51981369 [9] 51766629 51319134 Smallest eigenvalues: [1] 0.49517612 0.46702636 0.46030812 0.37365384 0.30437872 0.29419147 [7] 0.26634238 0.05348424 -0.38240033 -1.85343475 Largest eigenvalues: [1] 62616589 59859601 56893574 55508497 54562205 53666692 51796436 51758655 [9] 50656753 50399735 Smallest eigenvalues: [1] 0.6107704 0.5959310 0.4363606 0.4015563 0.3927078 0.3471172 [7] 0.3389834 0.3003118 0.2217068 -0.2236928 Largest eigenvalues: [1] 62572553 60086455 57003074 55463515 54741237 53739994 52179965 51830448 [9] 50918452 50689874 Smallest eigenvalues: [1] 0.3734243 0.3604829 0.2591976 0.2566262 0.1745959 0.1195805 [7] -0.2452559 -0.9685733 -2.4843297 -7.2228896 Largest eigenvalues: [1] 63830089 59475970 57042462 55474309 54823687 52887047 52408986 51697748 [9] 51496299 51193689 Smallest eigenvalues: [1] 0.4652176 0.4518893 0.3349425 0.3078752 0.2909437 0.2238323 [7] 0.1772416 0.1571681 -0.1935769 -1.5736215 Largest eigenvalues: [1] 64241914 60437850 57702649 55846659 55578117 54306790 52439258 52244021 [9] 51834051 51046829 Smallest eigenvalues: [1] 0.53286182 0.46920090 0.42146889 0.40534027 0.39012195 0.27968883 [7] 0.26849185 0.15613849 0.01780754 -0.01079647 Largest eigenvalues: [1] 64755773 59930939 57427084 56056610 55116066 53365782 52718185 52155644 [9] 51742084 51672283 Smallest eigenvalues: [1] 0.5055738 0.4800702 0.4302868 0.4250121 0.4168078 0.4007920 [7] 0.3421753 0.1133964 -0.4361021 -8.8812634 Largest eigenvalues: [1] 65187881 60564117 57842139 57111328 55258579 53272425 53242773 53154156 [9] 51762991 51696936 Smallest eigenvalues: [1] 0.27662826 0.21596750 0.08515786 0.01854048 -0.01242206 [6] -0.13177049 -0.44412948 -0.65678626 -0.75645412 -17.51209710 Largest eigenvalues: [1] 65337417 60241909 56966212 56592948 54484564 53066891 52462962 51933972 [9] 51334728 51245676 Smallest eigenvalues: [1] 0.563739560 0.447134514 0.407241252 0.401656389 0.348456630 [6] 0.293311330 0.256176858 0.224783826 0.012109739 -0.006663791 Largest eigenvalues: [1] 65688085 60546252 58187565 56871095 54961276 53732990 52997255 52130650 [9] 52070542 51492391 Smallest eigenvalues: [1] 0.42986404 0.36767492 0.28693080 0.24349950 0.23147894 0.21107853 [7] 0.19085499 0.11799006 0.03368411 -1.37220754 Largest eigenvalues: [1] 65312288 61264969 57973818 56419678 56403982 54745090 53280421 52626794 [9] 52427761 52079295 Smallest eigenvalues: [1] 0.37465773 0.35965816 0.35349947 0.26876609 0.20938226 0.16680784 [7] 0.08770754 0.01265497 -0.73606131 -6.45738175 Largest eigenvalues: [1] 63296685 59492829 56349918 54567409 54371156 52695002 51428765 50719490 [9] 50599165 50465109 Smallest eigenvalues: [1] 0.29655500 0.24376786 0.13905556 0.07580608 -0.61822502 [6] -0.81590333 -1.60298127 -3.82197167 -4.89840002 -10.79176979 Largest eigenvalues: [1] 65726498 60697895 58148637 55924085 55784091 54446787 52829627 52657213 [9] 52103003 51649252 Smallest eigenvalues: [1] 0.4967624 0.4151527 0.3899235 0.3847903 0.3663412 0.3645295 [7] 0.3067189 0.2630492 0.1228690 -0.5911202 Largest eigenvalues: [1] 62931446 60014696 57684440 55030737 54921580 53274199 52265258 51449345 [9] 51324662 51135905 Smallest eigenvalues: [1] 0.5175794 0.4866245 0.4217284 0.3787368 0.3714231 0.3299036 [7] 0.3205535 0.2464447 0.2051846 -0.7782507 Largest eigenvalues: [1] 62982466 59707205 56527780 55269602 54664204 53047764 51743112 51450948 [9] 51204344 50825625 Smallest eigenvalues: [1] 0.5923287 0.5170791 0.4890658 0.4174978 0.3868042 0.3862984 [7] 0.3549069 0.3270727 0.2503074 -0.3910644 Largest eigenvalues: [1] 63708920 60157345 57088009 55584728 55426886 53489407 52236718 52006099 [9] 51424483 51031211 Smallest eigenvalues: [1] 0.34331215 0.29768579 0.29571309 0.17665506 0.14946862 0.01307183 [7] -0.08212541 -0.47708149 -1.34392765 -9.07828358 Largest eigenvalues: [1] 63693719 60786766 58117203 55436852 55275336 53873719 52657820 52445284 [9] 51867990 51607802 Smallest eigenvalues: [1] 0.52147381 0.46908380 0.42995634 0.42661575 0.36464881 0.30499518 [7] 0.30339189 0.14064780 0.03851321 -3.19800498 Largest eigenvalues: [1] 63360255 59920491 56718929 55354704 55293135 53488277 52231951 51750700 [9] 51393812 51054783 Smallest eigenvalues: [1] 0.5773097 0.5166810 0.4548954 0.4349956 0.4335509 0.3909374 [7] 0.3675562 0.2591006 0.2202154 -0.1237997 Largest eigenvalues: [1] 63458025 60535725 57492574 55733391 55501661 54004070 52617085 51993703 [9] 51476977 51317794 Smallest eigenvalues: [1] 0.40968398 0.35411264 0.31820302 0.24463616 0.19075035 0.12670892 [7] 0.03809146 -0.25516592 -0.62598796 -5.10253827 Largest eigenvalues: [1] 64420158 59795993 56813006 55344506 54559576 52829983 51600430 51451542 [9] 51062802 50938200 Smallest eigenvalues: [1] 0.54996490 0.53709487 0.50980109 0.42660980 0.38797934 0.34306404 [7] 0.33244315 0.32252642 0.22530047 -0.08631331 Largest eigenvalues: [1] 65473235 60088850 57084299 55877840 54925934 53333597 52046965 51808276 [9] 51744133 51239453 Smallest eigenvalues: [1] 0.383432317 0.369824010 0.329982482 0.273084182 0.110635175 [6] 0.004946738 -0.044299684 -1.493547709 -1.941855283 -3.500027698 Largest eigenvalues: [1] 65243667 60906268 58076759 56660188 55632592 54264415 52796578 52469313 [9] 52270895 51866971 Smallest eigenvalues: [1] 0.5967675 0.5338444 0.3413342 0.3186640 0.2714519 0.2680787 [7] 0.2600090 0.2044596 -0.2883868 -1.2271485 Largest eigenvalues: [1] 64541085 60058494 57220054 56152082 54999387 53498364 52289013 52217953 [9] 51901497 51161671 Smallest eigenvalues: [1] 0.5043068 0.4496201 0.4076051 0.3432926 0.2913410 0.2430115 [7] 0.1270324 -0.2639423 -0.3134329 -1.5769235 Largest eigenvalues: [1] 65266961 60365342 56762083 56637000 54963151 53287142 52568579 51890928 [9] 51809909 50916874 Smallest eigenvalues: [1] 0.48448377 0.47064766 0.41980463 0.34779832 0.30066665 0.26384865 [7] 0.22789057 0.07499376 -0.07684330 -0.30797073 Largest eigenvalues: [1] 65844021 60397715 58030446 57056452 55004358 53164704 53058134 52913449 [9] 52114849 51904190 Smallest eigenvalues: [1] 0.38659037 0.35025000 0.30883234 0.21083425 0.17647958 [6] 0.12521346 0.10165116 0.02327131 -1.39496036 -49.41586896 Largest eigenvalues: [1] 65323713 60930496 57663971 56580326 56037125 54429600 52850046 52639791 [9] 52634834 52065373 Smallest eigenvalues: [1] 0.4203997 0.4020511 0.3957960 0.3546598 0.3376361 0.3259472 [7] 0.2579137 0.1929515 0.1621469 -5.1531192 Largest eigenvalues: [1] 63228742 59491266 56786189 55216033 54837299 53552529 51859725 51354193 [9] 50924931 50417382 Smallest eigenvalues: [1] 0.59439585 0.55838376 0.50000170 0.39503961 0.35127874 0.34264285 [7] 0.32296369 0.29056436 0.23524513 -0.04651653 Largest eigenvalues: [1] 63577621 60011058 57430459 55371885 55352261 53734389 52277045 51846993 [9] 51524993 51071770 Smallest eigenvalues: [1] 0.52748041 0.52085323 0.47282492 0.46016881 0.32532316 0.32355459 [7] 0.31122752 0.26143783 -0.04452624 -1.09048076 Largest eigenvalues: [1] 63649752 60463773 57507102 56300753 55602775 54561214 52709651 52331130 [9] 51624019 51133269 Smallest eigenvalues: [1] 0.48199996 0.42465156 0.34396084 0.29845772 0.29826492 0.26976838 [7] 0.26401978 0.04235792 -1.51236133 -2.94093567 Largest eigenvalues: [1] 64155790 59516753 56550482 55988703 54791713 53150186 51991478 51704450 [9] 51581074 50565427 Smallest eigenvalues: [1] 0.3752704 0.2700645 0.2545741 0.2491218 0.2314775 0.2027098 [7] 0.1196420 -0.1778295 -1.1648163 -1.3406418 Largest eigenvalues: [1] 63962414 61109501 58043067 56528210 55467432 54788579 52807508 52593739 [9] 51827295 51408134 Smallest eigenvalues: [1] 0.34788149 0.33487322 0.32489211 0.28086913 0.20070571 0.19130303 [7] 0.13929396 0.10583794 0.06913999 -0.80719810 Largest eigenvalues: [1] 63206745 60089953 57103197 55476322 55076247 53754875 52547994 52156477 [9] 51581934 51291721 Smallest eigenvalues: [1] 0.5489862 0.4958384 0.3754370 0.3634000 0.2586754 0.2459261 [7] 0.2343000 0.2309345 0.1146095 -0.1314114 Largest eigenvalues: [1] 64027934 60653198 57432371 56003729 55622074 53914822 52706591 52093004 [9] 52092036 51254230 Smallest eigenvalues: [1] 0.3946377 0.3539254 0.3196846 0.2481407 0.2326993 0.2322944 [7] 0.2103728 0.1694675 -0.8113792 -5.9997816 Largest eigenvalues: [1] 62120489 59394366 56257973 54897705 54188380 53165380 51818076 50758267 [9] 50282818 50052350 Smallest eigenvalues: [1] 0.53707202 0.48932306 0.40819672 0.40196587 0.37362444 0.34277781 [7] 0.30865320 0.25270616 0.17770408 -0.06253088 Largest eigenvalues: [1] 64644290 59781467 56933636 55909137 54942887 53198391 52002067 51560865 [9] 51390085 50634680 Smallest eigenvalues: [1] 0.5838101 0.5530808 0.3613776 0.3477666 0.3194009 0.3018902 [7] 0.2508838 0.1881792 0.1345991 -0.6132193 Largest eigenvalues: [1] 64521723 60424218 57548315 55735333 55243046 53582289 52272658 51761120 [9] 51725538 51264195 Smallest eigenvalues: [1] 0.4256473 0.3931636 0.3565357 0.3544706 0.2727139 0.1972685 [7] 0.1954288 0.1559285 -0.4121790 -0.7174116 Largest eigenvalues: [1] 64743195 60513746 57310242 56191215 55680830 53523236 53152410 52311618 [9] 52306146 51837495 Smallest eigenvalues: [1] 0.03512497 -2.28955971 -3.56035025 -3.78237017 -4.16686291 [6] -5.65276404 -5.75583044 -30.47610863 -35.99737529 -70.30215168 Largest eigenvalues: [1] 64979059 59927071 57040172 56609349 54576328 52971318 52873811 52078847 [9] 51937156 51124465 Smallest eigenvalues: [1] 0.4745703 0.4492614 0.3975022 0.3762097 0.3367198 0.3099774 [7] 0.2588097 -0.2679703 -0.3065810 -1.0882526 Largest eigenvalues: [1] 65531240 60139321 57570954 56602994 55229681 53534052 52804055 52730052 [9] 51965980 51697491 Smallest eigenvalues: [1] 0.57438758 0.47576818 0.47412315 0.33665090 0.22414532 0.19931718 [7] 0.04983179 -0.25040016 -0.28139087 -0.48746474 Largest eigenvalues: [1] 64642950 59978637 57336755 56279712 54909101 53279481 52223158 52131479 [9] 51884185 51154289 Smallest eigenvalues: [1] 0.471223606 0.443878680 0.379929702 0.221257858 0.190548867 [6] 0.184841202 0.070488609 0.021771895 -0.005558447 -0.355305018 Largest eigenvalues: [1] 62732318 60383453 57322100 56037109 54269251 54145142 52351919 51824191 [9] 50797277 50740398 Smallest eigenvalues: [1] 0.31202282 0.29779464 0.23817086 0.21194679 0.19063729 0.16796064 [7] -0.07426175 -0.81794293 -3.73933198 -4.12421016 Largest eigenvalues: [1] 66684690 60682149 58609066 56878427 55264730 53790713 52840685 52799296 [9] 52166320 52096862 Smallest eigenvalues: [1] 0.3620760 0.3113102 0.2995721 0.2950472 0.2329229 0.1873973 [7] -0.6881733 -1.5603092 -6.0852349 -6.3392510 Largest eigenvalues: [1] 65256836 60408090 57713954 56454726 55730408 54309879 52366279 52288782 [9] 52248147 51439908 Smallest eigenvalues: [1] 0.4459016 0.3807232 0.3576178 0.3353257 0.2629456 0.2070865 [7] 0.1476873 -0.2393412 -0.5145918 -0.7855670 Largest eigenvalues: [1] 63023767 60309143 57494801 55430197 54958970 53717248 52277383 52154793 [9] 51551160 51437789 Smallest eigenvalues: [1] 0.5187706 0.4642415 0.3359671 0.2477922 0.2285410 0.1859766 [7] 0.1714449 0.1456001 -0.1751883 -1.0665905 Largest eigenvalues: [1] 65373793 60987124 58138293 56265139 55987159 54749104 53310210 52467950 [9] 52219920 51985931 Smallest eigenvalues: [1] 0.4262290 0.4024308 0.3742407 0.2634124 0.2550825 0.1190769 [7] -0.1349040 -0.1685421 -0.7925196 -7.6016656 Largest eigenvalues: [1] 62819148 60788241 56966599 55944709 55535637 53559968 52433122 51817826 [9] 51598629 50626433 Smallest eigenvalues: [1] 0.55577240 0.43446897 0.41902560 0.33993349 0.32170116 0.23709011 [7] 0.17652381 0.09464753 0.01828675 -0.09441767 Largest eigenvalues: [1] 63526255 60457112 57401948 55704414 54894829 53845038 52425722 52035579 [9] 51266485 51034109 Smallest eigenvalues: [1] 0.4324403 0.4208085 0.4133311 0.3539754 0.2394450 0.1903392 [7] 0.1801038 0.1611402 0.1572008 -1.9735867 Largest eigenvalues: [1] 65138153 59657959 57116144 56764834 54472966 53239463 52530811 51860585 [9] 51590578 51139438 Smallest eigenvalues: [1] 0.47356042 0.39096753 0.36568296 0.36123935 0.31504894 0.23708620 [7] 0.18704086 0.09624224 -0.78948090 -1.29149872 Largest eigenvalues: [1] 64034350 59882415 56942354 55741970 55171011 53304338 52593904 51816111 [9] 51768567 51490362 Smallest eigenvalues: [1] 0.4108492 0.3877276 0.3725132 0.2686506 0.2656074 0.2435019 [7] 0.1674495 -0.2545117 -0.5957153 -0.6241742 Largest eigenvalues: [1] 66326526 59597349 57476267 56827425 54580306 53226231 52836348 51784316 [9] 51732317 51189121 Smallest eigenvalues: [1] 0.40790431 0.38059126 0.35759345 0.33178546 0.30666632 0.27075535 [7] 0.17069240 0.08667056 -1.16944187 -7.02873219 Largest eigenvalues: [1] 65193483 59993545 57024317 55793442 55251426 53734860 51938969 51930717 [9] 51697989 50940859 Smallest eigenvalues: [1] 0.4073014 0.3623563 0.3471461 0.3115334 0.2912702 0.2367067 [7] 0.1772343 0.1739464 0.1491958 -0.7247349 Largest eigenvalues: [1] 62935510 60235648 57734397 55608469 55066275 53944302 51864927 51795751 [9] 51108338 50912349 Smallest eigenvalues: [1] 0.4699147 0.3793932 0.3763677 0.3609598 0.3235279 0.3142769 [7] 0.2687971 0.2513977 0.1711949 -2.4107203 Largest eigenvalues: [1] 65019610 60862637 57686846 56629285 56005835 54355129 52869719 52542874 [9] 52455601 51829018 Smallest eigenvalues: [1] 0.4921833 0.4446038 0.4009392 0.3940784 0.3670845 0.3387744 [7] 0.3176323 0.1741172 0.1498292 -2.4320196 Largest eigenvalues: [1] 64427681 60540069 57425278 56487165 55525908 53825368 52595474 52400545 [9] 52340120 51591104 Smallest eigenvalues: [1] 0.4875495 0.4843307 0.4455267 0.4246734 0.4032467 0.3781196 [7] 0.3406281 0.2605955 0.1958454 -0.9397968 Largest eigenvalues: [1] 64362034 59888859 57072472 55913244 55117746 53452212 51773877 51728354 [9] 51651998 50827553 Smallest eigenvalues: [1] 0.40264033 0.31325205 0.30628064 0.28088188 0.25733521 0.17447651 [7] 0.16649813 -0.06481802 -0.72899936 -6.54224088 Largest eigenvalues: [1] 61372784 59105290 56549859 54243774 54162652 52559717 51275378 51186962 [9] 50428687 50236378 Smallest eigenvalues: [1] 0.2792596 0.2201584 0.1951173 0.1753320 0.0265760 -2.2120992 [7] -5.7463623 -12.7346491 -21.2329126 -21.5134892 Largest eigenvalues: [1] 65200766 60058219 57706057 55964560 55079918 53538228 52380583 52045752 [9] 51519894 51434454 Smallest eigenvalues: [1] 0.29641363 0.19853855 0.19482634 0.16883003 0.13821027 0.01942460 [7] -0.03854068 -0.41909868 -3.23326978 -7.15120234 Largest eigenvalues: [1] 63570573 59868792 56337855 55963439 54280394 52766669 51814269 51635003 [9] 51211637 50357496 Smallest eigenvalues: [1] 0.4453602 0.3889695 0.2696852 0.1979118 0.1868589 0.1654724 [7] 0.1209853 -1.4384469 -2.9832532 -10.9793433 Largest eigenvalues: [1] 64870798 59732786 56444227 55505074 54633797 52982657 51730431 51518656 [9] 51183754 51017705 Smallest eigenvalues: [1] 0.4793919 0.4616651 0.3741029 0.3169623 0.2885599 0.2753860 [7] 0.1927286 0.1137149 -0.1574263 -1.3859297 Largest eigenvalues: [1] 64104119 60136173 56992729 56122838 54963512 53041919 52376500 52077161 [9] 51921265 51317676 Smallest eigenvalues: [1] 0.42056618 0.41677220 0.38714762 0.36220404 0.29625758 0.26425761 [7] 0.15729375 0.08177521 0.06367278 -5.68002275 Largest eigenvalues: [1] 62381135 59892352 56944626 55331162 54865099 53619296 52009388 51992231 [9] 51088411 50925634 Smallest eigenvalues: [1] 0.60043450 0.55229516 0.55072741 0.46245176 0.38477186 0.33219781 [7] 0.32344441 0.26941693 0.26315159 -0.05605375 Largest eigenvalues: [1] 63908392 60840590 57686738 56164601 55483676 53618823 52165064 52121277 [9] 52005600 50962834 Smallest eigenvalues: [1] 0.40941992 0.39970536 0.25718644 0.20553070 0.05825044 -0.21487019 [7] -0.40347000 -0.67216517 -1.20492051 -1.20729750 Largest eigenvalues: [1] 64022154 60425718 57421453 55930293 55457524 53555159 52683443 52070640 [9] 51934521 51644078 Smallest eigenvalues: [1] 0.493962162 0.480239136 0.388753924 0.383544457 0.316339893 [6] 0.266802151 -0.005463708 -0.057161030 -0.454866654 -11.584169284 Largest eigenvalues: [1] 64550072 60731968 57726750 55692504 55617985 54160713 52769488 52157680 [9] 51755109 51610363 Smallest eigenvalues: [1] 0.40228173 0.31552111 0.29669447 0.26419610 0.20531856 0.06742672 [7] -0.59135502 -1.50742033 -3.62198587 -9.01804436 Largest eigenvalues: [1] 65242435 60689217 58535715 56848494 55350011 54038897 52858515 52711182 [9] 52412557 51846831 Smallest eigenvalues: [1] 0.4108772 0.3815098 0.3177356 0.2919447 0.2785749 0.2671502 [7] 0.1958608 0.1509537 -0.2691563 -34.3063728 Largest eigenvalues: [1] 64644945 60258691 57112245 56584953 54885143 53284782 52625848 51745499 [9] 51709720 50812727 Smallest eigenvalues: [1] 0.44570733 0.43136179 0.41884838 0.40844273 0.26684272 0.16679687 [7] 0.02689899 -0.26363691 -0.56835588 -6.17513348 Largest eigenvalues: [1] 65015620 60289391 57240238 56258634 55224556 53115947 52386670 52055030 [9] 51817682 51229007 Smallest eigenvalues: [1] 0.39076658 0.30620139 0.28027214 0.26838465 0.15545927 0.03372245 [7] -0.30181851 -0.59014368 -1.30480662 -3.89361080 Largest eigenvalues: [1] 63274055 59328273 56707389 55363613 54737784 52972874 51899737 51542285 [9] 51269827 50535279 Smallest eigenvalues: [1] 0.5161461 0.4873729 0.4869183 0.4456784 0.3816664 0.3645422 [7] 0.3024546 0.2536135 0.1387770 -0.3952990 Largest eigenvalues: [1] 63583667 59866340 56958344 55914915 54657952 53011737 51908880 51746140 [9] 51031240 50454538 Smallest eigenvalues: [1] 0.4386390 0.3911951 0.3651583 0.3458550 0.3192719 0.2740766 [7] 0.2487285 0.2103029 -0.5463044 -0.9132883 Largest eigenvalues: [1] 65842884 60379833 58197482 57211775 54905829 53728715 53197779 51953614 [9] 51758676 51267480 Smallest eigenvalues: [1] 0.51474003 0.42466393 0.36673532 0.35004713 0.34442364 0.31938393 [7] 0.28264187 0.26385162 0.01473139 -1.65254526 Largest eigenvalues: [1] 64232147 60026593 57159312 56536769 54811369 53353597 52431513 52221948 [9] 51986291 51028120 Smallest eigenvalues: [1] 0.36417741 0.30820353 0.27207555 0.26293412 0.23533050 0.21430500 [7] 0.15797233 0.06621228 -0.14256016 -1.40739999 Largest eigenvalues: [1] 66280439 60256873 58007988 56904667 55187195 53831909 52908858 52656650 [9] 51696109 51510384 Smallest eigenvalues: [1] 0.5416678 0.5261572 0.4922832 0.4147584 0.4141650 0.3949528 [7] 0.3035864 0.2643716 0.2221183 -0.1620976 Largest eigenvalues: [1] 64133405 60483524 57472989 55525894 55325342 53689331 51888854 51774456 [9] 51703666 51002115 Smallest eigenvalues: [1] 0.44371097 0.42403549 0.37521802 0.29202457 0.28603542 [6] 0.25322918 0.23373114 0.07113422 -4.62909282 -15.62692252 Largest eigenvalues: [1] 63790069 60537124 57091706 55872700 55198709 54044540 51862734 51630663 [9] 51246453 50530531 Smallest eigenvalues: [1] 0.38929995 0.37506573 0.36868954 0.32004458 0.31589619 [6] 0.27434874 0.18483187 0.17684090 -0.03761006 -14.14437463 Largest eigenvalues: [1] 62557588 59625581 56891784 55119558 54596424 53330207 51798207 51445110 [9] 50922762 50766874 Smallest eigenvalues: [1] 0.5272973 0.3849396 0.3841447 0.3205607 0.3150492 0.3093808 [7] 0.2720532 -0.4080563 -0.7311009 -0.7398283 Largest eigenvalues: [1] 65002529 60346942 57757186 56607651 55373300 53805874 52818378 52730570 [9] 52126266 51251488 Smallest eigenvalues: [1] 0.4527231 0.3520761 0.3125946 0.2835301 0.2639696 0.2433599 [7] 0.2346522 0.2129127 0.2121767 -47.0272980 Largest eigenvalues: [1] 63578345 59846460 56995950 55783146 54932017 53273873 51842079 51823057 [9] 51761321 50978558 Smallest eigenvalues: [1] 0.51053661 0.49367922 0.46542859 0.43739684 0.38594699 0.30683133 [7] 0.24551698 0.23853101 -0.05231138 -0.20058894 Largest eigenvalues: [1] 64472977 60302040 57456427 55974053 54856355 53509806 52053331 52009115 [9] 51746006 51239364 Smallest eigenvalues: [1] 0.55243864 0.50350228 0.48772750 0.39806217 0.35248170 0.30528158 [7] 0.21498327 0.20850888 0.01982676 -0.94523494 Largest eigenvalues: [1] 63876450 60715516 57608421 55852721 55762732 54294908 52550423 52157952 [9] 51882153 51274727 Smallest eigenvalues: [1] 0.34765242 0.23475870 0.20018750 0.19615798 0.17217104 [6] 0.07853328 0.07581293 -0.25391967 -14.60019297 -23.23722275 Largest eigenvalues: [1] 64846506 60100147 56859529 56326514 55396860 53765321 52289331 52232157 [9] 51755971 51339123 Smallest eigenvalues: [1] 0.35915809 0.34183643 0.29880684 0.29326309 0.02126389 -0.02008096 [7] -0.07364751 -0.90829768 -0.93172381 -1.97376623 Largest eigenvalues: [1] 64648089 59284634 56695111 55407157 53907633 52321700 51802478 51282756 [9] 50899172 50868645 Smallest eigenvalues: [1] 0.5945667 0.5912657 0.5732336 0.5059641 0.4862638 0.3333659 [7] 0.3173061 0.2106485 0.1670870 -0.9075313 Largest eigenvalues: [1] 64689216 60263316 56858979 56217166 55175319 53330521 52191077 52008612 [9] 51764950 50826176 Smallest eigenvalues: [1] 0.53067501 0.46535419 0.39059203 0.36303622 0.29862882 0.28498252 [7] 0.19101920 0.18783262 0.08313483 -0.01668797 Largest eigenvalues: [1] 63100317 61104240 58104763 56025735 55097270 54584448 52647018 52449401 [9] 51407199 51256021 Smallest eigenvalues: [1] 0.4649662 0.4456508 0.4451130 0.3995442 0.3427075 0.2968905 [7] 0.2295695 0.1795657 0.1278092 -0.5961903 Largest eigenvalues: [1] 65700641 60157099 57324520 56436964 55339609 53508899 52524768 52437061 [9] 51532328 51231568 Smallest eigenvalues: [1] 0.5577856 0.4527810 0.4458934 0.3835374 0.3776193 0.2802705 [7] 0.2154514 0.1445144 0.1419363 -0.3563632 Largest eigenvalues: [1] 65223421 60895085 57957820 56144633 56035443 54525575 52900697 52616035 [9] 52215987 51968281 Smallest eigenvalues: [1] 0.39782567 0.28823019 0.28446353 0.22069442 0.21553641 0.16863895 [7] -0.05032267 -0.31141126 -5.81575747 -7.69533560 Largest eigenvalues: [1] 64266262 60453536 57504345 55727525 55579695 54127336 52721205 52502688 [9] 51816277 51631943 Smallest eigenvalues: [1] 0.44744161 0.38635530 0.23092578 0.18898982 0.12466762 0.09420096 [7] -0.37322925 -0.58675489 -0.67412324 -0.68564567 Largest eigenvalues: [1] 62952282 59101338 56355655 55410283 54201069 52615221 51341441 51200414 [9] 51149735 50090481 Smallest eigenvalues: [1] 0.4273844 0.3784932 0.3661989 0.3221397 0.2524620 0.2348463 [7] 0.2198620 0.1243170 -0.1306255 -25.9120523 Largest eigenvalues: [1] 62738387 59750516 56664971 55210634 55045756 53362807 51999932 51205489 [9] 51059326 50578585 Smallest eigenvalues: [1] 0.44173118 0.41766847 0.29663689 0.21335419 0.20210994 0.19522354 [7] 0.12163997 0.08712377 -0.87484163 -0.94663227 Largest eigenvalues: [1] 63228112 60321751 57075243 55574710 55039494 53586446 51891349 51584565 [9] 50855745 50627836 Smallest eigenvalues: [1] 0.54377460 0.50828821 0.48854719 0.44163766 0.39240959 0.34669646 [7] 0.34436526 0.05140154 -0.11122891 -0.12596470 Largest eigenvalues: [1] 64972987 59924104 57022200 56462457 54575562 53044294 52397338 51748978 [9] 51333843 50759189 Smallest eigenvalues: [1] 0.4501406 0.3606449 0.3351489 0.3155514 0.2163558 0.2070481 [7] 0.1606351 0.1485936 -0.1166917 -0.2877739 Largest eigenvalues: [1] 67238662 60641681 57599752 56898376 55157188 53462277 53003532 52552273 [9] 52034346 51949087 Smallest eigenvalues: [1] 0.4855776 0.4711871 0.4461184 0.3601130 0.2894634 0.2743768 [7] 0.2119518 -0.1307573 -0.2655882 -0.9586734 Largest eigenvalues: [1] 64497109 59896533 57400680 55305819 55219157 53409811 52068333 51737399 [9] 51573997 50837992 Smallest eigenvalues: [1] 0.397829888 0.378073963 0.253567315 0.238277959 -0.004018831 [6] -0.052295377 -0.718975220 -4.879905883 -8.571938271 -21.245612591 Largest eigenvalues: [1] 65227248 60081534 57273826 56045157 54716364 53229891 52335017 51657238 [9] 51447147 50440667 Smallest eigenvalues: [1] 0.5777902 0.5285264 0.4764035 0.4534884 0.4225118 0.3819935 [7] 0.2901142 0.1287401 -0.1943729 -1.4644464 Largest eigenvalues: [1] 64501969 60242924 57223600 56167665 55240134 53424745 52657127 52244620 [9] 51582444 51246166 Smallest eigenvalues: [1] 0.4123787 0.3451237 0.3297252 0.3157962 0.2970803 0.2515298 [7] 0.2125220 0.1820318 -1.5221512 -4.7396950 Largest eigenvalues: [1] 64328113 60651351 57779927 55547709 55502927 54104763 52402784 51958694 [9] 51635639 51565368 Smallest eigenvalues: [1] 0.4577761 0.4134344 0.3510479 0.3415856 0.3107431 0.2597804 [7] 0.1743676 0.1305305 -1.8441918 -28.0020569 Largest eigenvalues: [1] 61973462 59664291 56461507 55476436 54390708 53466216 51743112 51099796 [9] 50388622 50217819 Smallest eigenvalues: [1] 0.5247866 0.4481411 0.3969670 0.3632418 0.3431483 0.2947796 [7] 0.2111178 -0.2536880 -0.4566583 -0.8078062 Largest eigenvalues: [1] 65334554 60569274 58060601 56851042 55045442 53257582 52875732 52745624 [9] 51926352 51763399 Smallest eigenvalues: [1] 0.5285832 0.5109925 0.4110934 0.3956321 0.3101972 0.3050851 [7] 0.2164226 0.2047794 0.1906650 -0.5883761 Largest eigenvalues: [1] 64711578 60930732 57488225 55999436 55603184 54019738 52340364 52305763 [9] 52104855 51531114 Smallest eigenvalues: [1] 0.4575469 0.4278374 0.3985803 0.3787255 0.3161689 0.3017975 [7] 0.2532425 0.2508443 -0.2244553 -11.3013510 Largest eigenvalues: [1] 64409557 60146794 57524712 56331382 55217776 53678895 52329437 51929172 [9] 51903538 50804662 Smallest eigenvalues: [1] 0.5660977 0.5614655 0.5025169 0.4962164 0.4902495 0.4348534 [7] 0.2947021 0.2288873 0.1432563 -0.0124105 Largest eigenvalues: [1] 64272907 60490907 57640892 55890379 55139834 53237009 52178205 52093895 [9] 51549961 51073268 Smallest eigenvalues: [1] 0.4431478 0.4399100 0.4218137 0.4167145 0.2463045 0.1689906 [7] -0.0104216 -0.2808190 -0.8529293 -3.8373678 Largest eigenvalues: [1] 64369733 60285334 57746115 55893417 55085712 53579532 52270457 52075367 [9] 51783573 51100670 Smallest eigenvalues: [1] 0.3130513 0.2887261 0.2371672 0.1944272 0.1386723 0.1364611 [7] 0.1232128 -1.9232410 -7.9194896 -13.1183649 Largest eigenvalues: [1] 64122534 60696893 57585419 55828909 55245155 54151600 52613778 52106942 [9] 51752157 51433019 Smallest eigenvalues: [1] 0.43999769 0.40226682 0.39649554 0.27970738 0.05430193 [6] -0.22573704 -1.05289146 -2.37022721 -11.90138962 -16.72403737 Largest eigenvalues: [1] 65449488 59823464 56982782 56805929 54551980 52740904 52379025 51820153 [9] 51381166 50837962 Smallest eigenvalues: [1] 0.579456899 0.502435226 0.482807395 0.421048881 0.410055727 [6] 0.381170650 0.261967219 0.178262799 -0.004355218 -0.480903358 Largest eigenvalues: [1] 64438436 60590422 57406434 55759978 55464624 53731275 52880215 51914190 [9] 51527865 51403591 Smallest eigenvalues: [1] 0.407300773 0.392086813 0.325684139 0.273974301 0.256428816 [6] 0.164179897 -0.004469679 -0.671087013 -1.378044525 -20.738203116 Largest eigenvalues: [1] 64822376 60634447 57631224 55769033 55603540 54267664 52559980 52310632 [9] 51797851 51487891 Smallest eigenvalues: [1] 0.4137713 0.3905699 0.3565862 0.3275166 0.2977538 0.2717841 [7] 0.1819313 0.0169558 -0.1748779 -0.1783005 Largest eigenvalues: [1] 65922539 60860854 57672089 56012614 55589909 53768319 52651681 52152045 [9] 51932414 51794458 Smallest eigenvalues: [1] 0.473353171 0.386313278 0.373284754 0.329610294 0.321103884 [6] 0.254320967 0.245538546 0.222118931 0.002710441 -1.949912830 Largest eigenvalues: [1] 65590939 60386123 57607027 56710983 55142854 53711026 52580888 52422018 [9] 51947321 51574801 Smallest eigenvalues: [1] 0.4945280 0.4238950 0.3803603 0.2546834 0.2224167 0.2060694 [7] -0.3301968 -0.4081751 -1.7085810 -3.1578185 Largest eigenvalues: [1] 66363963 60972172 58399351 56724628 55903984 54118487 52994515 52849238 [9] 52383466 52052659 Smallest eigenvalues: [1] 0.42914077 0.35112878 0.31436844 0.30790343 0.24369747 0.24065081 [7] 0.19301158 0.09533672 -0.15580056 -5.59920431 Largest eigenvalues: [1] 65193948 59359400 56842649 56018359 54657947 53084381 51988950 51280754 [9] 51181011 50571546 Smallest eigenvalues: [1] 0.44540364 0.39647879 0.38906845 0.28337812 0.24560944 0.21852804 [7] 0.17799999 0.09528115 -0.14839172 -0.31872084 Largest eigenvalues: [1] 66792483 61350523 58455361 56892051 55538783 53790808 53077143 52875836 [9] 52053187 51988881 Smallest eigenvalues: [1] 0.55952852 0.51764265 0.50001523 0.46404429 0.44538113 0.44402248 [7] 0.24070330 0.23478026 0.05481448 -0.04383853 Largest eigenvalues: [1] 62692441 60109822 56752820 55453947 55236769 53376613 52221842 51651821 [9] 51206136 50448952 Smallest eigenvalues: [1] 0.6267241 0.5998844 0.5530882 0.5524737 0.4416732 0.4369281 [7] 0.3279452 0.2550960 0.1971534 -0.8838666 Largest eigenvalues: [1] 64761478 60403651 57609591 56257067 55162259 53729655 52228340 52002230 [9] 51812555 50983509 Smallest eigenvalues: [1] 0.4826473 0.4228256 0.3656121 0.3600153 0.3477249 0.3439085 [7] 0.2083771 0.1947293 -0.5610049 -2.6252851 Largest eigenvalues: [1] 64008134 59959024 57243562 56178801 54866342 53224151 52107288 52055389 [9] 51687140 50616711 Smallest eigenvalues: [1] 0.6159226 0.5157152 0.5116598 0.4669934 0.4399881 0.3838208 [7] 0.3699063 0.3082080 0.1883525 -0.1889362 Largest eigenvalues: [1] 65133528 61181729 58309661 56526524 56293937 54673842 53450112 52625344 [9] 52499007 51921232 Smallest eigenvalues: [1] 0.4760437 0.4668003 0.4293443 0.3952245 0.3801807 0.3672524 [7] 0.3519612 0.1837539 0.1387142 -0.6580002 Largest eigenvalues: [1] 64887470 61097338 58163693 56198046 56038588 54481068 52530406 52495724 [9] 52176568 51678814 Smallest eigenvalues: [1] 0.46768616 0.45620225 0.39409128 0.35109722 0.34220883 0.31387560 [7] 0.30997247 0.11256245 0.06658107 -2.99363539 Largest eigenvalues: [1] 64334090 59488325 56631915 55969789 54474328 52777639 51983950 51483351 [9] 51476566 50541576 Smallest eigenvalues: [1] 0.43370938 0.37139639 0.36564579 0.29066053 0.24592875 0.24374540 [7] 0.21965733 0.09210695 -1.32531585 -7.57687311 Largest eigenvalues: [1] 64922553 60111053 57321327 55982375 55029462 53636310 52062716 51779950 [9] 51730159 50806505 Smallest eigenvalues: [1] 0.40150300 0.35584018 0.30906548 0.23974026 0.16015790 [6] 0.06549485 -0.01829593 -0.90373968 -1.40924301 -11.73826233 Largest eigenvalues: [1] 65594886 60841569 58168537 56319756 55590571 54082489 52811001 52331485 [9] 52074493 51587397 Smallest eigenvalues: [1] 0.51077279 0.47981713 0.46476457 0.45878954 0.43980515 0.40873839 [7] 0.40144307 0.31094595 0.08014935 -0.13509335 Largest eigenvalues: [1] 63646959 59607637 57339683 55419658 54936795 53229512 51584319 51530131 [9] 51421068 50469507 Smallest eigenvalues: [1] 0.3073931 0.2930366 0.2597274 0.2550049 0.2085749 0.1056647 [7] -0.2352336 -0.4998183 -1.3890788 -4.3409479 Largest eigenvalues: [1] 65416691 59465517 57051025 56035790 54260323 52730294 52149977 51766651 [9] 51470333 51088403 Smallest eigenvalues: [1] 0.4190005 0.3460691 0.3336302 0.3272618 0.2213292 0.1830725 [7] -1.0805507 -3.0684524 -3.3445998 -10.3133783 Largest eigenvalues: [1] 65737787 60089277 57436722 57309202 54759970 53183730 53151518 52437514 [9] 52249643 51672466 Smallest eigenvalues: [1] 0.36984410 0.32354837 0.24748929 0.22111587 0.14126368 [6] 0.13077740 0.10501490 0.06099851 -0.61134840 -14.18339231 Largest eigenvalues: [1] 65764822 59896029 57470203 56665039 54688670 53054987 52707939 51908814 [9] 51627244 51108944 Smallest eigenvalues: [1] 0.5819184 0.5608733 0.3754795 0.3612453 0.3017642 0.2798739 [7] 0.2691494 0.2636202 0.2414923 -1.4905963 Largest eigenvalues: [1] 65110472 60612278 57822830 56161695 55523546 54173962 52314028 52294596 [9] 52235862 51311441 Smallest eigenvalues: [1] 0.3524496 0.3458904 0.3260322 0.3108317 0.2751863 0.2682491 [7] 0.2303524 0.1790908 -0.6312919 -1.5618378 Largest eigenvalues: [1] 64602493 60763712 57862391 56431761 55977201 54216431 52373058 52224317 [9] 52088643 51186602 Smallest eigenvalues: [1] 0.4629705 0.4458128 0.4374147 0.3750568 0.3426212 0.3401255 [7] 0.2391934 0.1461593 0.0739874 -0.2468892 Largest eigenvalues: [1] 64424944 61143015 57717909 56311141 55838433 54251583 52467238 52125546 [9] 51997919 51275565 Smallest eigenvalues: [1] 0.47285252 0.43627100 0.38707403 0.32341508 0.31561133 0.19820748 [7] 0.13297387 0.02921038 -0.09971439 -3.74691374 Largest eigenvalues: [1] 61722328 59500264 56818489 54664848 54394991 52931245 51660575 51550804 [9] 50814602 50625100 Smallest eigenvalues: [1] 0.4035618 0.3801351 0.3149668 0.3064326 0.3054499 0.2614515 [7] 0.2355876 0.2210825 -0.4099762 -0.9586278 Largest eigenvalues: [1] 64106118 60272910 57575847 55655209 55192127 53702907 51909633 51723919 [9] 51719551 51042130 Smallest eigenvalues: [1] 0.47131514 0.45438683 0.35194818 0.27723457 0.25839899 0.24195155 [7] 0.22931960 -0.00658627 -0.17208871 -0.17659668 Largest eigenvalues: [1] 65248965 60892989 58104344 55747389 55560101 54328809 52647524 52370895 [9] 51816747 51663061 Smallest eigenvalues: [1] 0.5154123 0.4797545 0.3853984 0.3600652 0.3122994 0.2819511 [7] 0.2778904 0.2715248 -0.8974183 -1.5345765 Largest eigenvalues: [1] 64862637 59754598 57172231 55934843 54958512 53573132 51990718 51950527 [9] 51677258 51116495 Smallest eigenvalues: [1] 0.4214306 0.4110650 0.4050761 0.3763895 0.3110774 0.2695821 [7] 0.1962728 0.1687833 0.1519829 -0.1058320 Largest eigenvalues: [1] 64238636 60048155 57359374 55482445 55406002 53809849 52232140 51978960 [9] 51547965 51201307 Smallest eigenvalues: [1] 0.277144729 0.214681764 0.159625608 0.076487123 0.022964958 [6] 0.005611657 -0.111955304 -0.861141442 -15.397538787 -17.238356175 Largest eigenvalues: [1] 62449725 60143066 56267634 55237774 55162765 53416462 51961707 51875288 [9] 50966727 50446254 Smallest eigenvalues: [1] 0.5100599 0.4865241 0.4829214 0.4238372 0.4060621 0.3861233 [7] 0.3376398 0.3364275 0.2984327 -1.1160096 Largest eigenvalues: [1] 65260449 60596029 57727287 56696319 55462784 53943489 52572445 52297343 [9] 51834597 51258823 Smallest eigenvalues: [1] 0.57145427 0.55753269 0.53459171 0.53095143 0.44756498 0.37224306 [7] 0.35544234 0.32169649 0.31249705 -0.05275244 Largest eigenvalues: [1] 65558192 61059809 58282166 57127677 55603915 53980074 53089171 52803432 [9] 52324969 51803867 Smallest eigenvalues: [1] 0.37653562 0.36138815 0.35813638 0.27276133 0.19882070 -0.07922013 [7] -0.30848050 -1.08283429 -3.13802442 -9.46730544 Largest eigenvalues: [1] 63085319 60049489 56991183 55248438 55220761 53434653 52200551 51831758 [9] 51249734 51036070 Smallest eigenvalues: [1] 0.5203221 0.4873814 0.4515710 0.4095868 0.3490400 0.2566253 [7] 0.2142105 0.1203538 -0.4237941 -0.4264951 Largest eigenvalues: [1] 64156010 60635895 58362659 55865418 55442212 54608723 52762325 52204606 [9] 51595217 51412822 Smallest eigenvalues: [1] 0.4032245 0.3893146 0.3863251 0.3032663 0.2595042 0.2593872 [7] 0.2391131 0.2389307 0.2120504 -0.9185261 Largest eigenvalues: [1] 64574369 60691638 57758946 55713216 55647294 54280606 52424015 52010041 [9] 51820598 51168637 Smallest eigenvalues: [1] 0.36192509 0.26728992 0.03431254 -0.01634378 -0.04062130 -0.08608666 [7] -0.44391988 -0.66291506 -1.10601940 -1.15066329 Largest eigenvalues: [1] 62087352 60191546 56866220 55555559 55180859 53718368 52364337 51850741 [9] 50922203 50808616 Smallest eigenvalues: [1] 0.3772597510 0.3292329620 0.2687995420 0.2523414433 0.2378080414 [6] 0.2186807557 0.0560499362 0.0003070804 -2.6481189196 -6.3232371937 Largest eigenvalues: [1] 63782306 60608112 57859641 55782364 55779705 54129684 52668698 52177968 [9] 51786156 51648349 Smallest eigenvalues: [1] 0.5233690 0.4437868 0.4241692 0.4111181 0.4055430 0.3617718 [7] 0.3509802 0.3417824 0.3302832 -0.4323087 Largest eigenvalues: [1] 63482282 59878366 56893612 55701351 54776503 53199528 51696878 51464134 [9] 51183533 50362063 Smallest eigenvalues: [1] 0.4488624 0.4088865 0.3980209 0.3884198 0.3125796 0.2777834 [7] 0.2760359 0.2501593 0.1885041 -1.3077888 Largest eigenvalues: [1] 64149204 60041350 56955629 56047051 54999193 53376109 51993359 51850399 [9] 51711345 51028895 Smallest eigenvalues: [1] 0.4166548 0.2597084 0.2583535 0.2320402 0.2255468 0.1859566 [7] 0.1799141 -2.1804519 -4.1661929 -6.1697151 Largest eigenvalues: [1] 64882251 59920192 56949407 56574538 54648363 53160227 52342638 52232011 [9] 51734730 50997739 Smallest eigenvalues: [1] 0.5272917 0.4095600 0.3948305 0.3046950 0.2475154 0.2275251 [7] -0.1532177 -0.3268616 -0.7947572 -19.8696438 Largest eigenvalues: [1] 65358244 60066596 57055828 55849338 54942025 53381722 52059797 52009717 [9] 51628753 51226113 Smallest eigenvalues: [1] 0.50273204 0.50209258 0.46063776 0.37593047 0.36467257 0.35484522 [7] 0.26495825 0.23441842 -0.02816597 -0.40853757 Largest eigenvalues: [1] 62632943 59753858 56714706 55162487 54708107 53279468 51918442 51717350 [9] 50859528 50612904 Smallest eigenvalues: [1] 0.47437986 0.44415297 0.43620424 0.40146302 0.38365035 0.34035738 [7] 0.32023747 0.08923091 -0.01309224 -0.12941651 Largest eigenvalues: [1] 63703038 60259754 57314930 55437871 54815591 53387231 51959068 51488468 [9] 51477153 51118986 Smallest eigenvalues: [1] 0.4210618 0.4166619 0.3982851 0.2895063 0.2790783 0.2592374 [7] 0.1796040 0.1664031 0.1333599 -0.1070419 Largest eigenvalues: [1] 64587864 61193033 58200081 56047958 55685895 54144612 52822672 52197810 [9] 52170049 51940656 Smallest eigenvalues: [1] 0.4844979 0.4515795 0.3957639 0.3685315 0.3619856 0.2719537 [7] 0.2345142 -0.1887088 -0.2779968 -0.5223525 Largest eigenvalues: [1] 63709288 59778623 57400401 55296419 54912841 53616548 51897370 51476591 [9] 51207765 50669660 Smallest eigenvalues: [1] 0.47636033 0.41777917 0.41485096 0.36978931 0.32379331 0.31066984 [7] 0.28828535 0.20830662 0.15596870 -0.03956168 Largest eigenvalues: [1] 64191901 59420600 57241350 55558927 54466917 53029562 51836568 51712867 [9] 51253439 50822922 Smallest eigenvalues: [1] 0.4408627 0.4142176 0.4055389 0.3828166 0.3689204 0.3423735 [7] 0.3056915 0.2727094 -0.3386079 -35.0000879 Largest eigenvalues: [1] 66204329 60463825 57849191 57064284 55079541 53692004 53074905 51940792 [9] 51891991 51084282 Smallest eigenvalues: [1] 0.4481405 0.3482361 0.3100445 0.2780136 0.2669352 0.2583741 [7] -0.1721777 -0.4230542 -3.6672215 -5.0348088 Largest eigenvalues: [1] 65302807 59940230 57841173 56458913 55204677 53999009 52710915 52391616 [9] 52386422 51826046 Smallest eigenvalues: [1] 0.3431130 0.3033891 0.3020519 0.2658873 0.2407580 0.2294935 [7] -0.6470565 -0.7433620 -1.3538775 -8.8507396 Largest eigenvalues: [1] 62330565 59868631 57460374 55868313 54143647 54070883 52339890 52045901 [9] 50999348 50683380 Smallest eigenvalues: [1] 0.259414034 0.235911394 0.182107200 0.142726388 0.130404902 [6] 0.029811818 0.023267256 0.007202171 -0.994741717 -21.206815907 Largest eigenvalues: [1] 62877784 60705250 57741091 55542502 55186497 53948591 52171000 51819497 [9] 51353228 51205627 Smallest eigenvalues: [1] 0.5737969 0.4855040 0.4784855 0.4346783 0.3908720 0.3289955 [7] 0.3010678 0.2782222 0.2361162 -1.1183358 Largest eigenvalues: [1] 65216103 61054494 57854856 56793021 55371383 53880409 52798391 52707747 [9] 52163630 51912475 Smallest eigenvalues: [1] 0.5294325 0.4635894 0.4617910 0.4325612 0.4084160 0.3373342 [7] 0.2814365 0.2560524 0.1294240 -0.1843345 Largest eigenvalues: [1] 65449410 60014994 57825275 56587435 54687188 53050099 52825876 51791074 [9] 51467864 50887624 Smallest eigenvalues: [1] 0.4221387 0.4184757 0.4086284 0.3485475 0.3457772 0.2967528 [7] 0.1941861 0.1921846 -0.5077250 -21.1804028 Largest eigenvalues: [1] 64988465 60352046 57684700 56518824 55109053 53392058 52701138 51982890 [9] 51888836 50972132 Smallest eigenvalues: [1] 0.5082897 0.4282380 0.4250931 0.4011988 0.3824082 0.3780757 [7] 0.3031114 0.1892091 0.1795391 -1.7545148 Largest eigenvalues: [1] 62917392 60240179 57547923 55380784 54903530 53808175 51886213 51787727 [9] 51064877 50910118 Smallest eigenvalues: [1] 0.6067477 0.5927991 0.5574038 0.5474962 0.4485107 0.3760682 [7] 0.2543690 0.2059890 0.1842158 -0.8582076 Largest eigenvalues: [1] 64328609 60026389 56836071 55823284 54973607 53315746 51705917 51629483 [9] 51386606 50498134 Smallest eigenvalues: [1] 0.12910512 0.07293391 0.06951283 -0.05119517 -0.34512771 [6] -1.88304651 -9.40686953 -27.09433150 -33.18028364 -48.11054503 Largest eigenvalues: [1] 65153055 60164456 56442164 56310870 55170708 53288162 52298985 52261900 [9] 52154918 51110187 Smallest eigenvalues: [1] 0.37225355 0.34600652 0.34468136 0.31751447 0.28717586 0.08619961 [7] 0.07734499 0.05279732 -1.03268731 -3.56855177 Largest eigenvalues: [1] 62680167 59026230 56573960 54997849 54694230 53055512 51846640 51479952 [9] 50871104 50478001 Smallest eigenvalues: [1] 0.45239730 0.42975724 0.41104833 0.36258756 0.32181852 0.26670411 [7] 0.23487867 0.05102641 -0.17237684 -0.29572263 Largest eigenvalues: [1] 62220890 59303055 56861079 54802973 54441244 52855126 51857810 51233709 [9] 50933831 50785243 Smallest eigenvalues: [1] 0.3818677 0.3782604 0.3633752 0.3357047 0.2888086 0.2556823 [7] 0.2234954 0.1470575 0.1369593 -0.8735760 Largest eigenvalues: [1] 63566785 60083765 57099975 55489036 55235344 53896763 52321413 51908615 [9] 51385316 51165763 Smallest eigenvalues: [1] 0.4966688 0.4788885 0.3355494 0.3007781 0.2672923 0.2261897 [7] 0.2238763 0.1019961 -1.0912447 -6.6039892 Largest eigenvalues: [1] 64653666 60869496 57258495 56228121 55780385 53967814 52447747 52254164 [9] 51917458 51453584 Smallest eigenvalues: [1] 0.4381800 0.4316199 0.3983476 0.3187999 0.2771435 0.2724599 [7] 0.2346466 -0.1702307 -0.3342011 -0.6965179 Largest eigenvalues: [1] 64594942 60348314 57792539 56532087 55357813 53889448 52964796 52564120 [9] 52142880 51682595 Smallest eigenvalues: [1] 0.4496823 0.4016000 0.3382060 0.3209556 0.3098294 0.2719140 [7] 0.2412580 0.1896744 -0.1484066 -2.0483270 Largest eigenvalues: [1] 63997836 60440199 57335456 56061634 55668833 53991379 52219031 52098254 [9] 52005859 50985152 Smallest eigenvalues: [1] 0.4811915 0.4304199 0.3407603 0.3148029 0.2680707 0.2468190 [7] 0.2433870 0.1324856 0.1152177 -0.1885876 Largest eigenvalues: [1] 63562644 60086269 57788449 55269061 55220238 53850732 52230843 52143408 [9] 51429268 51262170 Smallest eigenvalues: [1] 0.43073613 0.39598935 0.33275605 0.30962494 0.27688007 0.23739327 [7] 0.19458683 0.02997172 -0.05313936 -0.28813060 Largest eigenvalues: [1] 64527663 61100911 57750556 56518302 55405523 53767320 52422619 52388936 [9] 51715561 51329513 Smallest eigenvalues: [1] 0.4527159 0.4336027 0.4120107 0.3264515 0.2806342 0.2378237 [7] 0.1783002 -0.1671808 -0.2362833 -5.3096692 Largest eigenvalues: [1] 61972903 60005066 56538383 55233509 54318343 53454239 52027901 51511951 [9] 50551854 50315658 Smallest eigenvalues: [1] 0.4417027 0.3347862 0.3318064 0.3074318 0.2699170 0.2271045 [7] 0.2229960 0.1944539 -1.7985666 -4.7750955 Largest eigenvalues: [1] 64265014 60124704 57239178 56157164 54913847 53564161 52347347 52224350 [9] 52190012 51355914 Smallest eigenvalues: [1] 0.47951890 0.47565483 0.43251610 0.34003769 0.31453153 0.12543344 [7] 0.10880617 0.08034982 -0.23906263 -0.25008458 Largest eigenvalues: [1] 64350979 59859908 57085181 56078613 54226984 52761362 52079246 51814823 [9] 51413064 50955594 Smallest eigenvalues: [1] 0.5019727 0.4918704 0.3884751 0.3039743 0.2629069 0.1860632 [7] 0.1098385 -0.1473894 -0.9991205 -4.6168133 Largest eigenvalues: [1] 63305817 60798931 57621039 56131025 55187364 54301559 52956833 52296974 [9] 51988309 51344844 Smallest eigenvalues: [1] 0.50341827 0.47562266 0.46253639 0.40748343 0.34715293 0.31451924 [7] 0.30546726 0.24999597 0.01766297 -1.45991536 Largest eigenvalues: [1] 65427219 60458005 57412597 56859672 55327476 53704865 52904921 52425012 [9] 51836097 51417679 Smallest eigenvalues: [1] 0.3351082 0.2863840 0.2438458 0.2166721 0.2130028 0.1592809 [7] -0.2582428 -4.6442186 -7.5484116 -8.3979607 Largest eigenvalues: [1] 66474731 61071583 58821985 57012305 55678299 54316549 52989560 52901448 [9] 52556932 52246237 Smallest eigenvalues: [1] 0.4002648 0.3428217 0.3320428 0.3271492 0.2514968 0.2120884 [7] 0.1016588 -0.2699683 -1.6983558 -6.6061162 Largest eigenvalues: [1] 66065561 59791156 56893225 56787147 54470057 52988021 52519534 51363955 [9] 51317347 50587361 Smallest eigenvalues: [1] 0.57368883 0.51412926 0.40952501 0.35193654 0.31713598 0.30383883 [7] 0.28670960 0.17305459 0.06471892 -0.48991242 Largest eigenvalues: [1] 63811778 60105002 57330817 55434262 54714645 53254830 51953399 51625900 [9] 51485871 50917303 Smallest eigenvalues: [1] 0.5223011 0.4422109 0.4303282 0.4099498 0.4033249 0.3882165 [7] 0.3328612 0.2392868 0.2249731 -0.7703900 Largest eigenvalues: [1] 64005988 61088038 57811873 56237333 55856227 54235906 52552181 52402561 [9] 52098404 51342715 Smallest eigenvalues: [1] 0.53425894 0.48777593 0.47289628 0.45649236 0.43235734 0.41169416 [7] 0.23800134 0.16890563 0.02712257 -4.13467303 Largest eigenvalues: [1] 63558925 59683960 57096125 55326559 55323519 53734377 52097261 52057624 [9] 51323889 51040636 Smallest eigenvalues: [1] 0.11308089 0.08086033 0.05926124 -0.06016864 -0.20375368 [6] -0.45388423 -0.48104215 -6.55025643 -8.53189029 -13.72622378 Largest eigenvalues: [1] 60203992 59667671 57183170 55558366 53778750 53539625 51805577 51783634 [9] 50886306 50188598 Smallest eigenvalues: [1] 0.6042306 0.5946579 0.5763476 0.4978116 0.4056226 0.2799841 [7] 0.2220836 0.1684605 -0.9054644 -1.3985510 Largest eigenvalues: [1] 65266362 60365648 57316716 56578301 55199894 53460254 52474940 52264363 [9] 52036026 51211656 Smallest eigenvalues: [1] 0.33016698 0.31910528 0.31804658 0.25808180 0.22520935 [6] 0.08478568 0.02300430 -1.50545489 -3.97236433 -12.94926674 Largest eigenvalues: [1] 66743039 60618127 58054794 57125957 55237153 53445825 53378151 52278860 [9] 52014812 51365546 Smallest eigenvalues: [1] 0.1735173 0.1715748 -0.1342431 -0.1597266 -0.2054492 -2.8952218 [7] -10.7840417 -14.1758333 -18.0135490 -45.6083195 Largest eigenvalues: [1] 64138061 60309180 57625721 55555563 55094754 53900992 52416953 52335947 [9] 51403954 51311170 Smallest eigenvalues: [1] 0.57309293 0.44400917 0.44251446 0.23416016 0.20330501 0.02873755 [7] -0.03499777 -0.07899451 -0.71605283 -9.51492122 Largest eigenvalues: [1] 63725117 60096339 57044148 55605588 55296935 53597972 52377618 52056956 [9] 51639836 51228933 Smallest eigenvalues: [1] 0.311450710 0.308014161 0.250101929 0.159539669 0.147845101 [6] -0.001237055 -0.020688332 -0.903911591 -1.458401957 -2.481793939 Largest eigenvalues: [1] 64610281 59993688 56506071 56059537 54536632 52879752 52107641 51544599 [9] 51427655 50596643 Smallest eigenvalues: [1] 0.1872282 0.1579812 -0.2458350 -0.3544927 -0.4591195 -0.7787538 [7] -1.3174774 -8.8873714 -13.9008192 -45.2157935 Largest eigenvalues: [1] 63120365 61160335 57527503 56025955 54968204 54341334 52253122 52129928 [9] 51002782 50883681 Smallest eigenvalues: [1] 0.44063593 0.43249308 0.37115635 0.33283345 0.28408980 0.26166240 [7] 0.17621458 -0.07496801 -0.43992879 -0.77208740 Largest eigenvalues: [1] 65235758 60405393 58106427 56865862 54876283 53201297 52729928 52399719 [9] 51871340 51615993 Smallest eigenvalues: [1] 0.5026744 0.4855860 0.3991645 0.3829994 0.3601882 0.3062121 [7] 0.2815905 0.2577905 0.1946266 -0.8318331 Largest eigenvalues: [1] 65908125 59662722 56591735 56327336 54420293 52682685 52338597 51785282 [9] 51510040 51030351 Smallest eigenvalues: [1] -0.07833204 -0.22851411 -0.43475687 -0.56387118 -1.24443253 -1.86830562 [7] -1.86846587 -2.06105839 -2.97130135 -9.29840438 Largest eigenvalues: [1] 63922135 60755539 57674741 55993591 55782357 54203302 52591939 52513450 [9] 51936391 51668677 Smallest eigenvalues: [1] 0.3949043 0.3722751 0.3620888 0.3573198 0.3550337 0.2158414 [7] -0.8612041 -0.9034753 -3.6333080 -5.0483643 Largest eigenvalues: [1] 65081248 59878627 57466677 56299282 54724920 53045273 52373184 52336020 [9] 51591981 51463356 Smallest eigenvalues: [1] 0.46041997 0.42956390 0.30742440 0.30708329 0.16968009 0.11858813 [7] -0.02366868 -0.36030556 -0.50952099 -6.73914304 Largest eigenvalues: [1] 64728409 59521913 56998297 55545598 54096031 52596825 52017726 51727375 [9] 51183439 51032262 Smallest eigenvalues: [1] 0.5228137 0.5136512 0.5100477 0.4758227 0.4681192 0.4335429 [7] 0.3860520 0.2912431 0.2538382 -0.5944993 Largest eigenvalues: [1] 63993162 60587833 57122163 56311162 55355661 53639219 52275395 52071700 [9] 51988670 51215584 Smallest eigenvalues: [1] 0.41861770 0.35889258 0.31835313 0.31077346 0.25839709 0.17377898 [7] 0.05758828 -0.05755575 -0.10683318 -0.41837805 Largest eigenvalues: [1] 61275159 60010721 57106995 55782390 53857925 53816823 52144297 51623684 [9] 50730371 50686008 Smallest eigenvalues: [1] 0.4842106 0.4727960 0.4235241 0.3743658 0.2943528 0.2790244 [7] 0.2174392 0.1951370 -1.6850298 -29.5821733 Largest eigenvalues: [1] 63811226 59939656 57051267 55643304 55142257 53280007 52132599 51657246 [9] 51541495 51022965 Smallest eigenvalues: [1] 0.4668311 0.4531328 0.3611645 0.2852611 0.2818005 0.2649809 [7] 0.1932553 -0.0333744 -0.2051055 -1.5172173 Largest eigenvalues: [1] 64699488 59422617 56593254 55971313 54259860 52791243 52000611 51680095 [9] 51184343 50827453 Smallest eigenvalues: [1] 0.4974162 0.4607634 0.4111369 0.3812524 0.3495022 0.2679391 [7] 0.2487249 0.1854849 -0.2348013 -6.0789563 Largest eigenvalues: [1] 63525673 60405429 57531887 55651021 55440330 54131804 52333415 52303281 [9] 51565656 51242176 Smallest eigenvalues: [1] 0.4121963 0.4092734 0.3806980 0.3575207 0.2573680 0.2354548 [7] 0.1720906 0.1185910 -0.3438910 -0.6660165 Largest eigenvalues: [1] 65121656 61135684 58455424 56536342 55851432 54276180 53101072 52543997 [9] 52034390 51916285 Smallest eigenvalues: [1] 0.4342009 0.3989505 0.3852095 0.3091908 0.3063040 0.2962070 [7] 0.2270725 0.2221306 -0.7151561 -1.1500861 Largest eigenvalues: [1] 64962457 59879953 57827566 56144945 55001552 53920448 52183031 52139025 [9] 51769687 51190569 Smallest eigenvalues: [1] 0.4837691 0.4318162 0.4270993 0.3581527 0.3362051 0.3085269 [7] 0.2935498 0.2416242 0.1891279 -1.1688314 Largest eigenvalues: [1] 64628789 59860891 57237313 55540903 54904925 53431359 52075358 51669393 [9] 51655421 51257737 Smallest eigenvalues: [1] 0.29248756 0.19965439 0.19247584 0.08293757 0.08224070 [6] -0.03897466 -0.03994578 -3.27708633 -8.37655305 -18.71079443 Largest eigenvalues: [1] 63071067 58713267 55994656 55243424 53857442 52663337 51408405 51123366 [9] 50884044 50045346 Smallest eigenvalues: [1] 0.3970637 0.3937481 0.3480658 0.3181406 0.3081975 0.3016968 [7] 0.2863138 0.2297331 0.1835831 -2.9488796 Largest eigenvalues: [1] 65114829 60428118 57096136 57033364 54940409 53441669 52799333 52540473 [9] 52009455 51656471 Smallest eigenvalues: [1] 0.4821478 0.4321006 0.4307401 0.3063427 0.2404440 0.1870286 [7] 0.1689045 0.1511480 0.1267058 -0.2770814 Largest eigenvalues: [1] 63705043 60319918 57271441 55266267 55221658 53423604 52897570 51790072 [9] 51718034 51469796 Smallest eigenvalues: [1] 0.4709553 0.4686872 0.4171933 0.4034580 0.3093342 0.2728820 [7] 0.1629109 0.1152926 -0.6973689 -1.3624365 Largest eigenvalues: [1] 65073384 59731159 57333085 56096258 54826182 53325745 52122491 52050217 [9] 51911350 51202078 Smallest eigenvalues: [1] 0.27250745 0.21846706 0.20965168 0.09725675 -0.00939362 [6] -0.43955782 -14.23894000 -16.07056221 -57.87512347 -68.26835266 Largest eigenvalues: [1] 63003664 59381268 56182687 54650493 54540268 52969259 51762313 51477914 [9] 50803443 50577504 Smallest eigenvalues: [1] 0.54667633 0.38980251 0.33372748 0.31956173 0.29728659 0.26991633 [7] 0.26944734 -0.08663531 -1.04504535 -1.18452027 Largest eigenvalues: [1] 62385185 59565030 57341102 55291269 54545542 53507424 52374201 51826888 [9] 50835599 50691868 Smallest eigenvalues: [1] 0.550223391 0.525924343 0.517918325 0.506911687 0.465598629 [6] 0.424860826 0.375987183 0.080182941 0.001190248 -0.014031902 Largest eigenvalues: [1] 65399013 59878085 57142158 56207364 54622400 52893762 52387161 51552133 [9] 51525100 50741746 Smallest eigenvalues: [1] 0.366823762 0.319180191 0.293875423 0.272850953 0.236965141 [6] 0.232195740 0.193625525 0.164064308 -0.006541406 -0.333933932 Largest eigenvalues: [1] 63775035 59217021 57019931 55091508 54479672 53123552 51377346 51325381 [9] 51078430 50358138 Smallest eigenvalues: [1] 0.4907138 0.4516266 0.4079258 0.3676228 0.3068431 0.2120014 [7] 0.1670168 -0.3884251 -2.8482545 -3.9321699 Largest eigenvalues: [1] 63525808 60044342 56767935 55036768 54909498 53108451 51765105 51022970 [9] 50989216 50703666 Smallest eigenvalues: [1] 0.56765003 0.52402795 0.46992327 0.36465294 0.30585874 0.30289750 [7] 0.23509138 0.21745366 0.20829651 -0.06848167 Largest eigenvalues: [1] 63041871 60208038 56844993 55548294 55172206 53708312 52054080 51878742 [9] 51290547 50866992 Smallest eigenvalues: [1] 0.5584792 0.4906320 0.4089252 0.3770547 0.3339411 0.2092842 [7] 0.1103486 -0.2060481 -0.4229839 -1.0691039 Largest eigenvalues: [1] 64929348 60217277 57422070 56502244 54983184 53422258 52442049 52080673 [9] 51573806 50969657 Smallest eigenvalues: [1] 0.5889441 0.5215414 0.4411243 0.4157165 0.3190951 0.3016080 [7] 0.2593738 0.2485206 -0.1325038 -0.5351529 Largest eigenvalues: [1] 65226507 59981115 56808633 56352941 54701185 52996120 52427966 51801599 [9] 51760707 51047748 Smallest eigenvalues: [1] 0.39718859 0.35128678 0.33118365 0.25306610 0.19290664 [6] 0.04594924 -0.43040197 -5.50962085 -12.21644820 -38.49245698 Largest eigenvalues: [1] 62769956 59683171 56394355 54931698 54836453 52811957 51783522 51095392 [9] 50836240 50387211 Smallest eigenvalues: [1] 0.4789005 0.4559953 0.3990029 0.2907194 0.2507092 0.2474317 [7] 0.2391723 -0.4709886 -0.7793261 -2.6247577 Largest eigenvalues: [1] 67132127 60650125 58580230 57394993 55255674 53606872 53550940 52884531 [9] 52216156 52054333 Smallest eigenvalues: [1] 0.5563766 0.5053720 0.3644869 0.3376697 0.2914989 0.2892991 [7] 0.2543838 0.1308287 0.1098330 -0.9911260 Largest eigenvalues: [1] 65965642 60953694 58391069 57303180 55520031 54112145 53246459 52755659 [9] 52451211 51736276 Smallest eigenvalues: [1] 0.43576162 0.41867014 0.35206250 0.28186734 0.27241947 0.22117037 [7] 0.14696657 0.13024964 0.09817621 -0.45435093 Largest eigenvalues: [1] 63333058 60437452 57138114 55507087 55225999 53883635 52401455 52300670 [9] 51375277 51245704 Smallest eigenvalues: [1] 0.4979374 0.4661988 0.4570703 0.3672545 0.2917200 0.2315145 [7] 0.2106453 0.1749869 -0.1315438 -0.3352843 Largest eigenvalues: [1] 62976081 59466654 56488345 54910953 54618364 52885919 51474137 51050076 [9] 50957164 50311061 Smallest eigenvalues: [1] 0.46079882 0.44038488 0.32332373 0.29822588 0.18894853 0.16291772 [7] -0.02099049 -0.14208520 -0.83208624 -2.29881614 Largest eigenvalues: [1] 65374307 60247216 57667844 56506216 55020699 53571552 52430179 52394908 [9] 52322313 51595311 Smallest eigenvalues: [1] 0.42016858 0.31741860 0.30699500 0.24756346 0.23962368 0.23007383 [7] 0.17421150 0.05369563 -0.21341390 -0.25729259 Largest eigenvalues: [1] 64886803 59489955 57131947 55706658 54690895 53328189 51783974 51703330 [9] 51236363 50717543 Smallest eigenvalues: [1] 0.4225963 0.2895787 0.2838451 0.2690289 0.1845481 0.1728189 [7] 0.1030672 0.0723467 -0.8260505 -1.2289281 Largest eigenvalues: [1] 64925557 60564137 57899968 55598272 55479431 53968439 52934865 52064048 [9] 51983777 51731481 Smallest eigenvalues: [1] 0.4667609 0.4374028 0.3997889 0.3994561 0.3443882 0.3341805 [7] 0.2868249 0.2244484 -1.0876611 -20.4349850 Largest eigenvalues: [1] 63508902 59989291 57127841 55847374 55292775 53597121 51983273 51952960 [9] 51775511 50937437 Smallest eigenvalues: [1] 0.55385261 0.51342060 0.43817217 0.41574485 0.38453103 0.27942107 [7] 0.27320378 0.27271548 0.25904802 -0.09261359 Largest eigenvalues: [1] 65307788 60735843 57810156 56834105 55341693 53717776 52910471 52409389 [9] 52149470 51339824 Smallest eigenvalues: [1] 0.52230262 0.51970535 0.47814213 0.36908567 0.30457429 0.30328106 [7] 0.21061115 0.06329256 0.04996261 -3.47754804 Largest eigenvalues: [1] 62660041 60235726 56907447 55564260 54816992 53781242 52209878 51653991 [9] 50997388 50780734 Smallest eigenvalues: [1] 0.29430075 0.24786529 0.21905304 0.16531437 0.05192744 [6] -0.17115461 -0.58350368 -10.60787097 -13.57307915 -27.51346592 Largest eigenvalues: [1] 62323970 59029021 56408397 54375113 54335987 52632027 51572028 51451611 [9] 50577764 50342695 Smallest eigenvalues: [1] 0.50570073 0.50105826 0.41825566 0.39406476 0.38547953 0.38098189 [7] 0.34199021 0.21766503 -0.09351116 -0.25112799 Largest eigenvalues: [1] 64408718 60099341 57641196 56280002 54637882 53194595 52324811 51832298 [9] 51686766 51056797 Smallest eigenvalues: [1] 0.5150850 0.4606915 0.4496685 0.4290225 0.3603103 0.3312539 [7] 0.2832682 0.1763414 -0.1717241 -0.3835961 Largest eigenvalues: [1] 65221829 60345850 56999490 56274396 55532917 53682279 52272483 52185730 [9] 51696216 51081621 Smallest eigenvalues: [1] 0.16295783 0.10940209 -0.01431263 -0.17549372 -0.36040939 [6] -1.69599575 -6.18910252 -18.44027507 -23.52418014 -93.67638236 Largest eigenvalues: [1] 65285636 60893104 57157784 56991096 55897968 53946619 53307229 52884357 [9] 51944954 51872070 Smallest eigenvalues: [1] 0.4843090 0.4765560 0.3883617 0.3621946 0.3170202 0.2869983 [7] 0.1916579 0.1580417 0.1226571 -0.4186822 Largest eigenvalues: [1] 64280452 60688772 57660677 56004615 55840809 54180270 52770967 52513343 [9] 52001747 51784654 Smallest eigenvalues: [1] 0.342589171 0.314095355 0.233616744 0.226361277 0.167102884 [6] -0.004610378 -0.148466286 -1.819808635 -1.841588275 -2.150308435 Largest eigenvalues: [1] 62457458 59824323 57074045 55636193 54186055 53786178 52074826 51549250 [9] 50679352 50480538 Smallest eigenvalues: [1] 0.2738956 0.2128682 0.1976286 0.1761831 -0.6796558 [6] -0.7544631 -0.8436561 -1.9246022 -5.7617735 -105.9143133 Largest eigenvalues: [1] 66850801 60694457 57911848 56583953 55477409 53507983 52898952 52149993 [9] 52085098 50979852 Smallest eigenvalues: [1] 0.5554700 0.4687543 0.4515623 0.3623186 0.3377533 0.2771617 [7] 0.2630704 0.2509233 0.2081849 -0.4036198 Largest eigenvalues: [1] 62895204 60591093 57301275 55764621 55088001 54167445 52742690 51879755 [9] 51257597 50960591 Smallest eigenvalues: [1] 0.4623208 0.3960992 0.3608581 0.3404803 0.3286677 0.2897268 [7] 0.2542337 0.2232213 0.2099607 -3.4260121 Largest eigenvalues: [1] 64913795 60291265 57452375 56615235 55076075 53488335 52457321 52412587 [9] 52401743 51433051 Smallest eigenvalues: [1] 0.52137701 0.42107219 0.37867713 0.31439916 0.30043682 0.18770837 [7] -0.06621509 -0.92483527 -2.37304612 -6.54656598 Largest eigenvalues: [1] 64498048 60078515 57297960 56529533 54844369 53134263 52324010 52283285 [9] 51746366 51170042 Smallest eigenvalues: [1] 0.44630930 0.42759673 0.42688949 0.40460563 0.37163615 0.21076585 [7] 0.17202490 0.14191609 0.02125368 -1.68825280 Largest eigenvalues: [1] 64169735 60441477 57313751 56012294 55298933 53387736 52691360 52039103 [9] 51655275 51548874 Smallest eigenvalues: [1] 0.3696885 0.3404754 0.2852101 0.2374753 0.1301295 -0.2279523 [7] -0.2763966 -0.5377590 -1.1613819 -3.6757600 Largest eigenvalues: [1] 65574655 60627445 58126389 56092139 55364498 53775197 52960896 52259757 [9] 52017150 51926825 Smallest eigenvalues: [1] 0.3875723 0.3769951 0.3533727 0.3457456 0.2687831 0.2387556 [7] 0.1367731 0.1345906 -0.9472159 -1.0323866 Largest eigenvalues: [1] 65757496 60775256 58189688 56355558 55608083 54240914 52412895 52397984 [9] 52336372 51661090 Smallest eigenvalues: [1] 0.5791801 0.5321776 0.4904700 0.4384957 0.4197904 0.3623652 [7] 0.2453059 0.1465593 0.1161608 -0.1420097 Largest eigenvalues: [1] 64852201 60368135 57248811 55272037 55108525 53506892 52045478 51488573 [9] 51477706 51166003 Smallest eigenvalues: [1] 0.52243628 0.42608586 0.30303085 0.24741161 0.20387804 0.02763839 [7] -0.06112667 -0.20349630 -2.05955743 -2.83854690 Largest eigenvalues: [1] 63273189 59392509 56701059 55147590 54860675 52958906 51794029 51479229 [9] 51248111 50675086 Smallest eigenvalues: [1] 0.5351256 0.4543007 0.3853692 0.3263224 0.2809709 0.2667325 [7] 0.1648275 -0.1159955 -0.2738532 -1.1538587 Largest eigenvalues: [1] 64427683 60698235 57271529 56607305 55429275 53470383 52714555 52481688 [9] 51867946 51046410 Smallest eigenvalues: [1] 0.6031815 0.5559160 0.4584568 0.4124849 0.3863325 0.3495184 [7] 0.3245471 0.2899357 0.1975683 -0.0352876 Largest eigenvalues: [1] 64280302 60355686 57255172 56218845 55510923 53662182 52524410 52314474 [9] 51835956 51077251 Smallest eigenvalues: [1] 0.24487732 0.21753507 0.19221810 0.17856029 0.09013428 -0.84026871 [7] -1.25591387 -1.89110812 -3.91100887 -5.60480730 Largest eigenvalues: [1] 65492130 59756004 57284589 56485049 54995108 53463778 52586875 52024990 [9] 51836361 50786609 Smallest eigenvalues: [1] 0.49473185 0.47685649 0.45313630 0.41967156 0.29485566 0.29099290 [7] 0.24567535 0.23809376 0.02008018 -0.03924129 Largest eigenvalues: [1] 64998887 60133900 57789946 55988230 55054740 53675389 52212469 52083434 [9] 51985403 51076331 Smallest eigenvalues: [1] 0.4895499 0.4804919 0.4710209 0.4374892 0.4097570 0.3207026 [7] 0.3139825 0.2967670 0.2232518 -0.2950731 Largest eigenvalues: [1] 64191665 59892952 57085198 55717890 55127016 53374738 52233725 51727474 [9] 51621961 50886650 Smallest eigenvalues: [1] 0.5095042 0.4858718 0.4560664 0.3546844 0.3475106 0.3219654 [7] 0.2721654 -0.3313732 -1.6121342 -2.0792855 Largest eigenvalues: [1] 67396510 60875571 58667186 57760226 55257361 53777342 53746130 52727777 [9] 52216301 51971187 Smallest eigenvalues: [1] 0.5701869 0.5571233 0.4616622 0.4133250 0.3971531 0.3589362 [7] 0.3393439 0.2717245 0.1910852 -1.8657771 Largest eigenvalues: [1] 64852573 60256431 57153972 56201674 55302096 53819958 52198612 52086247 [9] 52000434 50916451 Smallest eigenvalues: [1] 0.47377439 0.43946254 0.39472870 0.38505714 0.32420693 0.30274886 [7] 0.27431695 0.22410539 0.13329682 -0.07047193 Largest eigenvalues: [1] 65369469 59386051 56609219 56363255 54236033 52782865 52394333 51524410 [9] 51275851 50612115 Smallest eigenvalues: [1] 0.4717617 0.4049114 0.4031669 0.3579300 0.3046940 0.2768814 [7] 0.2427820 -0.2199484 -0.5824348 -2.5127247 Largest eigenvalues: [1] 64767877 60526803 57608372 56463659 55165161 53356164 52483942 52262587 [9] 52080639 51141668 Smallest eigenvalues: [1] 0.4697528 0.4641836 0.4607982 0.4359906 0.4033246 0.3991634 [7] 0.3404617 0.3153652 0.2880753 -0.2278895 Largest eigenvalues: [1] 64938253 60217973 57638866 56257256 55125233 53685919 52346024 52102205 [9] 51875954 51195039 Smallest eigenvalues: [1] 0.4755321 0.4584848 0.4539473 0.3939772 0.3788036 0.3641562 [7] 0.3595409 0.3313466 -0.2228871 -2.7397324 Largest eigenvalues: [1] 63028655 59970447 57152010 55596003 55140790 53506562 51888122 51671867 [9] 51409845 50535929 Smallest eigenvalues: [1] 0.33889090 0.22070169 0.16345909 0.15426066 0.13532187 0.02392872 [7] -0.04319617 -0.04913913 -1.02893506 -5.13652364 Largest eigenvalues: [1] 64277489 59968464 57057088 55805533 55804017 53915779 52094887 51764620 [9] 51732692 50661285 Smallest eigenvalues: [1] 0.3571057 0.3279767 0.3121123 0.2685279 0.2562704 0.2393176 [7] 0.2348980 0.1974721 -3.0385916 -10.6423744 Largest eigenvalues: [1] 64475717 60593456 57679329 55695014 55540867 54115683 52346157 52147853 [9] 51632276 51541988 Smallest eigenvalues: [1] 0.5483500 0.4564222 0.3880366 0.3301862 0.3274144 0.3009116 [7] 0.2495507 0.1832786 -0.5266163 -3.1807076 Largest eigenvalues: [1] 66564178 59649047 57126631 56854899 54335444 53216986 52530654 51741390 [9] 51353991 51042168 Smallest eigenvalues: [1] 0.4656972 0.4300061 0.4295841 0.3067134 0.3005345 0.2435236 [7] 0.1771190 0.1168031 -2.1912007 -4.9577529 Largest eigenvalues: [1] 63378742 59788896 57227558 55890768 54864910 53336037 52725611 52163593 [9] 51692602 51472577 Smallest eigenvalues: [1] 0.4171166 0.3774837 0.3622252 0.2245828 0.1381114 -0.1002495 [7] -0.1293906 -0.3961462 -3.9126751 -13.5229930 Largest eigenvalues: [1] 63678231 59146676 56544921 54974838 54181085 52529805 51317125 50964456 [9] 50962658 50423226 Smallest eigenvalues: [1] 0.4824038 0.4001162 0.3757384 0.3298817 0.3202459 0.2609935 [7] 0.2096062 0.1950268 0.1790065 -0.2876235 Largest eigenvalues: [1] 63346947 59693400 57002617 55526453 54781707 53265129 51757518 51660078 [9] 51573052 50776308 Smallest eigenvalues: [1] 0.4017196 0.3099829 0.3060601 0.2550064 0.2056617 0.1627810 [7] 0.1342936 0.1037703 -1.1493079 -4.2108173 Largest eigenvalues: [1] 65078752 59074422 56526244 56063135 53878681 52572950 52091441 51223415 [9] 51087864 50476204 Smallest eigenvalues: [1] 0.5272416 0.5054613 0.4903513 0.4308589 0.3776353 0.3573757 [7] 0.2921170 0.2826911 -0.4251678 -2.7358815 Largest eigenvalues: [1] 66599600 60981775 58124208 57774052 55189042 53810531 53364397 52419744 [9] 52096953 51510495 Smallest eigenvalues: [1] 0.44352102 0.36971851 0.36385556 0.31225080 0.26483173 0.25880484 [7] 0.25820962 0.19419127 -0.01820648 -1.00247676 Largest eigenvalues: [1] 65056606 60215757 57343812 56239633 55337147 53691532 52302398 51991954 [9] 51808179 50987505 Smallest eigenvalues: [1] 0.4244945 0.3552956 0.3220012 0.3077159 0.2877264 0.1979399 [7] 0.1076089 -0.5034533 -1.0337733 -3.7950455 Largest eigenvalues: [1] 63376511 60223485 57200536 55649710 55574674 53663464 51952046 51761827 [9] 51469738 51235669 Smallest eigenvalues: [1] 0.42132701 0.37521250 0.30924554 0.29312385 0.27712202 0.24223365 [7] 0.19316044 0.03794398 -0.13643478 -5.47684096 Largest eigenvalues: [1] 65345551 60556261 57809068 56562754 56163572 54244981 52586173 52399029 [9] 51938387 51240231 Smallest eigenvalues: [1] 0.2546413 0.2494736 0.2266284 0.2064892 0.1300866 -0.4342752 [7] -0.5593178 -1.2217019 -20.0815033 -39.4685869 Largest eigenvalues: [1] 64884322 59733086 56926564 56654483 54875031 53184780 52477787 51331660 [9] 51188295 50415105 Smallest eigenvalues: [1] 0.4375188 0.3411944 0.3239461 0.3085751 0.2607217 0.2339986 [7] -0.1312906 -0.4170674 -1.4996094 -13.2815155 Largest eigenvalues: [1] 63385042 59588275 56911855 54884094 54731446 52916608 51656084 51144916 [9] 50998802 50541110 Smallest eigenvalues: [1] 0.4811541 0.4742101 0.4539463 0.4451578 0.2700403 0.2442770 [7] 0.1207482 -0.0139907 -0.4748405 -9.7533969 Largest eigenvalues: [1] 64958591 60032158 57060435 55845321 54848867 53094376 52094341 51941215 [9] 51862042 51214104 Smallest eigenvalues: [1] 0.4412282 0.3926182 0.3834597 0.3668619 0.3175575 0.2852846 [7] 0.2167005 0.1989422 0.0679503 -1.2611754 Largest eigenvalues: [1] 64890205 61156686 58182066 56431292 56236087 54817982 53100533 52761345 [9] 52159653 51954800 Smallest eigenvalues: [1] 0.48549508 0.36848194 0.30088141 0.20034541 -0.09592838 [6] -0.36913493 -0.37442737 -1.23779526 -1.81110894 -24.87610184 Largest eigenvalues: [1] 65731682 60396458 57677093 56541092 55534263 53639803 52667410 52300771 [9] 52181253 51377750 Smallest eigenvalues: [1] 0.5517755 0.4154157 0.4103750 0.3795497 0.3781615 0.2874042 [7] 0.2562975 0.1691774 0.1384625 -1.3797954 Largest eigenvalues: [1] 65211114 60484917 57789617 56365442 55499866 54085952 52807485 52427418 [9] 52347525 51807585 Smallest eigenvalues: [1] 0.244674640 0.215752978 0.213419851 0.212298594 0.196549748 [6] -0.009611284 -0.038700521 -0.096844955 -1.347646435 -3.740604286 Largest eigenvalues: [1] 68010205 60653718 58542573 57718957 54943626 53936989 53737989 52337973 [9] 51771129 51672165 Smallest eigenvalues: [1] 0.4454781 0.4272542 0.3612084 0.3192339 0.3178917 0.2835763 [7] 0.2694921 0.2391410 0.2168436 -0.1538713 Largest eigenvalues: [1] 64702745 60367796 57275603 56268228 54893223 53343385 52485105 51731587 [9] 51700357 50841561 Smallest eigenvalues: [1] 0.38710900 0.36272787 0.35542668 0.26672463 0.25187289 0.24226184 [7] 0.22712123 0.06988783 -0.08184563 -0.80146537 Largest eigenvalues: [1] 64386971 60230569 57505664 55388288 55094147 53723589 52019774 51911124 [9] 51616110 51072783 Smallest eigenvalues: [1] 0.6397911 0.5237817 0.4350590 0.3548538 0.3145444 0.2486016 [7] 0.2295997 0.1351371 -0.1219736 -0.5428926 Largest eigenvalues: [1] 63167112 59955747 57475063 55286842 55022379 53711398 52316885 51788930 [9] 51183622 50815085 Smallest eigenvalues: [1] 0.4509615 0.4219120 0.3639738 0.3115124 0.3056710 0.2643480 [7] 0.1988579 0.1818644 -1.2520372 -16.6504080 Largest eigenvalues: [1] 64558552 59914805 56702593 55796313 55080575 53380930 52332457 51906123 [9] 51837458 51203438 Smallest eigenvalues: [1] 0.44798987 0.37484278 0.35734470 0.32751621 0.25422863 0.25162084 [7] 0.23210663 0.05834778 -0.77380815 -1.31161107 Largest eigenvalues: [1] 64412271 60336826 57178094 55433930 55433145 53783873 52146624 51843072 [9] 51386199 51126856 Smallest eigenvalues: [1] 0.47247321 0.43731939 0.42800514 0.41263904 0.35909698 0.29756946 [7] 0.20783115 0.17820098 0.16656171 -0.08737491 Largest eigenvalues: [1] 63304381 59504721 56824836 55065685 55031788 53160509 51844310 51478788 [9] 51142127 50639497 Smallest eigenvalues: [1] 0.5364489 0.4888863 0.4646458 0.4430279 0.3219069 0.3114664 [7] 0.2629622 0.2363482 0.2159001 -0.8350587 Largest eigenvalues: [1] 64451599 59917436 57083911 55842637 54845664 53374339 52299075 51887340 [9] 51617718 50994941 Smallest eigenvalues: [1] 0.4555598 0.4141347 0.3236819 0.2926560 0.2833387 0.2458844 [7] 0.2417143 0.2177797 0.1739207 -4.7560440 Largest eigenvalues: [1] 66784912 60154879 57631162 57143699 54877237 53514259 53132596 52203781 [9] 52046813 51459476 Smallest eigenvalues: [1] 0.49148507 0.44799225 0.37651062 0.36622368 0.31744605 0.27887903 [7] 0.25567139 0.17077949 -0.03381753 -0.50289311 Largest eigenvalues: [1] 65571359 60716135 57917675 56443603 55662642 54029117 53414252 52637942 [9] 52116383 51968468 Smallest eigenvalues: [1] 0.470088435 0.464224478 0.391518808 0.389368126 0.375985762 [6] 0.341729409 0.318103279 0.232783097 -0.001970510 -0.006211456 Largest eigenvalues: [1] 63114465 60325007 57915148 55306710 55178253 53982394 52351739 51762394 [9] 51368110 50941495 Smallest eigenvalues: [1] 0.42907799 0.41610627 0.29064990 0.25543067 0.24003664 0.20508469 [7] 0.15725446 0.06694527 -0.54133140 -0.82281241 Largest eigenvalues: [1] 67142309 60537948 57827465 57382428 54734914 53449823 53098561 52251383 [9] 51924484 51690757 Smallest eigenvalues: [1] 0.4181066 0.3867627 0.3822281 0.3351218 0.3270386 0.2238736 [7] 0.1830226 0.1512076 -0.2597841 -6.9723956 Largest eigenvalues: [1] 65069700 59721767 56872295 56333737 54512175 52698862 52400058 51631594 [9] 51537376 50920317 Smallest eigenvalues: [1] 0.3074794 0.3057437 0.2668262 0.2433242 0.1697352 -0.2505308 [7] -0.3755285 -1.0438328 -1.5444525 -2.6934692 Largest eigenvalues: [1] 65237474 60741912 57672903 56394164 55858527 54327783 52783278 52385975 [9] 52056787 51626678 Smallest eigenvalues: [1] 0.5842321 0.5439385 0.5220422 0.4844043 0.4752812 0.4631421 [7] 0.4197152 0.2924333 0.2630965 -0.2741088 Largest eigenvalues: [1] 64110132 59749677 56744453 55971926 54796706 53151431 51961119 51794728 [9] 51605348 50817931 Smallest eigenvalues: [1] 0.4161700 0.3987813 0.3890185 0.3483768 0.3017138 0.2951071 [7] 0.1120481 -0.3732939 -10.5473146 -18.0409035 Largest eigenvalues: [1] 65485083 60200490 57502093 56621302 54726232 53369536 52731891 51485488 [9] 51459974 50504923 Smallest eigenvalues: [1] 0.44456264 0.36018395 0.35957191 0.27792494 0.22881227 0.22025975 [7] 0.18238699 0.05028327 0.03185821 -6.11217840 Largest eigenvalues: [1] 61702597 59854986 57130846 55983937 54328504 53790224 52109966 51129479 [9] 50541351 50521184 Smallest eigenvalues: [1] 0.4482850 0.4392214 0.4138799 0.3871189 0.3434284 0.3379533 [7] 0.2350395 0.2264454 -0.6419894 -1.3997029 Largest eigenvalues: [1] 65162788 60259141 58227062 56426661 55227870 54009113 52524208 52495173 [9] 52165360 51753445 Smallest eigenvalues: [1] 0.46648543 0.38176729 0.34760703 0.29687820 0.04288414 -0.02987877 [7] -0.03561369 -0.10589229 -1.61225924 -2.23537397 Largest eigenvalues: [1] 65039093 59968201 56676752 56228034 54664749 52986433 52295477 52176354 [9] 51394842 51158536 Smallest eigenvalues: [1] 0.41181687 0.35092745 0.33513618 0.26560699 0.25800361 0.23422138 [7] 0.19919388 0.14672251 0.06517232 -2.73309574 Largest eigenvalues: [1] 61347523 59560434 56796569 55388306 53488630 53379571 51644262 50904266 [9] 50233030 50081801 Smallest eigenvalues: [1] 0.28250919 0.27223589 0.21345274 0.08412727 -0.10838682 [6] -0.89789055 -1.85833469 -2.54314852 -4.52537947 -27.49158451 Largest eigenvalues: [1] 62997784 60597268 57140072 55929170 55477783 54286446 52429981 52348776 [9] 51394000 51246637 Smallest eigenvalues: [1] 0.46752938 0.44699365 0.44605889 0.42096413 0.35844914 0.19402009 [7] 0.18957588 0.16765407 0.08535547 -0.31654780 Largest eigenvalues: [1] 65511982 60049876 56889558 56366133 54988510 53145557 52428362 52190051 [9] 51989228 51478460 Smallest eigenvalues: [1] 0.3911942 0.3051112 0.2374562 0.2033701 0.2027744 0.1955194 [7] 0.1478828 -0.5445392 -2.1472867 -30.4367665 Largest eigenvalues: [1] 65198905 60354516 57738810 56080783 54758331 53158568 52362712 52089075 [9] 51939519 51686001 Smallest eigenvalues: [1] 0.40859054 0.35185951 0.31981995 0.31713911 0.31588386 [6] 0.29767602 0.27128695 0.06159938 -0.01686441 -29.71729307 Largest eigenvalues: [1] 63006282 59454193 57069490 55214707 55156510 53388659 51704754 51440939 [9] 51276479 50576668 Smallest eigenvalues: [1] 0.36769598 0.34910195 0.33467407 0.33228324 0.24533693 0.22296072 [7] 0.17850995 0.06118942 -0.34423999 -2.42058708 Largest eigenvalues: [1] 64965063 60226377 57262266 55873684 55294297 53597414 51804072 51530574 [9] 51497340 50865848 Smallest eigenvalues: [1] 0.4876125 0.4788661 0.4512282 0.3296756 0.3022255 0.2930782 [7] 0.2866780 0.2715847 0.2200952 -0.4612267 Largest eigenvalues: [1] 61900594 59845930 56840985 55531103 54235127 53627553 52130485 51655042 [9] 50774638 50430847 Smallest eigenvalues: [1] 0.52577290 0.44791593 0.44507264 0.42522652 0.40956918 0.32030244 [7] 0.26905038 0.25116249 0.03949773 -3.55598146 Largest eigenvalues: [1] 64028388 60494596 57305659 55457985 55421628 53789062 52142663 51644882 [9] 51596122 50985361 Smallest eigenvalues: [1] 0.45927568 0.40792906 0.34647808 0.16756599 0.15008075 0.12221237 [7] 0.02620009 -0.04167823 -1.70533891 -4.75844230 Largest eigenvalues: [1] 63891147 60773041 57265620 55998321 55385328 53979768 52479540 52187052 [9] 51922218 51246787 Smallest eigenvalues: [1] 0.3658060 0.3344778 0.2609219 0.2585509 0.2447063 0.2104382 [7] 0.2077177 -0.7278696 -8.2276847 -15.0700102 Largest eigenvalues: [1] 64483348 61333696 57914624 56963065 56347620 55238270 53095534 52650016 [9] 52244831 51651957 Smallest eigenvalues: [1] 0.46336357 0.45592025 0.44394742 0.44011852 0.35075441 0.28089595 [7] 0.21568867 0.19742019 0.05017135 -1.02496290 Largest eigenvalues: [1] 65876945 59900772 57232945 57023840 54797503 53342754 52912172 52178580 [9] 52044331 51544345 Smallest eigenvalues: [1] 0.09331526 0.08430914 0.07642639 0.06544419 -0.21492851 [6] -0.62237701 -1.94636125 -6.75770299 -16.21286283 -72.71620056 Largest eigenvalues: [1] 63830985 59377991 56483001 54934838 54475152 52755719 51900839 51243473 [9] 51228092 50973095 Smallest eigenvalues: [1] 0.5208337 0.5094838 0.4714323 0.4199900 0.4109660 0.3748212 [7] 0.3635074 0.3141239 0.2957035 -0.5989800 Largest eigenvalues: [1] 63946712 60834585 57532401 56271544 55842777 54105767 52252869 52181186 [9] 52072040 51098075 Smallest eigenvalues: [1] 0.6228705 0.5367966 0.4539265 0.4428860 0.4382406 0.4312686 [7] 0.3611855 0.2584860 -0.1526940 -0.1740106 Largest eigenvalues: [1] 64778376 60168439 57600582 56058337 55245881 53448519 52497551 52228099 [9] 51788225 51390955 Smallest eigenvalues: [1] 0.5623987 0.5508477 0.4884565 0.4715541 0.3372215 0.3332619 [7] 0.3248973 0.3136648 0.2342237 -0.2901622 Largest eigenvalues: [1] 63353098 59648912 57169215 55339317 55195617 53672384 52006946 51659559 [9] 51238630 50802159 Smallest eigenvalues: [1] 0.46199620 0.41583094 0.40561975 0.37038139 0.34098673 0.24059476 [7] 0.04359031 -0.01212928 -0.18812592 -5.40076580 Largest eigenvalues: [1] 64392870 59572334 56665517 56002026 54296993 52655575 52049097 51588225 [9] 51216224 50650935 Smallest eigenvalues: [1] 0.5687584 0.5231477 0.4547006 0.3911932 0.3620886 0.3549302 [7] 0.2607110 0.1873131 0.1758160 -0.7588787 Largest eigenvalues: [1] 65028383 60744558 57500351 56671285 55760286 53936361 52903403 52602091 [9] 52441538 51759936 Smallest eigenvalues: [1] 0.52267425 0.50711209 0.48094858 0.43873683 0.41275434 0.32880348 [7] 0.31814716 0.03158521 -0.17098228 -0.21816864 Largest eigenvalues: [1] 62926712 59906413 56340071 54971011 54905555 52938512 51719281 50992644 [9] 50757307 49981242 Smallest eigenvalues: [1] 0.42374613 0.42248700 0.37151878 0.36214386 0.34850539 0.15052846 [7] 0.07696728 -0.07022859 -0.72900921 -6.81405877 Largest eigenvalues: [1] 64254464 59554755 56592807 55576483 54581035 53001255 51558422 51530729 [9] 51191222 50530038 Smallest eigenvalues: [1] 0.24794884 0.13277562 -0.02630301 -0.17926705 -0.23286774 -0.28406237 [7] -0.99511794 -2.43292388 -4.52280031 -8.82809816 Largest eigenvalues: [1] 64708373 60315898 57612249 55679761 55346327 53752051 52358657 51872342 [9] 51833624 51473634 Smallest eigenvalues: [1] 0.44675367 0.41600358 0.38652505 0.35633222 0.30386080 0.26809874 [7] 0.22320797 0.15526093 0.04887881 -0.67850821 Largest eigenvalues: [1] 64594404 59987723 56882404 56124773 54869510 53163929 52241606 52149971 [9] 51299313 51223473 Smallest eigenvalues: [1] 0.44595910 0.43518750 0.31623774 0.21598209 0.20568876 0.18448963 [7] 0.12054535 0.09483435 -0.36964111 -3.93732128 Largest eigenvalues: [1] 63992776 59493412 57027877 55678440 54762180 53168399 52077094 51677258 [9] 51508350 51101213 Smallest eigenvalues: [1] 0.4433661 0.4014599 0.3651950 0.3537610 0.3323528 0.2566188 [7] 0.2298878 0.1781846 -2.4815648 -2.9872113 Largest eigenvalues: [1] 64679687 59815762 57286583 55912331 55251418 53980271 52433559 52007626 [9] 51805514 51314304 Smallest eigenvalues: [1] 0.36158858 0.33892998 0.31593207 0.30452609 0.28671851 0.19124657 [7] 0.18861537 0.14971534 -0.09705962 -0.87385158 Largest eigenvalues: [1] 64307760 60416838 57698407 55724068 55691134 54063603 52475201 52232214 [9] 51789200 51488869 Smallest eigenvalues: [1] 0.53126014 0.51489103 0.48549203 0.46373719 0.35405130 0.27781297 [7] 0.14508453 -0.07970191 -0.54654659 -6.46910453 Largest eigenvalues: [1] 63707636 60689355 57666806 55780426 55162932 53733317 52361452 52198383 [9] 51797803 51368405 Smallest eigenvalues: [1] 0.4017686 0.3745679 0.3234126 0.2578434 0.2239854 0.1935594 [7] 0.1371283 -0.3670697 -0.7660613 -2.0296918 Largest eigenvalues: [1] 65996802 60318143 57872549 57238203 55491980 54033674 53088185 52840927 [9] 52057273 51872540 Smallest eigenvalues: [1] 0.5547056 0.4959835 0.3297929 0.3145666 0.2944331 0.2922839 [7] 0.2079433 0.1309476 0.1106708 -0.4161479 Largest eigenvalues: [1] 63735679 60454604 58026319 55444767 55236716 53957950 52067604 51925232 [9] 51732964 51076455
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.596198 | 0.8863222 | 15.4405 | 0 | 2.693242 | 7.028819 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + body_temp + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_noise_tempBody_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 17. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 470 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.254627 | 0.7154126 | 15.03311 | 0.18 | 3.3453 | 2.466049 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + n + body_temp + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_noise_tempBody_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 17. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 512 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.20459 | 0.705722 | 15.50223 | 0.195 | 3.365779 | 2.358078 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + speed + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
speed = speed_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_HR_alt_speed_PM25_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 31. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 444 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.80303814 0.80025109 0.79591494 0.64395486 0.59275608 0.58180483 [7] 0.47461210 0.44006250 0.34035829 -0.02212782 Largest eigenvalues: [1] 101924604 95288625 89618154 86660808 85727800 83149890 80240426 [8] 80142577 79455565 78144599 Smallest eigenvalues: [1] 0.9578227 0.7410638 0.7232372 0.6978029 0.6309295 0.6026807 [7] 0.5930601 0.5169529 0.3603450 -0.7130933 Largest eigenvalues: [1] 101739685 92685832 88014231 87914286 83967919 81932192 81595175 [8] 79054347 78612758 77164595 Smallest eigenvalues: [1] 0.9789891 0.9146893 0.8308172 0.6046982 0.5388086 0.5082604 [7] 0.4216574 0.4142075 0.3684576 -0.1526504 Largest eigenvalues: [1] 101015488 94216616 90057330 87230836 84933726 82715870 80995867 [8] 80268289 80101947 78403674 Smallest eigenvalues: [1] 0.98402389 0.92100906 0.85619242 0.81291225 0.79520223 0.69935647 [7] 0.68744471 0.60844435 0.51309756 -0.06082258 Largest eigenvalues: [1] 99098417 93385940 88509441 85265431 85006681 82624519 79627062 79069120 [9] 78228723 77260272 Smallest eigenvalues: [1] 1.0219525 0.9121243 0.7413772 0.6185044 0.5769625 0.4986761 [7] 0.4089405 0.2998299 0.2311689 -0.3125157 Largest eigenvalues: [1] 99253715 93353157 88677563 85552467 85268485 82678163 79741463 79410642 [9] 79197370 78193297 Smallest eigenvalues: [1] 0.96930984 0.95682727 0.84599942 0.78937414 0.70668587 0.70375146 [7] 0.67732389 0.60460004 0.54501371 -0.06140711 Largest eigenvalues: [1] 97027351 93029697 88456584 84692185 84532852 82618340 79643389 78309987 [9] 77451747 77079216 Smallest eigenvalues: [1] 0.9698603 0.9496725 0.9316423 0.6769017 0.6135550 0.5708756 [7] 0.4787908 0.4324105 0.3385942 -0.3027704 Largest eigenvalues: [1] 100418218 93281929 89215548 86443519 84800221 82796726 80270559 [8] 79803163 78443356 77452695 Smallest eigenvalues: [1] 1.35369662 1.11824226 0.90193982 0.85442737 0.83203937 0.80403034 [7] 0.72417644 0.63737172 0.63107180 -0.03517777 Largest eigenvalues: [1] 100476629 93473726 89775456 85868387 85258064 82804953 80078686 [8] 79809708 78851635 77698123 Smallest eigenvalues: [1] 0.9862023 0.8662345 0.7504058 0.7418887 0.7007132 0.6331729 [7] 0.5113809 0.5082773 0.4772174 -0.4453628 Largest eigenvalues: [1] 100702100 93523633 88470423 86747570 84859260 82684536 80569575 [8] 79654342 78835411 77259522 Smallest eigenvalues: [1] 0.9096825 0.8947335 0.8697531 0.7794065 0.5993544 0.5626623 [7] 0.4826807 0.4633000 0.4112802 -1.0857081 Largest eigenvalues: [1] 102825723 94258075 89559298 87285590 85681733 83570033 81122697 [8] 80517920 80288640 78198329 Smallest eigenvalues: [1] 0.7815919 0.7730961 0.7114449 0.7093999 0.6317899 0.5733451 [7] 0.4059138 0.1777360 -1.0121216 -1.0774387 Largest eigenvalues: [1] 100936581 94870795 89571318 86782403 86181366 83519669 80544192 [8] 80453638 80432924 78188289
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.603597 | 0.7075871 | 12.76307 | 0.005 | 1.156436 | 2.205751 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
HR ~ alt + speed + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- HR_fd
covariates <- list(altitude = altitude_fd,
speed = speed_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_HR_alt_speed_PM1_N200'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 31. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 452 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.81341976 0.80172464 0.78888646 0.65938550 0.59360590 0.58544932 [7] 0.48074686 0.45257201 0.34079378 -0.02648318 Largest eigenvalues: [1] 101848469 95212834 89540876 86599612 85633747 83078531 80164168 [8] 80091089 79393813 78090666 Smallest eigenvalues: [1] 0.9626420 0.7400741 0.7113889 0.6939494 0.6297731 0.5992602 [7] 0.5832355 0.5091785 0.3567443 -0.7105975 Largest eigenvalues: [1] 101720930 92662552 87993495 87898086 83947287 81914646 81581069 [8] 79034719 78592107 77151650 Smallest eigenvalues: [1] 0.9759312 0.8108620 0.8058702 0.5727452 0.5137479 0.5012124 [7] 0.4061430 0.3929668 0.3534176 -0.1714933 Largest eigenvalues: [1] 101002744 94200865 90044311 87219536 84918050 82701173 80986323 [8] 80251575 80089101 78393514 Smallest eigenvalues: [1] 0.98945178 0.91681273 0.84700046 0.81576046 0.80986661 0.70199243 [7] 0.68019397 0.60888265 0.50172875 -0.08501274 Largest eigenvalues: [1] 99051298 93338595 88465229 85224800 84961377 82579081 79586680 79032279 [9] 78186227 77223388 Smallest eigenvalues: [1] 1.0201935 0.9174463 0.7411120 0.6203104 0.5746062 0.4972004 [7] 0.4050046 0.2961912 0.2332851 -0.3167967 Largest eigenvalues: [1] 99189840 93272691 88593098 85500394 85174855 82579593 79654700 79347582 [9] 79150041 78130970 Smallest eigenvalues: [1] 0.9734237 0.9491729 0.8432285 0.8000740 0.7078493 0.7023319 [7] 0.6831534 0.5964720 0.5467915 -0.1156481 Largest eigenvalues: [1] 97002366 92998779 88428839 84660081 84508673 82591729 79618163 78290109 [9] 77428565 77056219 Smallest eigenvalues: [1] 0.9455775 0.9362206 0.9263068 0.6732952 0.5812299 0.5738530 [7] 0.4704938 0.4256222 0.3417548 -0.3249727 Largest eigenvalues: [1] 100400027 93251194 89186516 86427240 84765523 82759705 80256381 [8] 79773610 78421058 77426583 Smallest eigenvalues: [1] 1.35888213 1.11908321 0.90181129 0.85292339 0.83395623 0.80395421 [7] 0.72471701 0.63104400 0.62312820 -0.03696274 Largest eigenvalues: [1] 100423882 93403387 89709104 85823519 85179311 82733631 80008810 [8] 79770023 78802586 77635956 Smallest eigenvalues: [1] 0.9885411 0.8621542 0.7441775 0.7432723 0.7014195 0.6321689 [7] 0.5089159 0.5069203 0.4678219 -0.4565331 Largest eigenvalues: [1] 100660985 93468141 88417837 86711619 84803599 82633414 80537742 [8] 79605314 78792290 77220776 Smallest eigenvalues: [1] 0.9192864 0.8946082 0.8634820 0.7793226 0.5909177 0.5566973 [7] 0.4801440 0.4525031 0.4110680 -1.1381125 Largest eigenvalues: [1] 102796141 94222866 89527909 87259821 85648090 83540458 81100540 [8] 80488034 80260930 78174195 Smallest eigenvalues: [1] 0.7846323 0.7734625 0.7171531 0.7088025 0.6327957 0.5715181 [7] 0.4087505 0.1771194 -1.0470611 -1.1330396 Largest eigenvalues: [1] 100881447 94798889 89506914 86736755 86111989 83461934 80504123 [8] 80400141 80379770 78140037
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 7.608386 | 0.7074309 | 12.73253 | 0.005 | 1.186233 | 2.19348 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
Model comparison
Finally, we compare fitted functional models based on various criteria.
# Specify the models folders
models_path <- list.dirs(path = "figures/") |>
(\(x) x[grepl("^figures/model_HR.*_N200$", x)])() |>
sub("^figures/", "", x = _)
# Create a data frame where the characteristics will be stored
model_comparison <- data.frame(model = NA, N = NA, RMSE = NA, maxR2 = NA, integratedR2 = NA,
pval = NA, qval = NA, Fobs = NA)
# Load all models
for (model_path in models_path) {
load(file = paste0("figures/", model_path, "/model.RData"), verbose = FALSE)
model_comparison <- rbind(
model_comparison,
c(substr(model_path, 7, nchar(model_path) - 5),
length(model_1$common_IDs),
unlist(as.vector(model_2$df_res_metrics))))
}
model_comparison <- model_comparison[-1, ] |>
mutate(N = as.numeric(N),
RMSE = round(as.numeric(RMSE), 6),
maxR2 = round(as.numeric(maxR2), 6),
integratedR2 = as.numeric(integratedR2),
pval = as.numeric(pval),
qval = round(as.numeric(qval), 4),
Fobs = round(as.numeric(Fobs), 4))
model_comparison[rev(order(model_comparison$maxR2)), ]
| model | N | RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|---|---|
| <chr> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 16 | HR_alt_noise_steps_PM1 | 19 | 7.596198 | 0.886322 | 15.440500 | 0.000 | 2.6932 | 7.0288 |
| 17 | HR_alt_noise_steps_PM25 | 19 | 7.595585 | 0.882461 | 15.194607 | 0.000 | 2.7384 | 6.7673 |
| 14 | HR_alt_noise_speed_PM25 | 23 | 7.246352 | 0.850977 | 16.165170 | 0.000 | 2.0549 | 4.4484 |
| 13 | HR_alt_noise_speed_PM1 | 23 | 7.229381 | 0.846894 | 16.343329 | 0.000 | 2.0670 | 4.2697 |
| 12 | HR_alt_noise_speed | 39 | 8.373718 | 0.760873 | 12.628704 | 0.000 | 0.8301 | 2.4966 |
| 21 | HR_alt_noise_temp_speed | 33 | 8.263548 | 0.757306 | 14.611970 | 0.000 | 1.0788 | 2.8659 |
| 22 | HR_alt_noise_temp_steps | 32 | 8.262888 | 0.736877 | 13.816507 | 0.000 | 1.1071 | 2.3669 |
| 15 | HR_alt_noise_steps | 32 | 8.555006 | 0.718060 | 11.376717 | 0.000 | 0.9352 | 2.0435 |
| 24 | HR_alt_noise_tempBody_PM25 | 17 | 7.254627 | 0.715413 | 15.033106 | 0.180 | 3.3453 | 2.4660 |
| 30 | HR_alt_steps_Sex | 39 | 8.308018 | 0.710620 | 11.956099 | 0.000 | 0.7517 | 2.1195 |
| 28 | HR_alt_speed_PM25 | 31 | 7.603597 | 0.707587 | 12.763065 | 0.005 | 1.1564 | 2.2058 |
| 27 | HR_alt_speed_PM1 | 31 | 7.608386 | 0.707431 | 12.732527 | 0.005 | 1.1862 | 2.1935 |
| 23 | HR_alt_noise_tempBody_PM1 | 17 | 7.204590 | 0.705722 | 15.502226 | 0.195 | 3.3658 | 2.3581 |
| 29 | HR_alt_speed_Sex | 47 | 8.265521 | 0.680346 | 12.408756 | 0.000 | 0.7131 | 1.8909 |
| 19 | HR_alt_noise_temp_body_acc | 22 | 19.509485 | 0.673596 | 1821.111769 | 0.050 | 2.2815 | 2.3260 |
| 6 | HR_alt_noise_acc_PM25 | 19 | 7.557765 | 0.667754 | 15.215718 | 0.375 | 2.8854 | 1.5566 |
| 26 | HR_alt_noise_tempEntrant | 24 | 8.332604 | 0.656385 | 15.753599 | 0.040 | 1.3316 | 1.4692 |
| 5 | HR_alt_noise_acc_PM1 | 19 | 7.531307 | 0.651828 | 15.359033 | 0.465 | 2.6927 | 1.4462 |
| 18 | HR_alt_noise_temp_acc | 32 | 8.334506 | 0.557506 | 12.402946 | 0.145 | 1.0109 | 0.8306 |
| 7 | HR_alt_noise_acc_Sex | 31 | 8.668593 | 0.554813 | 12.215680 | 0.195 | 1.2572 | 1.0712 |
| 4 | HR_alt_noise_acc | 32 | 8.588232 | 0.539411 | 9.702973 | 0.115 | 0.8661 | 0.6865 |
| 20 | HR_alt_noise_temp_body_ENT | 28 | 8.399143 | 0.533202 | 11.206135 | 0.045 | 0.9175 | 0.9335 |
| 31 | HR_alt_temp_body_ENT | 34 | 8.464485 | 0.478750 | 8.416988 | 0.005 | 0.6000 | 0.7784 |
| 9 | HR_alt_noise_pollution1 | 23 | 7.666164 | 0.450873 | 9.603953 | 0.625 | 1.4022 | 0.7105 |
| 10 | HR_alt_noise_pollution25 | 23 | 7.685670 | 0.449567 | 9.376699 | 0.645 | 1.4781 | 0.6998 |
| 3 | HR_airpress_noise_temp | 25 | 8.724708 | 0.440012 | 9.678972 | 0.210 | 1.1793 | 0.9077 |
| 25 | HR_alt_noise_tempEmpatica | 33 | 8.567088 | 0.429390 | 9.358159 | 0.085 | 0.7230 | 0.6613 |
| 8 | HR_alt_noise | 39 | 8.736482 | 0.411138 | 6.871452 | 0.010 | 0.4733 | 0.6125 |
| 2 | HR_airpress_noise | 30 | 8.784591 | 0.401951 | 6.733928 | 0.040 | 0.6637 | 0.6927 |
| 33 | HR_alt_temp_pollution25 | 27 | 7.684850 | 0.393268 | 9.166168 | 0.430 | 1.0992 | 0.6483 |
| 32 | HR_alt_temp_pollution1 | 27 | 7.685915 | 0.393187 | 9.208156 | 0.445 | 1.1403 | 0.6482 |
| 11 | HR_alt_noise_Sex_Bspl | 38 | 8.518559 | 0.379981 | 9.999879 | 0.035 | 0.5320 | 0.5998 |
write.csv(model_comparison[rev(order(model_comparison$maxR2)), ],
file = "model_comparison_HR.csv")
MODELS for EDA
Now, we want to model EDA on other covariates. We use the functions defined above. For new model, we only change the first cell below and the second cell then computes everything for us. Especially, we have to specify:
outcome... fd objectcovariates... named list of the covariatespath_plot... path where to save the figuresbasis_params... list of the parameters used for defining B-spline basis for each covariate and interceptN_repeats... number of bootstrapped sampled used to construct pointwise CI's, it should be at least1000nperm... number of permutations for permutation $F$-test, it should be at least200nsim... number of simulations for calculating Global Envelope Test, it should be at least2499
# Set the numbers for all models
N_repeats <- 101#1001
nperm <- 200
nsim <- 2499
# Length of vector of time points
lenght_tt <- 501
# Specify that the outcome is EDA, not HR
HR <- FALSE
EDA ~ alt + noise
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd)
path_plot <- 'figures/model_EDA_alt_noise_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 178 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 1.026654 | 0.3563771 | 6.133042 | 0.265 | 0.6648075 | 0.4472435 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 8, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + Sex (B-spline for sex)
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
- If we specify for the name of the factor corresponding list of parameters, then the <b>B-splines</b> of specified order will be created
- Otherwise (if we do not specify the basis parameters for factor), the <b>constant basis</b> will be used for this parametric function.
- Be careful, the code is slightly different for cases with factors.
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd)
path_plot <- 'figures/model_EDA_alt_noise_Sex_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e6),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
Sex = list(nbetabasis = 90, norder = 4, lambda = 1e2))
factors <- list(Sex = participant_info$Sex |> as.factor())
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params,
factors = factors)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
for (fact in names(factors)) {
assign(fact, factors[[fact]][participant_info$ID %in% (model_1$common_IDs |>
substr(4, 9))] |> as.numeric())
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, factors = factors, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
if(!is.na(factors[1])) {for (fact in names(factors)) {
assign(paste0(fact, '_BS'),
factors[[fact]][participant_info$ID %in% (model_1$common_IDs |> substr(4, 9))][BS_sample] |>
as.numeric())}}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS'))
if(!is.na(factors[1])) {for(nam in names(factors)) {formula_BS <- paste0(formula_BS, '+', nam, '_BS')}}
formula_BS <- as.formula(formula_BS)
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 31. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 342 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 1.021243 | 0.3608707 | 8.206033 | 0.33 | 0.7591384 | 0.489331 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = FALSE, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
GET_res <- GET_function(J = j+1, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, sex = TRUE, lenght_tt = lenght_tt)
GET_results[[j+1]] <- GET_res
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + temp (Empatica)
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempEmpatica_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 844 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9806856 | 0.5026002 | 11.13673 | 0.01 | 0.8105395 | 0.953169 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + temp (Entrant)
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = air_temperature_ENT_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempEntrant_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 1022 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.4747687 0.4574177 0.4257354 0.3680904 0.3096263 0.2376351 [7] 0.2306224 0.1742160 0.1632070 -0.4374138 Largest eigenvalues: [1] 57010815 54102242 51503062 50768795 49258917 47733267 47425762 46522527 [9] 46340117 45844167 Smallest eigenvalues: [1] 0.4460772 0.4393647 0.3974302 0.3715897 0.2670383 0.2617466 [7] 0.2282979 0.1408668 -0.1643602 -1.2597654 Largest eigenvalues: [1] 57549532 54616092 51430193 50857337 49448282 48124440 47929747 47216213 [9] 46775471 46197597 Smallest eigenvalues: [1] 0.6450638 0.6167103 0.5900787 0.5547841 0.5233902 0.4371264 [7] 0.3835381 0.3237964 0.2595001 -1.6535915 Largest eigenvalues: [1] 57147373 53829059 51058383 50235017 48863331 47705179 47306491 46115412 [9] 46031724 45086121 Smallest eigenvalues: [1] 0.6182247 0.5909644 0.4716211 0.4552177 0.4454533 0.4228770 [7] 0.4076849 0.3296401 0.3102789 -0.2962637 Largest eigenvalues: [1] 57342325 53508083 50484868 49809124 48948458 47528254 47362086 45707269 [9] 45667467 44818068 Smallest eigenvalues: [1] 0.48188152 0.46267268 0.46059733 0.41401408 0.40938763 0.31256848 [7] 0.25681985 0.24910818 0.04919699 -3.77451313 Largest eigenvalues: [1] 57120570 53913226 51269742 50101393 48670730 47796932 47241527 46534055 [9] 46239842 45476534 Smallest eigenvalues: [1] 0.72402544 0.68438971 0.62110388 0.61853327 0.57479976 0.53536928 [7] 0.37270196 0.22364597 0.15110019 -0.09406395 Largest eigenvalues: [1] 56216438 54452903 50773788 50461334 49648383 48115585 47215797 47160305 [9] 46198353 45883265 Smallest eigenvalues: [1] 0.5549913 0.5019532 0.4317150 0.4065969 0.3835204 0.3355137 [7] 0.3346319 0.2205805 0.1478164 -0.4294444 Largest eigenvalues: [1] 58339225 54418258 51633050 51435862 49740254 48545961 47588584 46951519 [9] 46861206 46054341 Smallest eigenvalues: [1] 0.4791537 0.4751458 0.4451501 0.4295989 0.3990474 0.3015072 [7] 0.2609971 0.2010509 0.2008824 -0.4835392 Largest eigenvalues: [1] 57771136 54076342 51713407 51331619 49227746 48262636 47458069 46490010 [9] 46102273 45473600 Smallest eigenvalues: [1] 0.39566999 0.35852395 0.31737142 0.29458972 0.27060302 0.19524266 [7] 0.18250898 0.14147331 0.12899834 -0.05520984 Largest eigenvalues: [1] 57686111 53311657 52301038 51105859 49054844 48104058 46968092 46048924 [9] 46042289 45139979 Smallest eigenvalues: [1] 0.5845770 0.5538007 0.4682918 0.4601395 0.4442040 0.3169237 [7] 0.3066175 0.2725544 0.1815992 -0.1595323 Largest eigenvalues: [1] 58130534 54482869 52588102 51297152 49290799 49118980 47381065 46405338 [9] 46340560 45479447 Smallest eigenvalues: [1] 0.5517688 0.5305087 0.5243246 0.4645273 0.3579128 0.3305835 [7] 0.3084425 0.2457567 0.1358420 -2.3636817 Largest eigenvalues: [1] 58312246 55221952 52243045 50907878 50080027 48956934 48208910 47403952 [9] 46774211 46091862
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9711039 | 0.6344874 | 14.23971 | 0.095 | 1.889565 | 1.676169 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + t + acc
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd,
acceleration = acceleration_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_acc_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 31. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 478 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.71529531 0.65715715 0.64792174 0.64748316 0.62485081 0.61437600 [7] 0.45717784 0.24001428 -0.05688383 -0.05864894 Largest eigenvalues: [1] 104336178 101120577 94713204 92244050 91553646 88936312 86838039 [8] 86126116 85194082 84610587 Smallest eigenvalues: [1] 1.05996704 0.93413211 0.93328033 0.92355319 0.80464017 0.64028175 [7] 0.60194751 0.49722662 0.48281740 -0.02751828 Largest eigenvalues: [1] 104491813 99173309 93577024 91724163 90765912 88060081 85401110 [8] 85207132 84878235 83691649 Smallest eigenvalues: [1] 0.80458985 0.79608720 0.65299851 0.64806186 0.59300681 0.51281124 [7] 0.46586174 0.15709994 -0.04152955 -1.44037925 Largest eigenvalues: [1] 105591704 98871068 94179382 92455192 90107299 87560926 85805339 [8] 85750439 85532052 84426281 Smallest eigenvalues: [1] 0.9157942 0.8713203 0.7643244 0.6796424 0.5759326 0.5408278 [7] 0.5040664 0.3814823 -0.3521426 -0.7787503 Largest eigenvalues: [1] 102848533 99177367 93214441 91293211 90298242 88095052 85578931 [8] 84805975 83830870 83381463 Smallest eigenvalues: [1] 0.9819799 0.9504422 0.8845354 0.8211504 0.6299600 0.5931640 [7] 0.5768839 0.5288442 0.3028801 -0.1473391 Largest eigenvalues: [1] 105848228 100098178 93833409 92920639 91359789 88284660 86240055 [8] 86068079 85968122 84383682 Smallest eigenvalues: [1] 0.8805152 0.7861475 0.7819451 0.7410960 0.7368880 0.6239228 [7] 0.6217446 0.5700907 0.1062220 -0.6778086 Largest eigenvalues: [1] 106849408 100196431 94731283 92475308 91125728 88419248 86374542 [8] 85553904 85519077 83790875 Smallest eigenvalues: [1] 0.7900502 0.7809359 0.7402488 0.7329204 0.7259472 0.6505090 [7] 0.5576750 0.5567297 0.5446177 -1.0804488 Largest eigenvalues: [1] 103168843 99611748 94595090 91792239 90226060 89049471 86157465 [8] 85679277 84000705 83736233 Smallest eigenvalues: [1] 0.7999668 0.7761854 0.7142653 0.7101801 0.6072047 0.5046810 [7] 0.4640279 0.4621066 0.4588508 -0.6873907 Largest eigenvalues: [1] 103317462 100380249 94576920 91722525 91067107 88681455 86507927 [8] 85727214 84845521 84145253 Smallest eigenvalues: [1] 0.7114285 0.6018538 0.5828802 0.5329441 0.4852198 0.3981705 [7] 0.3755107 0.3632016 0.2399731 -1.5730160 Largest eigenvalues: [1] 103020179 99309423 94129407 90768249 90632376 88367993 86251060 [8] 84972859 83791509 83628049 Smallest eigenvalues: [1] 0.8294642 0.7889080 0.7717433 0.5074243 0.4982853 0.4728394 [7] 0.4637711 -0.2213382 -0.2777116 -0.8022646 Largest eigenvalues: [1] 104963540 99928983 93571404 93366686 90611711 88162341 86125702 [8] 85307762 85263255 83938231 Smallest eigenvalues: [1] 0.9403842 0.8138846 0.7939806 0.7466947 0.6186996 0.5924597 [7] 0.5364208 0.5078007 0.3342102 -1.4993228 Largest eigenvalues: [1] 104684972 99943249 94581898 91739359 91588733 88989798 86368165 [8] 85544457 85013414 84153078 Smallest eigenvalues: [1] 0.8190458 0.7958099 0.7926415 0.7522592 0.7090974 0.6802037 [7] 0.6410282 0.5262110 0.2806294 -0.1501503 Largest eigenvalues: [1] 104155092 99779755 93805648 91870485 91160199 88258315 85899377 [8] 85343072 84896099 84333207 Smallest eigenvalues: [1] 0.7942810 0.6982561 0.6779712 0.5945609 0.5787978 0.4573007 [7] 0.4423982 0.3486892 -0.2641523 -1.5036612 Largest eigenvalues: [1] 106201317 99779614 94307338 92276543 91215981 88398643 86111612 [8] 85948271 85468081 84590541 Smallest eigenvalues: [1] 1.0076487 0.9291392 0.9141106 0.7938150 0.7459482 0.7162959 [7] 0.7044750 0.5951691 0.5790196 -0.1838981 Largest eigenvalues: [1] 102980588 99444049 93384377 90939729 90706886 88151266 86176533 [8] 84878758 84063841 83550233 Smallest eigenvalues: [1] 0.6503689 0.6381602 0.6305463 0.6007480 0.5727479 0.5191914 [7] 0.5031690 0.3865452 -0.3486639 -1.2112455 Largest eigenvalues: [1] 104773776 99849573 94584854 91894754 91370287 88889426 86444614 [8] 85368920 85282628 83987064 Smallest eigenvalues: [1] 0.8508928 0.8154733 0.7889989 0.7198550 0.5797130 0.5455997 [7] 0.4576095 0.3295522 0.1648467 -1.7417164 Largest eigenvalues: [1] 103542247 99805340 94576022 91849347 90926886 89538569 87402549 [8] 84955212 84132453 83981741 Smallest eigenvalues: [1] 0.86434892 0.71191472 0.66773084 0.58820570 0.53176765 0.47241539 [7] 0.04233538 0.02190882 -0.34846668 -0.87841904 Largest eigenvalues: [1] 104459768 100643354 94752165 92096529 91614355 88910129 87173560 [8] 85829817 85074408 84343865 Smallest eigenvalues: [1] 0.8456069 0.7465641 0.6288245 0.6052800 0.5810443 0.4979016 [7] 0.4551947 0.3455334 0.3185152 -0.2205209 Largest eigenvalues: [1] 105520051 100528497 93908994 93039696 91392066 88305435 86448802 [8] 86326636 85895573 84744166 Smallest eigenvalues: [1] 0.8905142 0.8355155 0.6761222 0.6481694 0.5863778 0.4744086 [7] 0.4650638 0.4621487 0.2364487 -4.5114150 Largest eigenvalues: [1] 104776967 98847672 94354523 91447097 90695750 88580676 86278035 [8] 85667063 84677331 84181983 Smallest eigenvalues: [1] 0.87598298 0.86113938 0.78975814 0.76686869 0.51371504 0.50805878 [7] 0.34464378 0.34192928 -0.01327554 -0.19392059 Largest eigenvalues: [1] 103066549 98874815 93334518 91184491 91152863 87988784 85720183 [8] 84820579 84447319 83239556 Smallest eigenvalues: [1] 0.90708637 0.85489073 0.85148793 0.81152331 0.80868881 0.59858548 [7] 0.55842709 0.53160979 0.37886523 -0.08591264 Largest eigenvalues: [1] 105773731 101401800 94411704 92418693 91337633 88776590 86580064 [8] 86162368 85527183 84647787 Smallest eigenvalues: [1] 0.96105320 0.93672019 0.89052396 0.88373194 0.56469670 0.47863259 [7] 0.36120183 0.26395063 -0.09439721 -0.11575120 Largest eigenvalues: [1] 103100151 98765653 92943726 90904040 89520099 87279334 85711730 [8] 84640981 84010872 83447623 Smallest eigenvalues: [1] 1.07154982 0.98145244 0.87116725 0.83750530 0.72760255 0.64643464 [7] 0.53692575 0.30055805 -0.02088184 -0.42137468 Largest eigenvalues: [1] 103891658 100420734 94380565 92156702 91572140 89020489 86098254 [8] 85751893 85012058 84233866 Smallest eigenvalues: [1] 0.8226975 0.8034129 0.7898369 0.6697591 0.5698265 0.4855859 [7] 0.4276710 0.4091999 -0.1209642 -0.4437921 Largest eigenvalues: [1] 106444015 100954276 95040224 92825220 92092041 88885875 86892238 [8] 86326281 86132898 85379433 Smallest eigenvalues: [1] 0.73580674 0.71547592 0.60374002 0.52317564 0.49379349 0.47035492 [7] 0.37569714 0.23896398 0.22458028 -0.02580594 Largest eigenvalues: [1] 104020137 99291632 93508859 91233784 90028942 87323463 85152296 [8] 84733830 84465737 83669395 Smallest eigenvalues: [1] 0.8796374 0.8780907 0.8239308 0.7721236 0.6873911 0.5056303 [7] 0.4310891 0.3015257 0.3003582 -1.1422438 Largest eigenvalues: [1] 103441122 99497873 93672338 91520965 90831344 88363939 86813799 [8] 84515813 84444951 83357443 Smallest eigenvalues: [1] 0.8430146 0.7198505 0.7074024 0.6814185 0.6114685 0.4335933 [7] 0.3977367 0.3593130 -0.1388345 -1.2327597 Largest eigenvalues: [1] 105419334 99220768 93792330 91777138 90574755 87521985 85933188 [8] 85051824 84687125 84528451 Smallest eigenvalues: [1] 0.8386778 0.6537879 0.6139774 0.6053720 0.4878238 0.3639670 [7] 0.2237071 0.2179899 -0.2629713 -0.3340416 Largest eigenvalues: [1] 104480729 100634781 95153742 92243208 91833613 89287421 86854880 [8] 85735046 85610349 84328154 Smallest eigenvalues: [1] 0.8078024 0.7688366 0.7194096 0.5690648 0.5450135 0.5320275 [7] 0.5283654 0.4889537 0.3320814 -1.0096363 Largest eigenvalues: [1] 103033470 101166628 94232638 91458910 90492742 88571155 86301064 [8] 85201635 84038568 83816212 Smallest eigenvalues: [1] 0.8745098 0.7681173 0.6969455 0.6246933 0.5833410 0.4730661 [7] 0.4679226 0.4368091 0.4263006 -0.5865654 Largest eigenvalues: [1] 104457878 99493157 94089804 91604090 91442603 88408573 86248229 [8] 85531261 84818903 84407265 Smallest eigenvalues: [1] 0.8443338 0.7737227 0.6052366 0.6008664 0.5938124 0.5510738 [7] 0.4600482 0.4215770 0.4113577 -3.4367402 Largest eigenvalues: [1] 104664629 98951527 93578715 91175207 90339225 88014608 85712003 [8] 84760915 84327760 83408653 Smallest eigenvalues: [1] 0.7484673 0.7389982 0.7377629 0.7334076 0.6834172 0.4626127 [7] 0.4398324 0.3862404 0.0976895 -0.4748319 Largest eigenvalues: [1] 103589017 99355433 94281765 91905985 89815812 87630224 85962524 [8] 85568067 85073011 83737772 Smallest eigenvalues: [1] 0.7962071 0.7603090 0.7441163 0.7179555 0.6518519 0.5803225 [7] 0.5381808 0.4985848 0.1036667 -0.6044022 Largest eigenvalues: [1] 106511086 99822911 94183537 92557121 91971214 88969313 86987832 [8] 86362954 85763231 85025331 Smallest eigenvalues: [1] 0.7398333 0.7215139 0.6606134 0.6514172 0.4553336 0.4525559 [7] 0.3587850 0.2997641 -0.1003223 -0.7904825 Largest eigenvalues: [1] 106573775 99317610 94143514 92185752 90717909 88360388 85494394 [8] 85269182 85045181 84056108 Smallest eigenvalues: [1] 0.75839038 0.68246347 0.67902311 0.58827083 0.57354438 0.35780311 [7] 0.32803338 0.06960289 -0.60924555 -1.13343261 Largest eigenvalues: [1] 105990378 99922272 95365582 93472732 91159553 88774143 86934004 [8] 86604410 86035443 84923748 Smallest eigenvalues: [1] 0.8513186 0.7775980 0.6818863 0.6469987 0.6344979 0.4935909 [7] 0.4866547 0.4711691 0.3208297 -0.8497610 Largest eigenvalues: [1] 106237500 99380784 94301203 92931660 89998447 87636401 85859848 [8] 85541906 85473706 84047218 Smallest eigenvalues: [1] 0.9301248 0.8724659 0.7922428 0.7597574 0.5496032 0.5211803 [7] 0.4750837 0.4008746 0.2013147 -1.8428235 Largest eigenvalues: [1] 101964176 98878306 93509471 90671658 89639588 87948768 85562454 [8] 84501003 83441040 83102113 Smallest eigenvalues: [1] 0.8899350 0.8408969 0.7448646 0.6898572 0.6489925 0.5524051 [7] 0.4621801 0.2817378 -0.3614150 -1.0933649 Largest eigenvalues: [1] 104501304 99316054 93745896 91416986 91029807 88233722 85895607 [8] 85094520 84681101 83418420 Smallest eigenvalues: [1] 0.9381133 0.9188096 0.9144229 0.8822154 0.8179349 0.6496309 [7] 0.5982140 0.5957501 0.1731166 -0.7899581 Largest eigenvalues: [1] 107565574 99125609 94278013 93234682 91098156 88330081 86333100 [8] 85874402 85386024 84547408 Smallest eigenvalues: [1] 1.0529908 0.9049032 0.8427068 0.8127357 0.7828059 0.7689413 [7] 0.6174655 0.5710951 0.4215169 -2.4973977 Largest eigenvalues: [1] 103983159 97894163 93037265 90218028 90035822 87507968 85643115 [8] 84513599 83495773 82937669 Smallest eigenvalues: [1] 0.9654332 0.7821536 0.7798522 0.7454313 0.7134808 0.6406593 [7] 0.4728133 0.4152741 0.3649767 -1.1618239 Largest eigenvalues: [1] 104435978 99618955 94649326 91774154 91516095 88652488 86022406 [8] 85930882 85140459 84272633 Smallest eigenvalues: [1] 0.81773819 0.76909417 0.75269308 0.65035879 0.64022264 0.55498111 [7] 0.50953342 0.38756285 -0.03974764 -0.35407391 Largest eigenvalues: [1] 107464723 100622442 94435724 93748127 91142713 88333133 86928636 [8] 86234540 85197728 84442451 Smallest eigenvalues: [1] 0.8338658 0.6746731 0.6720420 0.6097554 0.5970376 0.5804414 [7] 0.5191579 0.3620539 0.0871708 -0.1099318 Largest eigenvalues: [1] 104519191 98642669 93223873 91073463 90385336 87586545 85561498 [8] 84782366 84473843 83725855 Smallest eigenvalues: [1] 0.8929311 0.7681394 0.7202351 0.6178122 0.5983453 0.4603386 [7] 0.4575106 0.3056823 0.1611379 -0.1974608 Largest eigenvalues: [1] 107049180 99163516 94538436 92471350 90419111 87550636 86516913 [8] 85717507 85693305 85194228 Smallest eigenvalues: [1] 0.8884553 0.8856775 0.7539470 0.6684768 0.6381232 0.5383722 [7] 0.4811965 0.4713399 0.4618388 -1.4110076 Largest eigenvalues: [1] 105351341 99369216 94995891 92067154 90930699 88565758 86285411 [8] 86119722 85237043 84405728 Smallest eigenvalues: [1] 0.9444013 0.9291426 0.8721264 0.8178605 0.7025553 0.6955132 [7] 0.5807001 0.3640566 0.3285204 -0.1308723 Largest eigenvalues: [1] 105194494 99065122 93528396 92444499 90539326 87822564 85476731 [8] 85365552 85326097 83816116 Smallest eigenvalues: [1] 0.97658559 0.97030419 0.90009971 0.88867702 0.74304795 0.63847534 [7] 0.59479255 0.53679144 0.43830732 -0.08021742 Largest eigenvalues: [1] 104157755 99208721 93401377 91929848 90497511 87865684 85867312 [8] 85192659 84793520 83665107 Smallest eigenvalues: [1] 0.8337573 0.7065419 0.6640999 0.5800426 0.5671935 0.5499698 [7] 0.5411207 0.4208867 -0.2280637 -1.0622205 Largest eigenvalues: [1] 106895212 100788329 95188750 94292247 91474874 89019523 87212633 [8] 86391092 86283859 84818930 Smallest eigenvalues: [1] 0.6967824 0.6442530 0.6012996 0.5768479 0.5731350 0.5432930 [7] 0.4675510 0.1281104 -0.2418260 -4.3489789 Largest eigenvalues: [1] 107029422 101080114 95287564 93335628 91290638 88506810 86690936 [8] 86493074 86090580 84705949 Smallest eigenvalues: [1] 0.8826730 0.8740377 0.8002370 0.6500185 0.6322033 0.5040362 [7] 0.4095338 0.2205173 0.1726404 -0.2255056 Largest eigenvalues: [1] 106829970 99643395 94867180 93677242 90688011 87930635 86656704 [8] 86255637 85632896 84605822 Smallest eigenvalues: [1] 0.8725536 0.8400439 0.8093211 0.7755989 0.7688947 0.5537328 [7] 0.4316948 0.2899139 -0.2391339 -0.7682721 Largest eigenvalues: [1] 105716612 99623780 93737216 92349414 91267469 88348283 85952927 [8] 85524296 84844391 83686582 Smallest eigenvalues: [1] 0.8818685 0.8740855 0.7737895 0.7466789 0.6284974 0.6185893 [7] 0.6122184 0.4828108 -0.2181644 -0.5219358 Largest eigenvalues: [1] 104649231 98541945 92933258 92135779 90135506 87524211 85568500 [8] 85388438 85089879 83935824 Smallest eigenvalues: [1] 0.99169984 0.85595259 0.84428134 0.78240254 0.77751121 0.59920223 [7] 0.58984954 0.54566010 0.06978536 -1.50926647 Largest eigenvalues: [1] 103872021 98527270 92934053 90787094 90177712 87041550 85297734 [8] 85153949 84146545 83875504
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9597557 | 0.5332638 | 14.44874 | 0.09 | 1.106629 | 1.014447 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + t + speed
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd,
speed = speed_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_speed_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 100, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e4),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e4),
speed = list(nbetabasis = 90, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 516 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.8023326 0.7306568 0.5930300 0.5784356 0.5660754 0.4486113 [7] 0.3847868 0.3455271 0.2515624 -0.1991579 Largest eigenvalues: [1] 96292771 92110720 86573470 85574960 84154838 81990063 80539458 79906470 [9] 77883632 77852314 Smallest eigenvalues: [1] 0.8130933 0.7657174 0.5990278 0.5959814 0.5311977 0.5213477 [7] 0.4962745 0.4469545 0.3857830 -0.3024419 Largest eigenvalues: [1] 95439344 92509953 87820472 85515156 84490174 82535084 80704250 79423703 [9] 79156954 78221011 Smallest eigenvalues: [1] 0.95360030 0.79554248 0.61498527 0.58710836 0.52652436 0.52243351 [7] 0.46332465 0.46239561 0.30109619 -0.02969841 Largest eigenvalues: [1] 96212271 92761282 86850468 86579804 83896613 81797478 80613539 79757593 [9] 78658487 77189551 Smallest eigenvalues: [1] 0.8667990 0.8625264 0.8457241 0.7588064 0.6484854 0.4891209 [7] 0.4686352 0.4625845 0.4112604 -0.1139496 Largest eigenvalues: [1] 96959878 92131671 86847039 86503916 84168532 81750369 80524947 79666280 [9] 78566937 77587356 Smallest eigenvalues: [1] 0.8507446 0.7772218 0.7363910 0.5669263 0.5406401 0.5272125 [7] 0.5089937 0.3605121 0.1736629 -0.5250817 Largest eigenvalues: [1] 96380906 92161514 86998980 85897990 84433475 82271723 80466092 79994440 [9] 78583933 77450409 Smallest eigenvalues: [1] 0.7879745 0.7184224 0.7100303 0.5989931 0.5827538 0.4897499 [7] 0.4790893 0.3112615 0.1526596 -0.2378991 Largest eigenvalues: [1] 96662563 91922391 86690050 86162257 84537752 82340003 80593058 80203277 [9] 78235319 77938036 Smallest eigenvalues: [1] 0.8270973 0.7748892 0.7664919 0.5443116 0.4468675 0.4406728 [7] 0.3466308 0.3176865 0.1447340 -0.0493373 Largest eigenvalues: [1] 96009923 91358284 86925984 85656715 84628297 82716677 80726114 80144369 [9] 78450400 78011592 Smallest eigenvalues: [1] 0.84749171 0.83644010 0.82322868 0.74751525 0.67307654 0.65059059 [7] 0.62256924 0.43098287 0.36947403 -0.01827428 Largest eigenvalues: [1] 95646294 92317290 86694244 85852548 84543185 82205788 80084197 79576240 [9] 78523879 77159717 Smallest eigenvalues: [1] 0.86009285 0.74860994 0.60229623 0.57807967 0.54081888 0.48055032 [7] 0.45924758 0.27363625 0.04797604 -0.05643324 Largest eigenvalues: [1] 95420026 91237449 85675088 85555028 84625624 81873091 79626472 79139858 [9] 77351183 77287963 Smallest eigenvalues: [1] 0.6988804 0.5381416 0.5169461 0.4440645 0.4429098 0.4199216 [7] 0.3539133 0.3491382 0.1359943 -0.8780256 Largest eigenvalues: [1] 96158590 91992731 87360328 86192567 83887723 82376332 80507375 80127623 [9] 78245467 77606244 Smallest eigenvalues: [1] 0.7524768 0.7486927 0.7354138 0.7008322 0.6579877 0.4992293 [7] 0.4714912 0.4055988 0.3710590 -0.2093639 Largest eigenvalues: [1] 96399156 91800480 85763194 85593892 83807080 81850976 80573383 79140318 [9] 78672889 77419405 Smallest eigenvalues: [1] 0.93209776 0.83536702 0.79677212 0.77498429 0.71394999 0.67694649 [7] 0.54520265 0.51255610 0.41150507 -0.01113285 Largest eigenvalues: [1] 96307042 91968831 86429401 86123562 84108121 82028702 80839774 79515824 [9] 77920666 77460336 Smallest eigenvalues: [1] 0.7830629 0.7070390 0.5885160 0.5747904 0.5672663 0.5430718 [7] 0.5361667 0.4649680 0.4065079 -0.2506416 Largest eigenvalues: [1] 98264475 92236769 87741807 87075538 84374336 81968609 81449334 79553376 [9] 78688667 77292962 Smallest eigenvalues: [1] 0.70546259 0.62760187 0.59316086 0.43921190 0.37966541 0.36184532 [7] 0.34035727 0.26602798 0.07259927 -0.09715703 Largest eigenvalues: [1] 98310919 92355241 87754627 87450377 84484656 82738596 81544582 80057618 [9] 78498418 77744690 Smallest eigenvalues: [1] 0.899030852 0.855844796 0.847746166 0.764017142 0.727826265 [6] 0.612152923 0.431827418 0.125784886 0.125488792 -0.008586478 Largest eigenvalues: [1] 98330573 91523235 86904072 86787261 84092398 82109556 81350341 79835873 [9] 78794387 77912923 Smallest eigenvalues: [1] 0.9244387 0.8599096 0.8284976 0.7885026 0.7461661 0.7182859 [7] 0.6504258 0.5253792 0.4368723 -2.5996317 Largest eigenvalues: [1] 97613423 91648543 86518457 86016073 83905756 82140003 79976457 78699033 [9] 78464549 77379351 Smallest eigenvalues: [1] 0.7623535 0.7039853 0.6698169 0.6052488 0.5885044 0.5183588 [7] 0.4401257 0.4322316 0.3472072 -0.8608683 Largest eigenvalues: [1] 95896130 90483110 85963577 85662653 83441379 81488409 79712679 79107844 [9] 77935794 77050543 Smallest eigenvalues: [1] 1.0010092 0.8616235 0.8329634 0.7870186 0.5835864 0.5060907 [7] 0.5003330 0.2902580 0.2091715 -0.3220562 Largest eigenvalues: [1] 96803606 91917252 86851218 86080707 84108338 82355907 80011399 79071608 [9] 78933428 77287942 Smallest eigenvalues: [1] 0.8238099 0.7815312 0.7652700 0.6555720 0.5812882 0.5733222 [7] 0.5531999 0.4326715 0.4127030 -0.3300745 Largest eigenvalues: [1] 94808210 90846892 86139300 84846745 83557223 81815506 79210424 78782066 [9] 77306270 77189146
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9784529 | 0.4986595 | 25.74513 | 0.765 | 1.321357 | 0.9232714 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + t + steps
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temperature = temperature_fd,
steps = steps_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_steps_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 31. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 448 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.8196595 0.8044466 0.6853499 0.6840547 0.6416641 0.5000847 [7] 0.4919223 0.4162059 0.3512690 -1.6095933 Largest eigenvalues: [1] 106261679 99644644 93848745 92985924 91207569 88436906 86003831 [8] 85722197 85399404 83821687 Smallest eigenvalues: [1] 1.0243802 1.0042661 0.9074820 0.8848076 0.6822417 0.6656719 [7] 0.6595394 0.5936150 0.5464485 -16.8462585 Largest eigenvalues: [1] 102952997 99264758 93314383 91395716 90396182 88191151 85656243 [8] 84903734 83921335 83480049 Smallest eigenvalues: [1] 0.93474535 0.88953946 0.86492019 0.79618887 0.77567234 0.64266068 [7] 0.47448650 0.45876537 0.39235486 -0.06361396 Largest eigenvalues: [1] 103835118 100126938 93913753 92095472 90603400 88014380 86347171 [8] 86104552 84947737 84571274 Smallest eigenvalues: [1] 0.6424902 0.5804021 0.4430021 0.4208843 0.3595852 0.2851461 [7] 0.1373264 -0.1128517 -0.2345978 -0.7043995 Largest eigenvalues: [1] 105952490 100186330 93940728 93017042 91460258 88381820 86342228 [8] 86161250 86049650 84483471 Smallest eigenvalues: [1] 1.0173485 0.8549337 0.8174713 0.8062163 0.7948853 0.5978083 [7] 0.5920966 0.4753799 0.3281027 -0.5971899 Largest eigenvalues: [1] 106954903 100284820 94840793 92571347 91224212 88516510 86456406 [8] 85652975 85611368 83890024 Smallest eigenvalues: [1] 0.38422372 0.22671987 0.19928928 0.12576788 0.10996263 0.09690684 [7] 0.03039322 -0.16705310 -1.02607067 -1.94259144 Largest eigenvalues: [1] 103125424 99395034 94232529 90868430 90728629 88465616 86332812 [8] 85072625 83886235 83723967 Smallest eigenvalues: [1] 0.94683153 0.82727887 0.77773333 0.66781492 0.52404798 [6] 0.49053237 0.30285488 0.08017989 -0.18854318 -37.14900405 Largest eigenvalues: [1] 105586688 100156622 94368592 93050418 91410704 88542240 86248204 [8] 86058775 85764301 83966875 Smallest eigenvalues: [1] 0.87129084 0.85692784 0.82183477 0.69695934 0.68216177 0.67006993 [7] 0.65826422 0.47638148 0.45361357 -0.08585576 Largest eigenvalues: [1] 104370583 100528836 94865266 92133549 91601193 89208480 86503024 [8] 85696452 85020705 84096407 Smallest eigenvalues: [1] 0.250108494 0.242523990 0.087507796 0.070919500 -0.001204408 [6] -0.016844338 -0.826135206 -1.704947970 -6.974567217 -24.603975432 Largest eigenvalues: [1] 101771717 99312013 93142237 91557752 89371803 88137168 85952737 [8] 83864954 82729797 82655034 Smallest eigenvalues: [1] 0.8387625 0.8273547 0.7879769 0.6854452 0.5280797 0.4976924 [7] 0.3818900 0.3189906 0.2045337 -12.2193458 Largest eigenvalues: [1] 103646808 99891303 94680836 91952032 91022791 89632045 87481257 [8] 85056756 84223969 84069409 Smallest eigenvalues: [1] 1.01442807 0.97275961 0.95795650 0.88684745 0.87107463 0.74558370 [7] 0.57022466 0.46913488 0.14578255 -0.03876611 Largest eigenvalues: [1] 104357352 98982818 93077712 91895437 90508861 87748742 85329004 [8] 85202504 84904788 83383727 Smallest eigenvalues: [1] 1.1049448 1.0592071 1.0523930 0.9276761 0.9232503 0.7781647 [7] 0.6550936 0.4882699 0.4236503 -0.6533081 Largest eigenvalues: [1] 104496448 99139433 93680086 92434623 90622925 87894492 85576715 [8] 85200908 85172017 83861451 Smallest eigenvalues: [1] 0.9249614 0.8820767 0.8196297 0.7358541 0.6754209 0.4264131 [7] 0.4047466 0.3883430 0.3849609 -0.6345571 Largest eigenvalues: [1] 107262331 100406807 94959708 93604209 91327790 88359696 86755444 [8] 86072587 85991151 84674536 Smallest eigenvalues: [1] 0.8951750 0.8094381 0.7268142 0.7030697 0.6052475 0.4918147 [7] 0.4310893 0.3931693 0.3801434 -0.4329674 Largest eigenvalues: [1] 103978975 99287902 93424526 91901233 91661691 88249710 85472008 [8] 84794646 84555675 83159828 Smallest eigenvalues: [1] 0.9290823 0.9074280 0.8649258 0.7850286 0.7024474 0.6751984 [7] 0.5240887 0.4496939 0.4027126 -2.6934274 Largest eigenvalues: [1] 104884607 98936568 94464302 91547350 90799037 88679521 86360307 [8] 85769972 84772520 84281823 Smallest eigenvalues: [1] 0.7836526 0.7320805 0.5906383 0.5859380 0.4428995 0.4386205 [7] 0.4302052 0.3978384 0.2668234 -0.3212869 Largest eigenvalues: [1] 105187183 100942427 95413563 92903751 91862136 89370885 86956994 [8] 86675299 86057980 85016786 Smallest eigenvalues: [1] 0.8909155 0.8746383 0.8343011 0.7560164 0.6183052 0.6158490 [7] 0.4889652 0.3491698 0.2147309 -0.9447103 Largest eigenvalues: [1] 105878929 101491096 94518007 92516120 91437295 88875704 86671164 [8] 86241685 85619389 84745437 Smallest eigenvalues: [1] 0.5343448 0.5238116 0.5219636 0.4860134 0.2741081 0.2480360 [7] 0.2248062 -0.5623572 -1.5396562 -86.9791467 Largest eigenvalues: [1] 103206512 98845791 93049584 91002514 89618385 87368941 85792539 [8] 84742558 84105268 83547035 Smallest eigenvalues: [1] 0.9263446 0.8719181 0.7827959 0.7564749 0.7333258 0.6480056 [7] 0.5060685 0.4596948 0.4303588 -0.2420529 Largest eigenvalues: [1] 107981945 101329640 95564272 94383361 91725065 88763531 87560757 [8] 86919555 86831387 85120954 Smallest eigenvalues: [1] 1.0616214 0.9766720 0.9277764 0.9209410 0.7994646 0.7586696 [7] 0.5606442 0.4983990 0.4796401 -0.4711130 Largest eigenvalues: [1] 107344634 100818994 94125231 94068780 91886672 88884787 86981669 [8] 86112649 85910283 84366288 Smallest eigenvalues: [1] 0.87925742 0.85964046 0.73783219 0.71225394 0.61185693 0.45277877 [7] 0.35651200 0.32761879 -0.01542535 -0.91171730 Largest eigenvalues: [1] 105919357 98244322 93468363 92715722 89673270 86899232 85840512 [8] 84658237 84198951 83292554 Smallest eigenvalues: [1] 0.7494719 0.6579574 0.6324924 0.5690456 0.4733595 0.4669362 [7] 0.4581893 0.3612288 0.2915466 -0.2245592 Largest eigenvalues: [1] 102584868 99856527 94257667 91367664 90696731 88090486 86189476 [8] 85849059 84649432 84000760 Smallest eigenvalues: [1] 0.6938824 0.6844554 0.6772146 0.6605042 0.5666201 [6] 0.3192113 0.1544394 0.1214697 0.1172577 -111.2578620 Largest eigenvalues: [1] 105526798 99310442 93896206 91877853 90676258 87622033 86036043 [8] 85136935 84786774 84627351 Smallest eigenvalues: [1] 0.7839034 0.6677506 0.6483113 0.5470486 0.5081555 0.5029692 [7] 0.3993546 0.3190194 0.3120477 -0.2696197 Largest eigenvalues: [1] 105722127 100225546 94675091 93133449 91003530 88503737 86238636 [8] 85716527 85281569 83878103 Smallest eigenvalues: [1] 0.52142718 0.43728438 0.41453525 0.37892685 0.21906974 0.11353888 [7] -0.01496437 -0.09717759 -0.26969856 -0.54465620 Largest eigenvalues: [1] 104587298 100724335 95256757 92341962 91938056 89387340 86938856 [8] 85839867 85703828 84419337 Smallest eigenvalues: [1] 0.62727973 0.53182308 0.42810272 0.22792692 0.12242602 0.02302653 [7] -0.01326906 -0.16570588 -0.31323935 -1.32354506 Largest eigenvalues: [1] 104561932 99589333 94193032 91699365 91543678 88508858 86344031 [8] 85616290 84911910 84504424 Smallest eigenvalues: [1] 0.8908322 0.8851475 0.8446448 0.7755036 0.7660910 0.7456906 [7] 0.6363262 0.5030096 0.4544611 -4.3796006 Largest eigenvalues: [1] 104776347 99044022 93688384 91276687 90445616 88117132 85795209 [8] 84868271 84424471 83512079 Smallest eigenvalues: [1] 0.7806053 0.6809623 0.5683034 0.5269032 0.4690017 0.4515576 [7] 0.4404079 0.4269714 0.3618563 -0.6147707 Largest eigenvalues: [1] 106156485 100463913 95033229 92896246 92455854 89619792 86715285 [8] 86335632 85981407 84446956 Smallest eigenvalues: [1] 1.0038761 0.9135669 0.8347945 0.7240845 0.7147767 0.6517433 [7] 0.4985436 0.4861040 0.4254801 -0.4997422 Largest eigenvalues: [1] 106615719 99917535 94287427 92652684 92074892 89065256 87085112 [8] 86444184 85854364 85125296 Smallest eigenvalues: [1] 0.85802596 0.74570393 0.72215775 0.67460185 0.52876759 0.52765608 [7] 0.52489237 0.49958474 0.25989217 -0.03833498 Largest eigenvalues: [1] 105638709 100052414 94421267 92418535 91023732 88806392 86437826 [8] 85707399 85096092 84626840 Smallest eigenvalues: [1] 0.8426319 0.7629597 0.7627586 0.7535063 0.7045397 0.5384999 [7] 0.4363654 0.3660655 0.3585452 -0.3635503 Largest eigenvalues: [1] 105198558 99906862 94095225 92670188 90842280 88408363 86361106 [8] 86346150 85707331 84334146 Smallest eigenvalues: [1] 1.07301313 1.05007555 0.83878861 0.72550068 0.67434711 [6] 0.61661829 0.41223986 0.26342700 0.09501782 -29.09794935 Largest eigenvalues: [1] 105255090 100751804 94957016 92072793 91743890 88976092 86563261 [8] 86451486 85333163 84575312 Smallest eigenvalues: [1] 0.84649187 0.78203849 0.68553864 0.61112767 0.52192843 0.47494514 [7] 0.42719277 0.11098407 -0.02413549 -0.04802989 Largest eigenvalues: [1] 106098181 100015601 95470295 93573147 91261909 88876826 87031679 [8] 86698456 86121176 85025885 Smallest eigenvalues: [1] 0.80418551 0.78367278 0.70880372 0.68984633 0.59806619 0.51986245 [7] 0.51612547 0.51123790 0.40000075 -0.05287891 Largest eigenvalues: [1] 105329211 100537758 94783997 92726337 91850141 89244364 86788607 [8] 86089671 85271433 84401052 Smallest eigenvalues: [1] 0.7590050 0.7055272 0.5921747 0.5320261 0.5276959 0.5030242 [7] 0.4891627 0.3555474 0.3303684 -0.1386635 Largest eigenvalues: [1] 105664425 100415948 94901863 93474657 91864342 89276718 86763490 [8] 86517450 86351623 84792522 Smallest eigenvalues: [1] 0.38939703 0.26811735 -0.03329406 -0.20080089 -0.27962565 -0.32020108 [7] -0.64573332 -0.74294933 -1.13191880 -2.78097339 Largest eigenvalues: [1] 104607323 99401924 93844078 91514007 91129372 88330448 85976032 [8] 85200270 84774891 83517741 Smallest eigenvalues: [1] 0.8701757 0.8359618 0.7756885 0.7173479 0.6313990 0.6008591 [7] 0.4155364 0.3360510 0.2319035 -0.7099531 Largest eigenvalues: [1] 108506838 100921191 94756896 93703607 91512905 88786914 87010038 [8] 86106737 85779851 84459959 Smallest eigenvalues: [1] 0.8660840 0.8379707 0.8032716 0.6981793 0.6283414 0.5457798 [7] 0.4662889 0.3442181 0.3039907 -0.1382705 Largest eigenvalues: [1] 105140831 100226140 93976177 92974535 91679707 88867396 86445388 [8] 85586439 85252980 83484128 Smallest eigenvalues: [1] 0.8878128 0.8856357 0.8721985 0.8001869 0.7693452 0.6224080 [7] 0.6169580 0.4386508 0.2647493 -0.2861727 Largest eigenvalues: [1] 104731022 100852422 94413882 91971036 91820171 89045923 86743214 [8] 85507572 85186965 83933670 Smallest eigenvalues: [1] 1.0520046 0.9636423 0.7910852 0.7746524 0.6950678 0.6746206 [7] 0.6241497 0.4532057 0.4249675 -0.4286315 Largest eigenvalues: [1] 106716597 99369237 94061588 93306600 90650691 87662102 86232573 [8] 85421768 85093904 83853578 Smallest eigenvalues: [1] 0.9912773 0.9767569 0.7615214 0.6283479 0.5598192 0.5424520 [7] 0.4858531 0.3630912 0.2837625 -1.0471986 Largest eigenvalues: [1] 106934487 99728605 94974389 93772034 90783787 88029905 86746371 [8] 86348266 85712694 84702566 Smallest eigenvalues: [1] 0.9179462 0.7996117 0.7907295 0.7574301 0.6766746 0.6585297 [7] 0.6142183 0.4744912 0.4020389 -0.5154558 Largest eigenvalues: [1] 105810535 100331874 94151115 92777331 91019076 88135876 86245923 [8] 85832870 85614005 84462328 Smallest eigenvalues: [1] 0.9301329 0.8944272 0.7914852 0.7887828 0.7134680 0.7065633 [7] 0.5760252 0.4407584 0.2610854 -0.3981682 Largest eigenvalues: [1] 102109375 100130698 93718856 91627563 90453132 88835254 86895765 [8] 85780179 84056712 83758460 Smallest eigenvalues: [1] 0.9077808 0.8981995 0.8582748 0.7888569 0.7596013 0.5052185 [7] 0.4777994 0.4397059 0.3007343 -0.6416396 Largest eigenvalues: [1] 105819126 99710026 93836059 92443282 91365638 88441599 86029217 [8] 85612459 84942220 83783311 Smallest eigenvalues: [1] 0.92405633 0.72106321 0.55220536 0.54775112 0.41949204 0.33623383 [7] 0.32327985 0.25608123 0.04364464 -1.72722280 Largest eigenvalues: [1] 106689852 100269518 94799029 93003180 91247418 88727221 86998260 [8] 86736684 86318851 85138976 Smallest eigenvalues: [1] 0.8247083 0.8111348 0.8019690 0.7584728 0.6976873 0.5529231 [7] 0.5424216 0.4783611 0.4535837 -2.2503883 Largest eigenvalues: [1] 107865231 101197175 95176002 94334583 91551338 88900760 87293079 [8] 86146705 85561124 83927520 Smallest eigenvalues: [1] 1.08318561 0.89952892 0.78688449 0.74957939 0.69768806 0.65558491 [7] 0.57659461 0.48818150 0.41798730 -0.01727594 Largest eigenvalues: [1] 104745840 100437166 94869555 91705325 91527211 89085504 86579797 [8] 85985856 84978659 84212738 Smallest eigenvalues: [1] 1.0352508 0.9897234 0.8236016 0.7787709 0.7295700 0.6998424 [7] 0.6357687 0.4797202 0.4550250 -0.1599307 Largest eigenvalues: [1] 105176363 99465392 94681385 92005338 90229470 87925164 85572072 [8] 85247392 85187900 83431362 Smallest eigenvalues: [1] 0.8995431 0.7500717 0.7238995 0.6673440 0.6138038 0.4698957 [7] 0.4247194 0.3684657 0.3247149 -2.6122985 Largest eigenvalues: [1] 104754790 98630815 93038068 92231986 90236935 87618670 85642257 [8] 85478656 85180050 84033121
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9677958 | 0.4842474 | 13.27987 | 0.26 | 1.347121 | 0.9114945 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
temp_body = body_temperature_ENT_fd
)
path_plot <- 'figures/model_EDA_alt_temp_body_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 28. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 126 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 1.017492 | 0.337989 | 6.511186 | 0.19 | 0.8152904 | 0.5145628 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd
)
path_plot <- 'figures/model_EDA_alt_noise_temp_body_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temp_body = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 194 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.5580166 0.5558347 0.5381929 0.4805582 0.4721537 0.4282874 [7] 0.4069764 0.3271206 0.1738422 -0.7051061 Largest eigenvalues: [1] 71914345 66588453 63903546 63076720 60598711 59944374 58587721 57366838 [9] 57243487 56153851
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 1.015597 | 0.4567955 | 13.11223 | 0.285 | 1.362067 | 0.8815355 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
pollution = pollution25_fd
)
path_plot <- 'figures/model_EDA_alt_noise_pollution25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 20. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 344 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.59766275 0.57714156 0.56519578 0.45717817 0.45280857 0.44303853 [7] 0.39168946 0.28010084 0.23224744 -0.03949094 Largest eigenvalues: [1] 60608346 56039797 53525623 53019615 51347891 50471481 49458177 48511765 [9] 48467796 47643946 Smallest eigenvalues: [1] 0.5927592 0.5540943 0.5127549 0.4704407 0.4596631 0.4098020 [7] 0.3718021 0.3348278 0.3105294 -0.2917947 Largest eigenvalues: [1] 61425982 56508413 53716581 53207965 52258415 50853010 50558159 48816562 [9] 48582404 47848773 Smallest eigenvalues: [1] 0.5730787 0.5173521 0.5096257 0.5091916 0.4746070 0.3652126 [7] 0.3363023 0.3275646 0.2563110 -0.3730923 Largest eigenvalues: [1] 59908270 56625609 53949224 52994040 52315184 51341582 49777845 49711054 [9] 48563635 48177646
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.432118 | 0.675262 | 12.74966 | 0.015 | 1.683717 | 1.945614 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + temp + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
temperature = temperature_fd,
pollution = pollution25_fd
)
path_plot <- 'figures/model_EDA_alt_temp_pollution25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 27. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 386 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.322605 | 0.4649318 | 16.2151 | 0.1 | 0.9856302 | 0.7987283 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
pollution = pollution1_fd
)
path_plot <- 'figures/model_EDA_alt_noise_pollution1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 20. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 372 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.5949359 0.5729446 0.5629381 0.4542439 0.4484370 0.4316471 [7] 0.3782772 0.2833228 0.2319732 -0.1124750 Largest eigenvalues: [1] 60587206 56007235 53505086 52989592 51315156 50451702 49419279 48480162 [9] 48438864 47619347 Smallest eigenvalues: [1] 0.5868226 0.5502143 0.5128114 0.4662680 0.4585074 0.4105382 [7] 0.3670269 0.3342109 0.3075513 -0.3539924 Largest eigenvalues: [1] 61415394 56493900 53707209 53194862 52245944 50844328 50543316 48803149 [9] 48570224 47836208 Smallest eigenvalues: [1] 0.5721323 0.5098603 0.5072900 0.5028651 0.4633471 0.3730525 [7] 0.3281127 0.3159918 0.2619605 -0.3615199 Largest eigenvalues: [1] 59901588 56618855 53945196 52989338 52307992 51334661 49775093 49706916 [9] 48560502 48173137
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.426543 | 0.6791619 | 13.04562 | 0.025 | 1.719113 | 1.946984 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + temp + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
temperature = temperature_fd,
pollution = pollution1_fd
)
path_plot <- 'figures/model_EDA_alt_temp_pollution1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2),
pollution = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 27. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 378 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.312653 | 0.4661084 | 16.47744 | 0.12 | 0.9843847 | 0.7875081 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ air pressure + noise
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(air_pressure = airpressure_fd,
noise = noise_fd
)
path_plot <- 'figures/model_EDA_airpress_noise_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 25. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 184 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.10647289 0.10546970 0.10475571 0.10441301 0.10334892 0.10153813 [7] 0.10098287 0.05533742 0.05212848 -0.23792976 Largest eigenvalues: [1] 15507332 15386060 15270604 15101780 14931862 14711134 14664505 14499720 [9] 14418718 14366087 Smallest eigenvalues: [1] 0.11399720 0.11343162 0.11061244 0.10857894 0.10817622 0.10097086 [7] 0.10022515 0.06204365 0.05630579 -0.75793805 Largest eigenvalues: [1] 15497329 15265435 15165329 15030179 14975714 14825577 14725503 14685036 [9] 14564747 14448756 Smallest eigenvalues: [1] 0.13951882 0.13885938 0.13738446 0.13606086 0.13534702 0.13369462 [7] 0.12628514 0.07203423 0.07043961 -0.13303745 Largest eigenvalues: [1] 15388617 15292917 15149733 15100482 14945311 14782932 14683466 14598492 [9] 14495046 14409507
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.576449 | 0.3785018 | 8.174668 | 0.405 | 1.040496 | 0.4829507 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ air pressure + noise + air temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(air_pressure = airpressure_fd,
noise = noise_fd,
temperature = temperature_fd
)
path_plot <- 'figures/model_EDA_airpress_noise_temp_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
air_pressure = list(nbetabasis = 90, norder = 4, lambda = 1e2),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e2),
temperature = list(nbetabasis = 90, norder = 4, lambda = 1e2)
)
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 25. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 322 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.10049050 0.09870038 0.09683498 0.09604983 0.09565113 0.09325221 [7] 0.09139448 0.05526609 0.04407148 -0.32047288 Largest eigenvalues: [1] 16355053 16198674 16132178 15903323 15792269 15611790 15471286 15345177 [9] 15263289 15199542 Smallest eigenvalues: [1] 0.10760275 0.10682632 0.10317115 0.10090800 0.09703859 0.09303815 [7] 0.08418235 0.06159548 0.04931716 -1.22004555 Largest eigenvalues: [1] 16361221 16100095 15977299 15853573 15809618 15699875 15574450 15511030 [9] 15414523 15261930 Smallest eigenvalues: [1] 0.13587619 0.13276008 0.13207705 0.12912577 0.12441757 0.12243005 [7] 0.09461737 0.07095360 0.06942470 -0.22605266 Largest eigenvalues: [1] 16254373 16132921 16014237 15926807 15820685 15699559 15536213 15475377 [9] 15326802 15241950 Smallest eigenvalues: [1] 0.082537385 0.081961386 0.079301818 0.078346931 0.076345831 [6] 0.073700496 0.068863082 0.043700523 0.031455814 -0.009860154 Largest eigenvalues: [1] 16404595 16215084 16190676 15860716 15797660 15695601 15490967 15395130 [9] 15287997 15235032 Smallest eigenvalues: [1] 0.0579022118 0.0560362018 0.0546029674 0.0532622023 0.0514941030 [6] 0.0510026453 0.0487051856 0.0471930905 0.0278328470 -0.0001433643 Largest eigenvalues: [1] 16432027 16160121 16156371 15928699 15903793 15677388 15561430 15426807 [9] 15346551 15292998
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.313302 | 0.5794782 | 16.32764 | 0.04 | 1.152863 | 1.382889 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + acc
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd)
path_plot <- 'figures/model_EDA_alt_noise_acc_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 450 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.9739181 0.9070555 0.9044741 0.8227855 0.7871775 0.5797282 [7] 0.5447441 0.5304211 0.1462120 -0.3233728 Largest eigenvalues: [1] 107757898 102082451 95875388 93692545 92991159 90103538 87300144 [8] 87123994 86805321 85850434 Smallest eigenvalues: [1] 0.9600672 0.7639749 0.7222864 0.6831188 0.5820995 0.4457554 [7] 0.4429751 0.4157449 0.3607366 -0.3871306 Largest eigenvalues: [1] 106461459 102714673 96523396 93752390 93550486 90720069 87770294 [8] 87276932 86752277 85605894 Smallest eigenvalues: [1] 1.12144307 1.06242080 0.87649874 0.79347665 0.74439217 0.66350438 [7] 0.60190233 0.55378957 0.51711597 -0.02045023 Largest eigenvalues: [1] 105829349 103394034 97749405 93653001 93095508 91441423 88374627 [8] 88050165 86682215 86102144 Smallest eigenvalues: [1] 0.9973730 0.8630682 0.8204420 0.7664982 0.7029154 0.5189685 [7] 0.5145405 0.5063051 0.2355076 -1.1446937 Largest eigenvalues: [1] 106262500 101803413 96408942 93325711 93038505 90436544 88368260 [8] 87122424 86188854 85614843 Smallest eigenvalues: [1] 0.9380506 0.9057991 0.7974583 0.7854969 0.7488043 0.6271615 [7] 0.6157394 0.5951337 0.4298249 -0.1027140 Largest eigenvalues: [1] 105888788 103182592 97000905 93468480 93316605 91022840 88196838 [8] 87249699 86366499 85750471 Smallest eigenvalues: [1] 0.9959630 0.9587178 0.8511334 0.7057276 0.6709490 0.6441068 [7] 0.5804226 0.5782194 0.2786083 -1.2692560 Largest eigenvalues: [1] 108097038 101658959 96210444 93879148 92044067 89873924 87499400 [8] 87105833 86999861 85447673 Smallest eigenvalues: [1] 1.0602412 0.9374022 0.9279722 0.8926586 0.7895102 0.7717937 [7] 0.7001134 0.5497410 0.4865444 -0.6337533 Largest eigenvalues: [1] 105569136 102515039 96393532 93228582 92611669 90551635 87551044 [8] 87399116 85880860 85533123 Smallest eigenvalues: [1] 1.0522998 0.9887746 0.9156795 0.8701023 0.8261606 0.7990901 [7] 0.7593079 0.7167662 0.3340540 -0.5894481 Largest eigenvalues: [1] 107082135 102200653 96209165 93509252 92524823 90588967 87853406 [8] 87276167 86071986 85207164 Smallest eigenvalues: [1] 0.9342266 0.9163383 0.7692761 0.6682715 0.6471987 0.5963400 [7] 0.5617708 0.4187039 0.1625168 -0.2475219 Largest eigenvalues: [1] 106501411 101930061 95686593 93077685 92859929 90129501 87533204 [8] 86946163 85672585 85317158 Smallest eigenvalues: [1] 0.9954587 0.9656373 0.8385163 0.8183769 0.7468686 0.6036963 [7] 0.5662285 0.4359675 0.4074427 -0.1552247 Largest eigenvalues: [1] 107088196 99984352 95383721 92982159 91605599 89076474 86263273 [8] 86181958 85876111 84957046 Smallest eigenvalues: [1] 0.7824925 0.7510949 0.6095060 0.5779382 0.5731246 0.5522463 [7] 0.4849424 0.4824695 0.1987788 -0.6091327 Largest eigenvalues: [1] 106546940 102558831 96903721 93204445 92896778 90696179 88422239 [8] 87555852 86250195 85709403 Smallest eigenvalues: [1] 0.93256259 0.78722467 0.74130118 0.73611676 0.69867149 0.58071432 [7] 0.58037770 0.33130211 0.27698438 -0.08817705 Largest eigenvalues: [1] 105273231 101492058 96093008 93039779 92595070 90284383 87895010 [8] 87259920 86134106 85754897 Smallest eigenvalues: [1] 1.0254990 0.9100123 0.8884040 0.8660469 0.8539111 0.6463336 [7] 0.5813533 0.4988011 0.2079018 -1.3079552 Largest eigenvalues: [1] 107247314 101561558 96239419 93415521 92490345 90227034 87886485 [8] 86957699 86542579 85578622 Smallest eigenvalues: [1] 0.8154282 0.7877572 0.6802313 0.6671185 0.5109802 0.4850972 [7] 0.4836900 0.4629582 0.3260486 -0.7163060 Largest eigenvalues: [1] 108469806 103343989 96547874 94687313 93766980 90407563 87987230 [8] 87847784 87623981 86167216 Smallest eigenvalues: [1] 0.9456455 0.8984036 0.8866654 0.8832891 0.6631040 0.6600169 [7] 0.5796109 0.5008270 0.2935479 -0.6530128 Largest eigenvalues: [1] 109676154 102844716 96957559 94695928 93532279 90818974 88235819 [8] 87967576 87890004 86409684 Smallest eigenvalues: [1] 1.0483063 0.8318142 0.8043516 0.7301932 0.7110074 0.6254776 [7] 0.5638472 0.3718597 0.3240146 -0.1978363 Largest eigenvalues: [1] 105316952 102459779 96476288 92681962 92509315 90220461 87594586 [8] 86441673 85771783 84897398 Smallest eigenvalues: [1] 1.09141225 1.07669232 1.01665677 0.95552947 0.88231725 0.87835712 [7] 0.67359767 0.63757596 0.60719812 -0.01507027 Largest eigenvalues: [1] 106739727 102068652 96163577 93570663 92969149 90671731 87256747 [8] 87163185 86163665 85607077 Smallest eigenvalues: [1] 1.1193088 1.1184372 1.0164019 0.8572574 0.8291404 0.7187604 [7] 0.6574832 0.6528185 0.5952092 -0.4579073 Largest eigenvalues: [1] 106539673 102642731 96460135 93646440 93437770 90865029 87464845 [8] 87428334 86687024 85779571 Smallest eigenvalues: [1] 1.0188610 0.7415235 0.7170481 0.6089356 0.5346981 0.4727927 [7] 0.3380275 0.2920763 -0.1335225 -0.8869777 Largest eigenvalues: [1] 106558703 100221025 95320206 92834115 91450142 88326528 87130785 [8] 86452796 86020181 85313657 Smallest eigenvalues: [1] 1.1361328 1.0545885 0.9298457 0.8439620 0.6850588 0.6830385 [7] 0.5856037 0.5693867 0.4086119 -0.5385280 Largest eigenvalues: [1] 107256592 101498566 96535298 94008026 92603884 90202423 87387895 [8] 87069620 86620373 85870043 Smallest eigenvalues: [1] 0.6890101 0.6524320 0.6485062 0.5782830 0.5497101 0.3645368 [7] 0.3133968 0.2086596 -0.2817090 -1.9828159 Largest eigenvalues: [1] 108480312 100853582 96589590 93113610 92255329 89341376 87134928 [8] 86562125 86355509 85727803 Smallest eigenvalues: [1] 1.0955902 1.0409376 0.9183825 0.8478418 0.7498295 0.6879591 [7] 0.5251165 0.5117385 0.3928066 -0.2432927 Largest eigenvalues: [1] 105371754 100416913 95027949 92137122 92118418 89287405 86990511 [8] 86118875 85278386 84780001 Smallest eigenvalues: [1] 0.8654643 0.8501803 0.6557305 0.5953598 0.5876937 0.5624438 [7] 0.3403873 0.3399493 0.2272461 -0.2142548 Largest eigenvalues: [1] 108756210 102682611 97522858 95741999 93430264 90957393 88257961 [8] 88173520 87932791 86326087 Smallest eigenvalues: [1] 0.9306975 0.8753051 0.7986481 0.7878632 0.7436808 0.5883950 [7] 0.5191112 0.2534280 0.1071440 -0.2756760 Largest eigenvalues: [1] 108704297 103010102 97278702 95999986 93890698 91396459 88522334 [8] 88095321 87615291 86411240 Smallest eigenvalues: [1] 1.0399542 0.9155670 0.8671659 0.8337449 0.7370843 0.6036512 [7] 0.5964418 0.5219686 0.2235807 -0.3133140 Largest eigenvalues: [1] 106550292 101841994 96294820 93131214 92786668 90355335 88269321 [8] 86948202 86243817 85548646 Smallest eigenvalues: [1] 1.1321073 1.0896680 1.0208217 0.9838445 0.8353567 0.8005417 [7] 0.7259968 0.6940746 0.5083624 -0.6082429 Largest eigenvalues: [1] 108733158 101307471 96119582 93759244 92736810 89999366 87644581 [8] 87069819 86996291 86205278 Smallest eigenvalues: [1] 0.8549064 0.7923236 0.7761904 0.7292166 0.6752019 0.6499100 [7] 0.5727572 0.5258840 -0.2340326 -0.6195309 Largest eigenvalues: [1] 107800389 102038357 97031044 94184788 92623989 90196274 88117397 [8] 87752913 87406320 86562664 Smallest eigenvalues: [1] 0.84665529 0.79642648 0.66157459 0.59468960 0.59095047 0.44760698 [7] 0.43947429 0.41525945 0.29558469 -0.07780902 Largest eigenvalues: [1] 107486780 102397613 96246139 94955101 92493242 90317269 87811284 [8] 87600492 87218129 85772277 Smallest eigenvalues: [1] 1.0399587 1.0004180 0.7030955 0.6702356 0.6508857 0.6409989 [7] 0.5537590 0.5534124 0.4161613 -0.9415906 Largest eigenvalues: [1] 105226174 101384146 96207126 92667623 91916540 90129115 87578087 [8] 86834390 85760947 85265229 Smallest eigenvalues: [1] 1.0740236 0.9699365 0.9257382 0.8976239 0.8814413 0.8189048 [7] 0.7087698 0.5209375 0.4943526 -0.6475468 Largest eigenvalues: [1] 105432599 101961961 96632200 93200940 92903891 90942382 88527626 [8] 86921735 85813932 85438444 Smallest eigenvalues: [1] 0.9613563 0.8535764 0.8520412 0.8291887 0.7795163 0.6968560 [7] 0.5084520 0.4892364 0.3059006 -0.0407415 Largest eigenvalues: [1] 108389100 101563713 96232884 94956012 92782694 90057687 87408472 [8] 87205428 86912569 85714317 Smallest eigenvalues: [1] 0.9539057 0.9133985 0.8185856 0.6942262 0.6925654 0.4889985 [7] 0.4595531 0.4110463 0.1071997 -0.1582165 Largest eigenvalues: [1] 109272464 102640614 96526103 95468141 93805268 90601919 88419732 [8] 88145744 87126209 86505585 Smallest eigenvalues: [1] 0.8484347 0.6440976 0.6061702 0.5426354 0.5336470 0.4505841 [7] 0.4443875 0.2906917 -0.3276361 -1.4825787 Largest eigenvalues: [1] 108071369 102573761 96562558 94781465 92606132 90093096 87891813 [8] 87851695 86869427 85747906 Smallest eigenvalues: [1] 1.02355361 0.96973626 0.90924679 0.89008064 0.83161944 0.72567351 [7] 0.58141891 0.58048383 0.44611625 -0.08229867 Largest eigenvalues: [1] 106467640 100899267 95673039 93050578 92103650 89236240 87316141 [8] 87098983 86233727 85986087 Smallest eigenvalues: [1] 0.7859443 0.7827471 0.7658371 0.6862303 0.6082995 0.5313227 [7] 0.5001402 0.4797584 0.4562193 -0.8163203 Largest eigenvalues: [1] 106338183 101741941 96582443 92904785 92145666 90014135 86924138 [8] 86333393 86194225 84856749 Smallest eigenvalues: [1] 1.070407878 0.933948588 0.898295072 0.860893853 0.810180977 [6] 0.655686908 0.562261570 0.557175728 0.550095770 -0.001107183 Largest eigenvalues: [1] 106724776 101722385 96206922 93328293 93124718 90456090 87294056 [8] 86751106 86173386 85034085 Smallest eigenvalues: [1] 0.8775099 0.8684947 0.7630967 0.6250612 0.5756749 0.5541340 [7] 0.3185507 0.3141688 0.1140295 -1.1804514 Largest eigenvalues: [1] 105311288 99680273 94926540 91728595 90973605 88726663 86707190 [8] 86238942 85344718 85008989 Smallest eigenvalues: [1] 1.0698727 0.9825964 0.9636048 0.7260857 0.6620844 0.6241240 [7] 0.4912535 0.4525449 0.3955901 -2.3864842 Largest eigenvalues: [1] 105085125 100817852 95057283 92591380 92386877 89547713 87597386 [8] 85899385 85526899 84540699 Smallest eigenvalues: [1] 1.0582997 1.0423215 0.9252621 0.9156458 0.8376192 0.8134114 [7] 0.7389213 0.6342170 0.5806265 -0.6904383 Largest eigenvalues: [1] 106831057 102251934 96516194 93007097 92784583 90216579 87734029 [8] 86941752 86198545 85166290
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.239632 | 0.3421001 | 7.981684 | 0.295 | 0.8108634 | 0.5254974 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + speed
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
speed = speed_fd)
path_plot <- 'figures/model_EDA_alt_noise_speed_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e4),
speed = list(nbetabasis = 90, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 33. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 500 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 1.0965649 0.9741293 0.8189636 0.7045693 0.7012212 0.5996803 [7] 0.5656703 0.4772370 0.1095383 -1.7848981 Largest eigenvalues: [1] 98898182 93456398 88382267 87668332 85531624 83157159 82223612 81011797 [9] 80468305 78952990 Smallest eigenvalues: [1] 0.9213638 0.8376573 0.7542189 0.5963766 0.5003226 0.4665080 [7] 0.4563031 0.4402115 0.3712504 -1.9122791 Largest eigenvalues: [1] 99393129 93910459 88950787 88387511 86025266 83910127 82495443 81740389 [9] 80018970 79344358 Smallest eigenvalues: [1] 0.9037080 0.8090196 0.7764319 0.7730590 0.7506336 0.6406840 [7] 0.5591572 0.4885665 0.3182691 -0.7492455 Largest eigenvalues: [1] 98403892 92293795 87502464 87150079 84972043 82927066 80737437 79964849 [9] 79734995 78733767 Smallest eigenvalues: [1] 0.6510428 0.5934467 0.5194604 0.4265543 0.3529960 0.2930514 [7] 0.2189307 -0.1254805 -0.5687495 -2.5864173 Largest eigenvalues: [1] 98398602 93636609 88724524 88060260 85706731 84110648 82311189 81217383 [9] 79553930 78954059 Smallest eigenvalues: [1] 1.0785916 1.0618919 0.9747039 0.8367183 0.7119334 0.5965782 [7] 0.5815541 0.5390983 0.2694387 -0.1762636 Largest eigenvalues: [1] 97748068 93706598 88815917 87783974 86247562 84620180 81602774 81515880 [9] 79921630 79235465 Smallest eigenvalues: [1] 0.9826523 0.8172134 0.7969923 0.6510303 0.5502280 0.5270022 [7] 0.4419622 0.3566591 -0.1429335 -0.9232720 Largest eigenvalues: [1] 99794340 93669350 88589699 88036751 85521394 83841655 81744408 81606651 [9] 79569340 79059377 Smallest eigenvalues: [1] 0.9728999 0.9379950 0.8394080 0.6392351 0.6201838 0.5692414 [7] 0.4984737 0.4181252 0.3358790 -0.4244707 Largest eigenvalues: [1] 98590909 94757458 89501604 87997138 86730883 85053656 82423267 81980215 [9] 80212216 79870142
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.224626 | 0.3320367 | 11.06011 | 0.71 | 1.207222 | 0.6771296 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + steps
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
steps = steps_fd)
path_plot <- 'figures/model_EDA_alt_noise_steps_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 90, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 90, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 90, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 32. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 444 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 1.1183631 1.0176210 0.9297772 0.8452723 0.7416317 0.7239285 [7] 0.6755437 0.6392289 0.4596060 -7.0519949 Largest eigenvalues: [1] 97342625 89767749 85927968 85393823 82761422 80416058 79617758 77874284 [9] 77830476 76648885 Smallest eigenvalues: [1] 0.8210996 0.7967740 0.7775604 0.6622976 0.5964201 0.4700285 [7] 0.3924557 0.3526923 0.2299710 -1.9672223 Largest eigenvalues: [1] 97687654 91789160 86679747 86363060 83441144 81363035 81221010 79222884 [9] 77766615 76801490 Smallest eigenvalues: [1] 0.7809085 0.7613850 0.7280797 0.6448397 0.6044466 0.5885938 [7] 0.3637156 -0.3397471 -0.4689503 -0.9617772 Largest eigenvalues: [1] 94616108 92014319 87189576 84496714 83900342 82116066 79681349 78839727 [9] 78226421 77210041 Smallest eigenvalues: [1] 0.8790409 0.8762651 0.8668854 0.8083423 0.6172791 0.4986781 [7] 0.4639298 0.4487909 0.3879823 -83.8401403 Largest eigenvalues: [1] 95013428 90569749 85918908 84249953 83632789 81235229 79313667 79022815 [9] 77538099 77432421 Smallest eigenvalues: [1] 0.8182690 0.6401740 0.5501843 0.5120892 0.4566674 0.4324881 [7] 0.3822173 0.3785554 0.3085159 -0.2504592 Largest eigenvalues: [1] 96966908 91255816 86770080 85821377 83067470 81559868 80487231 78717159 [9] 77957178 76823548 Smallest eigenvalues: [1] 0.8443321452 0.7014341727 0.5375279694 0.4550888811 0.4201822598 [6] 0.4051580069 0.3375296354 0.1761667111 0.0007127554 -0.0165973187 Largest eigenvalues: [1] 96806438 91300290 86815235 86162579 83218191 81217851 80537921 78963757 [9] 78268287 77282901 Smallest eigenvalues: [1] 0.9823531 0.8947998 0.8728813 0.8447557 0.8135737 0.6899906 [7] 0.6732836 0.5242621 0.4675930 -1.3404609 Largest eigenvalues: [1] 95451019 91570758 86104006 85195379 83155760 80992776 79440481 78670863 [9] 78018942 76633417 Smallest eigenvalues: [1] 1.0390931 0.9529703 0.9339237 0.8237270 0.7792322 0.7282763 [7] 0.6451593 0.5112481 0.3376959 -28.3220241 Largest eigenvalues: [1] 95834393 90947640 85769393 83874098 83688641 81565216 78836824 78824626 [9] 77592514 76924571 Smallest eigenvalues: [1] 1.0335811 0.9599569 0.8353745 0.7895177 0.7619191 0.6985246 [7] 0.6390835 0.5487342 0.3134193 -0.1837513 Largest eigenvalues: [1] 96205870 90409373 85933555 85664122 83076060 80855113 80097453 78266143 [9] 77974082 76646107 Smallest eigenvalues: [1] 0.8848091 0.8357054 0.8175768 0.6723973 0.6027441 0.5282721 [7] 0.4208806 0.3864270 -0.5034857 -1.3005486 Largest eigenvalues: [1] 96600178 90314570 84956974 84778438 83021410 81098185 79706643 77985859 [9] 77523600 76252610 Smallest eigenvalues: [1] 0.9727185 0.8713698 0.8211615 0.8076140 0.7866359 0.5450408 [7] 0.4848952 0.3819790 0.3526645 -0.6073986 Largest eigenvalues: [1] 98159840 91550927 86406960 85948383 83750655 81535491 80511086 79445043 [9] 78057025 76963392 Smallest eigenvalues: [1] 0.7994454 0.7980990 0.7727976 0.7306752 0.6654204 0.5804071 [7] 0.4938032 0.4620601 0.3854601 -5.2689323 Largest eigenvalues: [1] 96236424 89930310 85186737 85037654 82927329 80801786 79964170 78108661 [9] 76365710 75632436 Smallest eigenvalues: [1] 0.9987405 0.8282154 0.7820841 0.7083499 0.7068107 0.6720074 [7] 0.6550574 0.5963241 0.3904962 -26.0125030 Largest eigenvalues: [1] 95897137 90277161 86094230 85415539 83015600 80970027 79298922 78717499 [9] 77342657 76535222 Smallest eigenvalues: [1] 0.9106482 0.8725599 0.8068087 0.7525102 0.6446547 0.5736019 [7] 0.5572219 0.4385993 0.3041376 -0.1036589 Largest eigenvalues: [1] 94785674 89700105 84956515 84689601 81917125 80247314 79217789 77990231 [9] 76801161 76283336 Smallest eigenvalues: [1] 0.8493593 0.7656852 0.7633727 0.6794515 0.6147809 0.5883757 [7] 0.4586596 0.4099439 0.2995486 -0.2556937 Largest eigenvalues: [1] 94698839 89899913 85030277 83892467 82941184 80746361 78672462 77918520 [9] 77092099 76206674 Smallest eigenvalues: [1] 0.7597501 0.7359965 0.6113205 0.5533182 0.4643636 0.4331087 [7] 0.4169669 0.2676231 -1.2904106 -7.4245328 Largest eigenvalues: [1] 96694596 90550331 85791487 85504495 83231538 81174834 80138656 78776778 [9] 77743858 76746502 Smallest eigenvalues: [1] 0.8096768 0.8080229 0.6192397 0.5808576 0.5696829 0.5216424 [7] 0.4242342 0.3107008 0.2545836 -4.0480507 Largest eigenvalues: [1] 97234301 91336989 87023326 86981303 83801467 81663531 80789482 79297968 [9] 78308457 76932022 Smallest eigenvalues: [1] 0.8345835 0.7678830 0.7280397 0.6273266 0.6126059 0.5681748 [7] 0.4992526 0.4169739 0.2130704 -1.1686863 Largest eigenvalues: [1] 97173752 91673607 87080868 86734701 84034652 82325471 81185718 79060794 [9] 78263298 76991975 Smallest eigenvalues: [1] 0.70745480 0.63708534 0.62267342 0.52474762 0.49496496 0.41734368 [7] 0.40898477 0.32801835 0.09583426 -2.29334387 Largest eigenvalues: [1] 92521415 89854653 85216031 82706697 82653520 81250894 78875544 76959270 [9] 76841184 76474316 Smallest eigenvalues: [1] 0.9656954 0.9408413 0.8876182 0.7705218 0.7403162 0.6023363 [7] 0.5968584 0.2868750 0.2190016 -0.2576864 Largest eigenvalues: [1] 97038967 89604736 85449932 85242478 82450162 79980244 79463271 78075041 [9] 76964527 76154970 Smallest eigenvalues: [1] 0.8880987 0.8879066 0.8675313 0.7690868 0.6384597 0.5964105 [7] 0.5667384 0.4505765 0.4454542 -6.3000596 Largest eigenvalues: [1] 97086238 90234362 85995703 85770637 83112879 81081677 81039049 78791957 [9] 77757862 76853844 Smallest eigenvalues: [1] 0.8777975 0.8357658 0.7048800 0.6263099 0.5689071 0.5550204 [7] 0.4405208 0.4316264 0.4193840 -0.1576789 Largest eigenvalues: [1] 96700338 92147228 86839380 86180997 83471622 81246164 80646263 79252846 [9] 78243911 77133471 Smallest eigenvalues: [1] 0.7569901 0.6930407 0.6167104 0.5166723 0.4608167 0.3336871 [7] 0.2862939 0.1773101 -0.2638416 -1.8712947 Largest eigenvalues: [1] 97862004 91019788 86122981 85669038 83412634 81367364 80406622 78584223 [9] 78086890 76877454 Smallest eigenvalues: [1] 1.006842016 0.803337527 0.760850995 0.742796120 0.711957733 [6] 0.682263884 0.532263495 0.398594162 0.001300631 -0.056494873 Largest eigenvalues: [1] 93189303 91116267 85755306 83621079 82556698 81711333 78863027 77549826 [9] 77484557 76886579 Smallest eigenvalues: [1] 0.9254361 0.8677790 0.6952662 0.6213181 0.5171152 0.4233124 [7] 0.4127589 0.3896964 0.3616560 -20.0647939 Largest eigenvalues: [1] 97517421 90887275 86741133 86308801 83738187 81727076 80767522 79247290 [9] 78308366 77071954 Smallest eigenvalues: [1] 0.9221112 0.6273579 0.6017540 0.5419971 0.4840735 0.3566440 [7] 0.3321478 0.3161846 0.2590900 -5.8431321 Largest eigenvalues: [1] 98336627 90609523 86826911 86802791 83156548 80831082 80515045 78748336 [9] 77845632 76744263 Smallest eigenvalues: [1] 1.0152904 0.9485014 0.8074888 0.7356652 0.7132664 0.5698418 [7] 0.5522237 0.5110457 0.3421706 -1.6223099 Largest eigenvalues: [1] 96436714 90775402 86565474 85370198 83043566 80878595 80146647 79007926 [9] 78213492 77122380 Smallest eigenvalues: [1] 0.6262398 0.6030298 0.5897837 0.5417284 0.4639333 0.4227664 [7] 0.3858953 0.1800709 0.1686028 -0.1691043 Largest eigenvalues: [1] 96109951 91196818 85990241 85785450 82846540 81125703 80281543 78891487 [9] 77473128 76810432 Smallest eigenvalues: [1] 0.9225509 0.9007225 0.8430807 0.7667531 0.7384909 0.6761920 [7] 0.6278637 0.4378571 0.4051111 -0.4958256 Largest eigenvalues: [1] 94926675 90415114 85419204 84769461 82684548 80510406 79162966 78518963 [9] 77207221 76592112 Smallest eigenvalues: [1] 0.89785602 0.79423905 0.65984252 0.64846354 0.59898882 0.51796339 [7] 0.44763014 0.32853625 0.23615514 -0.09008767 Largest eigenvalues: [1] 96760475 91025403 85965696 85347750 83328351 81417932 80083727 78734951 [9] 76977323 76886583 Smallest eigenvalues: [1] 0.8579348 0.8448779 0.7492269 0.6510432 0.5938614 0.5244255 [7] 0.4847245 0.4549396 0.2810066 -10.8838739 Largest eigenvalues: [1] 96582844 91841933 86374739 85300909 83113508 81140530 79398771 78749502 [9] 77522302 76396169 Smallest eigenvalues: [1] 0.9813092 0.8430597 0.6818274 0.5987037 0.5922118 0.5200347 [7] 0.4079037 0.3899331 0.3627472 -0.1262698 Largest eigenvalues: [1] 94178693 88700630 84615615 83088373 81502142 79580880 77815670 77771354 [9] 76629914 75973029 Smallest eigenvalues: [1] 0.8986536 0.8660044 0.7985145 0.7141116 0.6439741 0.5981077 [7] 0.4698929 0.4130062 0.1723396 -0.4823159 Largest eigenvalues: [1] 94888908 91178708 85724452 84807081 83789787 81504809 79743807 79626801 [9] 77364800 77146917 Smallest eigenvalues: [1] 0.8245662 0.8212721 0.7058040 0.5876186 0.5287688 0.4516459 [7] 0.3917832 0.3289544 0.3176127 -54.4242583 Largest eigenvalues: [1] 95537133 88814399 84941291 83430609 82419458 80144807 77745157 77230520 [9] 77136002 76392147 Smallest eigenvalues: [1] 0.7935410 0.7711320 0.7223435 0.5948197 0.5520337 0.5169339 [7] 0.5151069 0.3901845 0.3163592 -3.5536421 Largest eigenvalues: [1] 94931478 91268911 85460407 85458955 83142289 81245998 79212731 78801384 [9] 77537339 77066987 Smallest eigenvalues: [1] 0.738303921 0.718467994 0.696675291 0.657685616 0.563580808 [6] 0.449522496 0.374952228 0.258969352 0.186110053 -0.004662431 Largest eigenvalues: [1] 95568795 92218054 87347682 85337592 84414188 82440341 80068791 79232920 [9] 78757811 77819859 Smallest eigenvalues: [1] 0.83487953 0.80007875 0.65175969 0.61502176 0.58914868 0.54243355 [7] 0.50488690 0.22633978 0.16764347 -0.01283282 Largest eigenvalues: [1] 97871149 90012619 86656062 85658486 82504679 80649890 80352807 78139276 [9] 77199974 76007852 Smallest eigenvalues: [1] 0.9063662 0.8437767 0.6882514 0.6507760 0.5958862 0.4931903 [7] 0.4465234 0.4002606 0.2787049 -11.0352552 Largest eigenvalues: [1] 95831899 91329581 86490907 85397769 83382993 81706383 80070057 79095968 [9] 77735560 76838843
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.237065 | 0.3534545 | 8.077096 | 0.52 | 1.100534 | 0.5554857 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + acc + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_acc_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 604 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.3572400 0.3241591 0.3175724 0.2539564 0.2211844 0.1429275 [7] 0.1386985 -0.1192288 -0.1583929 -4.0563352 Largest eigenvalues: [1] 64057025 60144807 57579659 55680452 55075247 53420479 52147618 51727274 [9] 51700094 51150786 Smallest eigenvalues: [1] 0.20815480 0.19527708 0.13001476 0.07394004 0.05268478 -0.02520543 [7] -0.03022643 -0.04639147 -0.18712336 -2.86933727 Largest eigenvalues: [1] 63362686 61063658 57705778 55877424 55340792 53945203 52744004 52432708 [9] 51874744 51619834 Smallest eigenvalues: [1] 0.320485037 0.308484457 0.294083995 0.287061731 0.236586395 [6] 0.161861584 0.032725122 -0.005492232 -0.144953778 -0.522917077 Largest eigenvalues: [1] 64171547 61147712 58395964 55891118 55767221 54364253 53237999 52349784 [9] 52116894 51922555 Smallest eigenvalues: [1] 0.4918629799 0.4834773366 0.4230672504 0.3498649743 0.3391757226 [6] 0.2622011103 0.2493391868 0.0006027109 -0.0047136550 -0.0656738895 Largest eigenvalues: [1] 61992275 60517246 57617107 55854646 54975045 54089904 52470477 52433817 [9] 51229294 51014200 Smallest eigenvalues: [1] 0.3364004 0.3289831 0.2962855 0.2262138 0.2071379 0.1997672 [7] 0.1718978 0.1221774 -0.3798499 -2.5629421 Largest eigenvalues: [1] 65213933 59900563 57366967 56070586 54801621 53236418 52165572 52027160 [9] 51510823 51178965 Smallest eigenvalues: [1] 0.43960886 0.40739004 0.38036940 0.29119135 0.28331892 0.15010614 [7] 0.04677086 -0.03605983 -0.10474583 -0.32354130 Largest eigenvalues: [1] 64395757 60692182 57313959 56079725 55705692 53907634 52786711 52051200 [9] 51774711 51464929 Smallest eigenvalues: [1] 0.2763762 0.2154392 0.1824499 0.1802923 0.1437914 0.1125075 [7] -0.2037908 -0.2308594 -0.3786692 -0.4594503 Largest eigenvalues: [1] 65043228 61026199 57678547 56174052 55510518 53897637 52985881 52156865 [9] 52064095 51786866 Smallest eigenvalues: [1] 0.35130208 0.32195043 0.25929832 0.21560677 0.19993165 -0.06684521 [7] -0.12772567 -0.30386030 -0.42230894 -0.56429931 Largest eigenvalues: [1] 64887832 59884269 56538136 56494640 54526093 52725113 52491518 52190857 [9] 51718398 51256374 Smallest eigenvalues: [1] 0.50100352 0.43554188 0.41233819 0.30676249 0.28168009 0.23034198 [7] 0.20108541 0.07812386 -0.00289683 -0.14461111 Largest eigenvalues: [1] 63905801 59824571 57232425 55822166 54696749 53191030 52245752 51787068 [9] 51659209 51048402 Smallest eigenvalues: [1] 0.38226613 0.36936228 0.36840363 0.34104063 0.22871764 0.22722070 [7] 0.21700001 0.13023772 0.07185889 -0.01500420 Largest eigenvalues: [1] 64551889 60467163 58052828 55668533 55378222 54135552 52760185 52159002 [9] 51911737 51745547 Smallest eigenvalues: [1] 0.44454890 0.39600696 0.35937368 0.33392174 0.20398786 0.06862949 [7] -0.43067560 -0.45885425 -1.07110227 -3.59165125 Largest eigenvalues: [1] 64721302 60074629 57264269 55818235 55237105 53021585 52213272 51976403 [9] 51734457 51260959 Smallest eigenvalues: [1] 0.36073040 0.32762768 0.32553822 0.28244905 0.27152783 0.17385777 [7] 0.12877348 0.02402656 -0.26864776 -1.67871407 Largest eigenvalues: [1] 63336801 59899788 57139555 55231761 54844198 53644892 52169184 52061273 [9] 51363479 51023299 Smallest eigenvalues: [1] 0.38919150 0.38198269 0.35993389 0.27814312 0.27361771 0.21880853 [7] 0.21064366 -0.04733215 -0.22615366 -1.18213899 Largest eigenvalues: [1] 64876586 59738225 57167871 56545952 54793387 53322920 52552913 52191143 [9] 51496041 50778932 Smallest eigenvalues: [1] 0.56599589 0.51522001 0.49716308 0.42173562 0.37622006 0.37414837 [7] 0.26249298 0.21907298 0.15529848 -0.01614275 Largest eigenvalues: [1] 65044260 59528686 56804412 55982911 54935764 53289992 52171507 51972175 [9] 51898375 51231592 Smallest eigenvalues: [1] 0.48076328 0.38622990 0.37523225 0.32448140 0.23316474 0.21960765 [7] 0.14829284 0.09201754 -0.09826087 -0.11605853 Largest eigenvalues: [1] 66301320 59326859 57246433 56655941 54051276 53267548 52561339 51334121 [9] 51137182 50525665 Smallest eigenvalues: [1] 0.5181210 0.5010810 0.4883916 0.4406659 0.4190410 0.3673086 [7] 0.2696495 0.1548473 -0.1228540 -0.2300485 Largest eigenvalues: [1] 63366952 60111230 56810156 55261569 55002375 53483030 52025304 51386874 [9] 50856721 50536505 Smallest eigenvalues: [1] 0.3934942 0.2690784 0.2653280 0.2518613 0.2162878 0.1790993 [7] 0.1593644 0.1175771 -0.1392969 -0.5375719 Largest eigenvalues: [1] 66530749 60558415 57877572 57276985 55065660 53399490 53207130 52953137 [9] 51671805 51516286 Smallest eigenvalues: [1] 0.47095992 0.41151151 0.39009730 0.23555497 0.22889025 0.12739543 [7] 0.11521296 0.08318608 0.06435559 -0.78822906 Largest eigenvalues: [1] 65784661 60536220 56993951 56779371 55145628 53496493 52748314 52261602 [9] 52051702 51288186 Smallest eigenvalues: [1] 0.49795664 0.49293705 0.46341960 0.39675058 0.34727816 0.27428560 [7] 0.16133323 0.02520763 -0.08061078 -0.67548394 Largest eigenvalues: [1] 63446078 59919192 57098632 55394866 54909682 53829454 52461465 51827299 [9] 51013573 50912857 Smallest eigenvalues: [1] 0.4059169 0.3553364 0.3515291 0.3078905 0.2967307 0.2566029 [7] 0.2360790 0.1652289 0.1104114 -0.0558672 Largest eigenvalues: [1] 64299467 61503460 58102473 56629090 55669088 54037930 52798274 52541105 [9] 52485403 51789855 Smallest eigenvalues: [1] 0.4460437 0.4370955 0.3816666 0.3473450 0.3281377 0.3055509 [7] 0.2611311 0.2450317 0.1088500 -0.1154320 Largest eigenvalues: [1] 64841249 61117481 58031276 56429263 56429118 54727577 53077512 52603011 [9] 52328076 51720325 Smallest eigenvalues: [1] 0.29172716 0.26705452 0.16475462 0.11652670 0.09431992 0.01559144 [7] -0.10874491 -0.10925043 -0.44551949 -1.44650426 Largest eigenvalues: [1] 64767110 60244226 57025007 55944094 54913161 53357316 52009406 51944806 [9] 51579422 50906645 Smallest eigenvalues: [1] 0.36347944 0.29839340 0.29050353 0.27232831 0.27195074 0.24277733 [7] 0.19766683 0.09278354 -0.46095206 -0.47329183 Largest eigenvalues: [1] 63926626 59805241 57282049 55213482 54470430 53013311 51953515 51381162 [9] 51152429 51105799 Smallest eigenvalues: [1] 0.33389114 0.28761147 0.25725293 0.24741809 0.23223098 0.21213310 [7] 0.20080965 0.08105087 -0.15044906 -0.24208737 Largest eigenvalues: [1] 65795003 60475623 57891783 56764538 55158152 53459724 53025740 52786711 [9] 52031389 51942040 Smallest eigenvalues: [1] 0.4327472 0.3712711 0.3592195 0.3255310 0.2916081 0.2505628 [7] 0.1975630 0.1294015 0.1226310 -1.0956320 Largest eigenvalues: [1] 65018324 59900371 57227164 56061496 55095751 53287288 52129538 52095714 [9] 51571133 51184690 Smallest eigenvalues: [1] 0.49976091 0.44936337 0.35862225 0.35276438 0.34221020 0.29944621 [7] 0.27312165 0.15231482 -0.06882362 -0.99085301 Largest eigenvalues: [1] 63552092 59153520 57013572 55547625 54473665 52932118 51610368 51507431 [9] 51463963 50580109 Smallest eigenvalues: [1] 0.44000755 0.39221958 0.32075230 0.31369847 0.26194793 0.21126722 [7] -0.04150861 -0.04166315 -0.04180957 -0.26528260 Largest eigenvalues: [1] 61138081 59059968 56149375 54859398 54134902 52952757 51834903 50853739 [9] 50135535 49964435 Smallest eigenvalues: [1] -0.2384820 -0.3236995 -0.3343005 -0.3601049 -0.4290560 -0.5295021 [7] -0.5546944 -0.9277185 -1.1302971 -1.2198926 Largest eigenvalues: [1] 64898588 61095112 58239056 55669635 55579062 54249523 52480127 52006758 [9] 51696025 51445370 Smallest eigenvalues: [1] 0.284032075 0.269374108 0.243847802 0.228442778 0.185862668 [6] 0.037836381 0.008364788 -0.257175665 -0.420003497 -0.881523873 Largest eigenvalues: [1] 64854170 61072067 57743302 56639843 55610572 54015814 52784207 52606800 [9] 52385667 51809985 Smallest eigenvalues: [1] 0.39745675 0.30378715 0.28698407 0.26038800 0.21561967 0.12034930 [7] 0.09870136 -0.08735814 -1.11663102 -1.26942154 Largest eigenvalues: [1] 64523575 60174634 56672842 56286533 55328894 53334607 52575618 52264961 [9] 52213394 51231045 Smallest eigenvalues: [1] 0.465164853 0.381467739 0.338419493 0.285814524 0.255618713 [6] 0.189508223 0.141939371 -0.007267245 -0.668396315 -1.002118380 Largest eigenvalues: [1] 64041823 58837004 56494584 55832043 54013667 52296979 51760999 51300462 [9] 51038577 49991980 Smallest eigenvalues: [1] 0.42135977 0.33064526 0.24581927 0.22783270 0.22315299 0.19639218 [7] 0.17289158 0.12267540 0.04686315 -5.31312804 Largest eigenvalues: [1] 61838534 59832243 56893230 55076043 54672635 53480740 52126963 51470915 [9] 50730290 50528299 Smallest eigenvalues: [1] 0.28167814 0.22157573 0.21288895 0.19779428 0.07514761 0.05132728 [7] -0.11726279 -0.18719471 -1.32155859 -2.87728671 Largest eigenvalues: [1] 66521296 60602632 57417818 56450468 55360607 53713243 52566459 52437993 [9] 51819287 51677782 Smallest eigenvalues: [1] 0.43084282 0.36104450 0.34359855 0.34209815 0.26088381 0.24825747 [7] 0.22729943 0.19323460 0.06281628 -0.05721952 Largest eigenvalues: [1] 64606593 60791818 58246345 55827890 55634400 54284458 52799172 52472818 [9] 51810122 51555398 Smallest eigenvalues: [1] 0.31737948 0.29517252 0.28227197 0.22005093 0.21848316 0.17054747 [7] 0.09857276 -0.16891386 -0.20307817 -2.19901137 Largest eigenvalues: [1] 65092502 60587247 57765907 55910841 55845101 54172541 52449565 52256703 [9] 52217606 51368550 Smallest eigenvalues: [1] 0.38163167 0.37451189 0.29926363 0.28470765 0.20351932 0.09792982 [7] 0.04525726 -0.12321008 -0.19859943 -1.45050876 Largest eigenvalues: [1] 63906345 59932378 57057508 55237595 55061015 53491821 52205040 51514534 [9] 51373076 51216214 Smallest eigenvalues: [1] 0.46659129 0.38597616 0.35789100 0.32751038 0.32706560 0.31221075 [7] 0.25349908 0.01068126 -0.01013948 -0.07940873 Largest eigenvalues: [1] 65265428 60401834 57500936 56436683 54876402 53095347 52565577 52149870 [9] 51327532 50910693 Smallest eigenvalues: [1] 0.37669338 0.36404481 0.34189170 0.26190141 0.24874713 0.20737541 [7] 0.05400449 -0.02976017 -0.09473307 -2.55934522 Largest eigenvalues: [1] 63181444 59833074 56975787 55162188 55000313 53385834 51720296 51676789 [9] 51154527 50900452 Smallest eigenvalues: [1] 0.49248639 0.40960297 0.38621108 0.36023736 0.25673056 0.21464356 [7] 0.19234884 0.12075105 0.04248594 -0.74549449 Largest eigenvalues: [1] 65248302 59959049 57181583 57138421 54533561 53101756 52865862 52025574 [9] 51921307 51080228 Smallest eigenvalues: [1] 0.39334122 0.33047064 0.32629501 0.19379635 0.16812416 0.13090414 [7] -0.05477706 -0.18408445 -0.58098414 -0.73843717 Largest eigenvalues: [1] 65099505 61015316 58085042 56802595 55375841 53431849 53031496 52679607 [9] 51855798 51724354 Smallest eigenvalues: [1] 0.30548339 0.24554368 0.23642478 0.15987535 0.12703925 0.09378831 [7] -0.01922214 -0.04353630 -0.76229442 -0.80612734 Largest eigenvalues: [1] 64876948 60619630 58099614 56431443 55108354 53540208 52736423 52490566 [9] 52120586 51811918 Smallest eigenvalues: [1] 0.32426554 0.28197256 0.27470200 0.22563615 0.14239162 0.02433923 [7] -0.10797768 -0.37291393 -0.37486837 -1.13147897 Largest eigenvalues: [1] 64183660 59619217 56887479 54899471 54800085 53098550 51321536 51264428 [9] 51136247 50515792 Smallest eigenvalues: [1] 0.40126316 0.25364061 0.22030842 0.21609708 0.17124851 -0.02436149 [7] -0.03301147 -0.03839447 -0.14124017 -1.71023636 Largest eigenvalues: [1] 63345061 59846669 56972690 55212679 54762249 53165915 51686538 51499515 [9] 51314190 50892958 Smallest eigenvalues: [1] 0.5420560 0.5337247 0.4513997 0.4431111 0.4387204 0.3984351 [7] 0.3288936 0.3042720 0.2969365 -0.1362922 Largest eigenvalues: [1] 64190092 60453721 57603505 55851775 55388324 53681934 51747159 51708031 [9] 51587499 50661375 Smallest eigenvalues: [1] 0.55073374 0.54297222 0.51082963 0.41523274 0.37805263 0.34798850 [7] 0.21287291 0.10695564 0.02502659 -0.30731463 Largest eigenvalues: [1] 62155485 59563751 56678418 55281099 54357100 53446897 51731277 51612997 [9] 50474959 50330190 Smallest eigenvalues: [1] 0.45152808 0.34221015 0.30429844 0.20070174 0.14375819 0.13941621 [7] 0.08835044 0.07877502 -0.05718764 -1.53016412 Largest eigenvalues: [1] 63522551 59582375 56789777 55303776 55069116 53402280 52399364 51864767 [9] 51457574 51231107 Smallest eigenvalues: [1] 0.5290067 0.5073476 0.4420684 0.3898846 0.3662684 0.3397274 [7] 0.3302179 0.2940417 0.2693324 -0.3899703 Largest eigenvalues: [1] 63840064 59665589 57254705 55531452 54728658 52972436 51716648 51544130 [9] 51094943 50413086 Smallest eigenvalues: [1] 0.38186404 0.31882138 0.28269268 0.26221908 0.20873195 0.15620325 [7] -0.02502617 -0.30825898 -0.31270897 -1.12140298 Largest eigenvalues: [1] 64256357 60086955 57105046 56034737 55098977 53576186 52434184 51980495 [9] 51940992 51457099 Smallest eigenvalues: [1] 0.39110953 0.34511263 0.31179453 0.27568164 0.22779465 0.19631693 [7] 0.19355203 0.04445829 -0.11891403 -0.22965545 Largest eigenvalues: [1] 64839947 61068909 58364751 56124469 55809464 54409762 52478759 52320824 [9] 52033838 51550025 Smallest eigenvalues: [1] 0.35694152 0.34963105 0.34781769 0.31988503 0.31902393 0.28779090 [7] 0.22480478 0.01865781 -0.21348169 -0.30714021 Largest eigenvalues: [1] 65504655 60510141 57714234 56596733 55246141 53717935 52512222 52195935 [9] 52006730 51271604 Smallest eigenvalues: [1] 0.4909675452 0.4701221131 0.4694390051 0.3028352919 0.2452801542 [6] 0.2434072671 0.2156807159 0.1587221503 0.1034061497 -0.0001388593 Largest eigenvalues: [1] 62734711 59648912 56895573 55276388 54848491 53646421 52111196 52070200 [9] 51026420 50847040 Smallest eigenvalues: [1] 0.48689541 0.48576490 0.42829449 0.42401995 0.34528136 0.34205796 [7] 0.28160503 0.25025727 0.22272704 -0.02304821 Largest eigenvalues: [1] 65413861 60757798 57982157 56637338 56053608 54461964 52624305 52393563 [9] 52307239 51374075 Smallest eigenvalues: [1] 0.3527634 0.3377088 0.2587051 0.2288362 0.2127325 0.1806885 [7] 0.1418255 -0.5672442 -0.7168194 -0.8473275 Largest eigenvalues: [1] 66350945 60730408 57995685 57153080 55114805 53539171 53286408 52343010 [9] 51910982 51533345 Smallest eigenvalues: [1] 0.339633151 0.310616532 0.291608181 0.277225532 0.252504765 [6] 0.169082446 0.162774847 0.001912881 -0.319071006 -0.434709805 Largest eigenvalues: [1] 63904353 60530472 57176519 55799468 55759682 54076998 52933246 52229310 [9] 51972024 51712235 Smallest eigenvalues: [1] 0.46803290 0.40007338 0.39735059 0.38421421 0.28975389 0.25730761 [7] 0.23455695 0.20195783 0.06326498 -0.10195046 Largest eigenvalues: [1] 64926444 59584366 57024175 56457057 54213155 52691044 52451666 51421785 [9] 51182888 50350749 Smallest eigenvalues: [1] 0.489624709 0.476595477 0.442252616 0.426693886 0.366338445 [6] 0.304354167 0.286983162 0.071696970 -0.009922337 -0.447757310 Largest eigenvalues: [1] 65282066 60214595 57649067 56349320 55503948 53486895 52614501 52116710 [9] 51764200 51074615 Smallest eigenvalues: [1] 0.26667410 0.26436845 0.22151618 0.19676606 0.16215809 0.03159199 [7] -0.14277823 -0.42581091 -0.60823173 -5.49263649 Largest eigenvalues: [1] 66280509 60867634 57250468 57233839 55635451 53794764 53255816 52423911 [9] 52234572 51477171 Smallest eigenvalues: [1] 0.28709078 0.20331330 0.20177601 0.12799313 0.07467996 -0.13078776 [7] -0.28376289 -0.37779122 -1.02675664 -1.90156009 Largest eigenvalues: [1] 64433506 60553778 57915879 56646316 55549939 53877112 52605303 52435448 [9] 52267266 51276730 Smallest eigenvalues: [1] 0.16609193 0.09717454 -0.02646772 -0.07053619 -0.20321858 -0.27499109 [7] -0.60901198 -1.23618886 -1.32677766 -1.47023854 Largest eigenvalues: [1] 66253058 60130437 57946127 55909172 54888313 53086936 52370053 51736024 [9] 51309271 50971911 Smallest eigenvalues: [1] 0.46975502 0.43519165 0.37942305 0.36708858 0.27975748 0.23585324 [7] 0.19380726 0.15939322 0.05698807 -0.11427379 Largest eigenvalues: [1] 65529438 61280097 58090169 56867114 55920524 54308978 53501979 52863928 [9] 52407450 52105472 Smallest eigenvalues: [1] 0.30493520 0.30361421 0.25118172 0.23662969 0.18855208 0.13848131 [7] 0.12401362 0.02835327 -0.79716026 -2.16432190 Largest eigenvalues: [1] 63520605 59810322 56988333 55559966 54828332 53227450 51975931 51770147 [9] 51535491 50967707 Smallest eigenvalues: [1] 0.30810328 0.29251766 0.28242599 0.25433050 0.24175884 0.21017416 [7] 0.13656731 0.09620963 -0.05430687 -4.88009646 Largest eigenvalues: [1] 63371756 60622385 57209715 55854883 54924041 53937623 51970148 51808118 [9] 51042825 50743218 Smallest eigenvalues: [1] 0.32692241 0.29829005 0.27990019 0.20355077 0.17774474 0.12937465 [7] 0.12499896 0.09147319 -0.02837267 -1.63256340 Largest eigenvalues: [1] 65896751 60994812 58298313 56665523 55690281 54023518 53070445 52622140 [9] 52504727 52218025 Smallest eigenvalues: [1] 0.29123360 0.25552098 0.24744107 0.18772308 0.14368051 0.13594990 [7] 0.08102463 -0.01648910 -1.26516585 -1.66643920 Largest eigenvalues: [1] 66363864 60452546 57785218 56830800 55104627 53950293 52662443 52521438 [9] 52403732 51841080 Smallest eigenvalues: [1] 0.3176570 0.2599552 0.2206302 0.1857760 0.1767845 0.1608564 [7] -0.1829376 -0.2739934 -0.3076590 -0.9759104 Largest eigenvalues: [1] 66225723 59997228 57408594 56895546 54695757 53083737 52883697 52487458 [9] 51680595 51629488 Smallest eigenvalues: [1] 0.28363349 0.21716033 0.17639894 0.14059422 0.08211850 -0.02726647 [7] -0.07456445 -0.45684450 -0.46106893 -0.66625631 Largest eigenvalues: [1] 63988847 60206749 57672892 55438938 54789217 53584650 51631636 51550552 [9] 51538830 50952331 Smallest eigenvalues: [1] 0.42425696 0.38013073 0.37781261 0.32415938 0.23073376 0.22262037 [7] 0.15176636 0.08159191 0.08022446 -0.18023148 Largest eigenvalues: [1] 64625430 60376646 57509574 56341473 55326289 53849102 52404494 52394558 [9] 52196673 51321110 Smallest eigenvalues: [1] 0.5191467 0.4686153 0.4516688 0.3730825 0.3441009 0.3229599 [7] 0.3111210 0.1283469 0.1048464 -0.1217506 Largest eigenvalues: [1] 64787356 59680482 57150602 55766186 54922128 53520921 51937823 51870435 [9] 51333616 50441071 Smallest eigenvalues: [1] 0.37900607 0.37579912 0.27173130 0.21796658 0.19640719 -0.01881112 [7] -0.02828844 -0.05670632 -0.06603805 -1.09931498 Largest eigenvalues: [1] 64317344 60501775 57312053 55711535 55517062 53842750 52919276 52012859 [9] 51925415 51669765 Smallest eigenvalues: [1] 0.50712127 0.48934228 0.45347655 0.41772840 0.31821041 0.31608375 [7] 0.25888299 0.21728037 0.21681046 -0.05002221 Largest eigenvalues: [1] 64251988 59601604 57278581 55460939 54652246 53099431 51707945 51415652 [9] 51329183 50664169 Smallest eigenvalues: [1] 0.3815020 0.3807990 0.3111092 0.2517962 0.2453625 0.2000132 [7] 0.1690091 -0.3948289 -0.6721841 -1.5067667 Largest eigenvalues: [1] 62652338 59239403 56794264 55101152 54862422 53183050 51910360 51763619 [9] 50959454 50629579 Smallest eigenvalues: [1] 0.60482897 0.59706653 0.55296030 0.44912071 0.40053895 0.35550987 [7] 0.28081158 0.22796525 0.13531928 -0.01172452 Largest eigenvalues: [1] 62827970 60198068 57100827 55800015 54823978 54143832 52473105 52220781 [9] 51084783 50859672 Smallest eigenvalues: [1] 0.28537640 0.27041960 0.25421609 0.25285332 0.21962138 0.14971529 [7] 0.04060564 -0.64100655 -0.89371618 -1.60482220 Largest eigenvalues: [1] 64845499 60310134 57853417 56182016 55183337 53355559 52475901 52174561 [9] 52123980 51625946 Smallest eigenvalues: [1] 0.4340012 0.3854872 0.3431338 0.3090682 0.2976295 0.1498647 [7] 0.1238922 0.1113390 -0.1564700 -1.0322496 Largest eigenvalues: [1] 65537564 60563339 57489206 56242934 55155758 53406753 52397355 52341330 [9] 51946283 51357532 Smallest eigenvalues: [1] 0.05972360 0.05200599 -0.04472271 -0.16168531 -0.16186883 -0.24938951 [7] -0.37060917 -0.50403192 -0.69908135 -1.45177859 Largest eigenvalues: [1] 63057342 59950075 57158487 55183252 54773629 53154759 52203185 51393303 [9] 51172907 50947017 Smallest eigenvalues: [1] 0.45780726 0.41737971 0.39189471 0.34565040 0.33201705 0.32925516 [7] 0.27582942 0.26857818 0.22532502 -0.02481878 Largest eigenvalues: [1] 61730421 59149979 56795635 54872641 54315883 53110801 51467664 51098763 [9] 50403432 50107821 Smallest eigenvalues: [1] 0.3833729 0.2971821 0.2509440 0.2385454 0.2273118 0.1989267 [7] 0.1780260 0.1460718 -0.1974149 -0.2472994 Largest eigenvalues: [1] 64559982 60233243 57646543 56378330 54917363 53389939 52527544 51636354 [9] 51499126 50476047 Smallest eigenvalues: [1] 0.3646963 0.3595078 0.3072282 0.2735260 0.2448138 0.2367198 [7] 0.1456193 0.1061710 -0.4978399 -0.7282223 Largest eigenvalues: [1] 65333194 60302100 58379970 55608168 55542254 54454931 52877525 52716338 [9] 51870592 51565797 Smallest eigenvalues: [1] 0.39905585 0.34746703 0.33720530 0.29311411 0.22012125 0.16280442 [7] 0.14794924 0.09903528 -0.24700643 -0.40767001 Largest eigenvalues: [1] 63695027 59342693 57346795 55885049 54196878 52875004 51793667 51721753 [9] 51423784 50701111 Smallest eigenvalues: [1] 0.434026699 0.420192491 0.371494212 0.358349883 0.347354950 [6] 0.346054388 0.288792083 0.260117823 -0.003616318 -5.376752724 Largest eigenvalues: [1] 64232300 60079341 57133128 55612150 55126506 53351497 52136211 51729628 [9] 51640725 50865858 Smallest eigenvalues: [1] 0.4585522 0.3856040 0.3708957 0.3625370 0.3149726 0.2731110 [7] 0.2052727 0.1783903 0.1507486 -0.1390350 Largest eigenvalues: [1] 64071662 59743549 57114570 55988912 54757544 53261189 52106801 51859210 [9] 51843735 50950023 Smallest eigenvalues: [1] 0.52550429 0.45846857 0.42359247 0.36130431 0.35432233 0.27856730 [7] 0.25876853 0.17755187 0.04585812 -0.02392554 Largest eigenvalues: [1] 61461227 59847398 56981738 56081301 54131884 53957016 52768555 51638564 [9] 50771560 50680765 Smallest eigenvalues: [1] 0.50990672 0.46278808 0.41709809 0.35218117 0.32965894 0.31780317 [7] 0.30296146 0.28301839 0.18501853 -0.00942292 Largest eigenvalues: [1] 63736727 60732480 57344755 55938129 55842612 54144641 52561228 52046197 [9] 51892779 51503323 Smallest eigenvalues: [1] 0.45191564 0.40166766 0.37066922 0.36635833 0.34610321 0.30301743 [7] 0.26437871 0.22812645 0.08560410 -0.04506491 Largest eigenvalues: [1] 61841680 60861022 57523438 55652906 55024490 53882842 52145718 52133906 [9] 51249343 50993076 Smallest eigenvalues: [1] 0.35778838 0.32313732 0.28070710 0.23478564 0.18571347 0.17820559 [7] 0.08602546 -0.09724300 -0.44512864 -0.61094981 Largest eigenvalues: [1] 64625903 61385440 58300290 56597975 55845160 54012351 53779061 52835131 [9] 52238935 52088055 Smallest eigenvalues: [1] 0.4258179 0.4123385 0.4066811 0.3173327 0.2935820 0.2873354 [7] 0.2741114 0.2036702 -0.1543384 -3.3223935 Largest eigenvalues: [1] 64939930 60522264 57799431 56325991 55224145 53740974 52412394 52134671 [9] 52080729 51217120 Smallest eigenvalues: [1] 0.270139743 0.258125051 0.203855010 0.077238656 -0.001353699 [6] -0.053471372 -0.118071092 -0.423497535 -0.585571198 -1.222890407 Largest eigenvalues: [1] 64910131 59792874 56955673 55471984 54675711 53020805 51973689 51656018 [9] 51318182 51136891 Smallest eigenvalues: [1] 0.39030630 0.36431513 0.36048649 0.33081098 0.32275195 0.30510288 [7] 0.30134017 0.19091043 0.13860613 -0.08821795 Largest eigenvalues: [1] 65305567 60809308 57448752 57138166 55260736 53667722 52883231 52679282 [9] 52342210 51421750 Smallest eigenvalues: [1] 0.4336938 0.3811972 0.3025028 0.2152404 0.2143854 0.2104441 [7] 0.1731974 -0.0584411 -0.5365725 -0.6975240 Largest eigenvalues: [1] 65336805 61045320 57411766 56236779 56023012 54133555 53072179 52554321 [9] 52224186 51677922 Smallest eigenvalues: [1] 0.5561153 0.4781759 0.4731293 0.4199611 0.3779361 0.3670875 [7] 0.3379363 0.3342902 0.2321161 -0.1889379 Largest eigenvalues: [1] 64128295 60229662 57354590 56035765 55393982 53533497 52070744 51986858 [9] 51783110 50818410 Smallest eigenvalues: [1] 0.31847471 0.27490608 0.23103712 0.22072614 0.18654000 0.15055378 [7] 0.13807697 0.05449083 0.04996715 -0.14503993 Largest eigenvalues: [1] 62145682 58953799 56457959 54823954 54766718 53069711 52032662 51514143 [9] 50725101 50484234 Smallest eigenvalues: [1] 0.54542371 0.54113868 0.48147653 0.43825609 0.40116155 0.39243073 [7] 0.36925263 0.22188467 0.13469984 -0.06763395 Largest eigenvalues: [1] 63989765 60064953 56688317 55432189 55317750 53611973 52250079 51468344 [9] 51428732 50599410 Smallest eigenvalues: [1] 0.357807286 0.349088475 0.306174172 0.277724705 0.261292687 [6] 0.173233031 0.162480802 0.025775202 0.003066232 -0.123847602 Largest eigenvalues: [1] 64934958 59195924 56706974 56383183 54608310 53050491 52425423 51637283 [9] 50773408 50214397 Smallest eigenvalues: [1] 0.38691058 0.37914400 0.33736700 0.31413882 0.29839175 0.22319961 [7] 0.03296122 -0.21851472 -0.23160158 -2.89636509 Largest eigenvalues: [1] 65486301 60407178 57524222 56061381 55528873 53988543 52680697 52180972 [9] 52000827 51801406 Smallest eigenvalues: [1] 0.191085559 0.065989762 0.008864738 -0.183355908 -0.232380493 [6] -0.334767617 -0.398897637 -0.657233726 -0.801103140 -4.031988330 Largest eigenvalues: [1] 62467877 59642617 56815956 55395970 54469087 53479396 52096444 51827825 [9] 51053428 50696642 Smallest eigenvalues: [1] 0.4398407 0.4306110 0.3948517 0.3484145 0.2794921 0.2648174 [7] 0.1589810 0.1463925 0.1036701 -1.7050408 Largest eigenvalues: [1] 63980535 60398989 57544343 55407189 55338956 53847128 52225912 52135617 [9] 51542032 51339157 Smallest eigenvalues: [1] 0.4169138 0.3747850 0.3499980 0.3279687 0.2570091 0.2533887 [7] 0.1829724 0.1039144 -0.3099311 -0.4348086 Largest eigenvalues: [1] 63146644 60498559 56882123 55837653 54962582 53275487 52182459 51720406 [9] 51549935 50745190 Smallest eigenvalues: [1] 0.3863383 0.3725693 0.3402612 0.3273823 0.2639087 0.2452811 [7] 0.2289172 0.1238991 -0.1618517 -1.8142402 Largest eigenvalues: [1] 61949083 59617663 56877805 54958154 54410347 53058589 51373009 51229911 [9] 50626749 50419702 Smallest eigenvalues: [1] 0.46990848 0.40559481 0.35611387 0.34376946 0.32571544 0.30474885 [7] 0.28793421 0.19319505 0.14470277 -0.02924618 Largest eigenvalues: [1] 64953733 59868091 57465829 56072246 54744131 53119010 52212536 51873610 [9] 51791675 51033031 Smallest eigenvalues: [1] 0.54957838 0.54463200 0.54083681 0.49891923 0.44485620 0.32740063 [7] 0.19661494 0.12678108 0.06429228 -0.11750755 Largest eigenvalues: [1] 63577287 60261787 57455345 55593772 55191894 53664021 52175088 51940753 [9] 51687081 51055238 Smallest eigenvalues: [1] 0.4709673 0.4291171 0.4028882 0.3893349 0.3609741 0.1549805 [7] 0.1294421 0.1147023 -0.2065128 -1.2897480 Largest eigenvalues: [1] 64544441 59253113 56768190 54881410 54868360 53166589 52188223 51313191 [9] 51236105 50625199 Smallest eigenvalues: [1] 0.45164240 0.44019667 0.40313259 0.37379501 0.29893470 0.17303321 [7] 0.15966312 0.10582758 0.04361385 -1.57612389 Largest eigenvalues: [1] 64465797 60173534 56910177 55991850 55341440 53346972 52389483 52067523 [9] 51626043 51233134 Smallest eigenvalues: [1] 0.27477744 0.19467440 0.15954488 0.13991501 0.04603371 0.03438404 [7] -0.14440284 -0.35007133 -0.71840349 -1.00148048 Largest eigenvalues: [1] 64265707 60898864 57567800 55670013 55293760 53592729 52122966 51866676 [9] 51558509 51228311 Smallest eigenvalues: [1] 0.4639443 0.3820820 0.3295740 0.3076395 0.2967086 0.2568272 [7] 0.2402834 0.2292922 -0.1798325 -1.5247088 Largest eigenvalues: [1] 63195149 60080687 57331128 55870705 54715203 53362558 52176900 51718922 [9] 51652835 51199680 Smallest eigenvalues: [1] 0.39226084 0.37562998 0.29721386 0.25695495 0.22287605 0.21889827 [7] 0.03522171 -0.01706078 -0.08423336 -4.77415802 Largest eigenvalues: [1] 63384454 59723997 56753544 55135280 55009229 52935019 51489509 51476458 [9] 51242597 50468580 Smallest eigenvalues: [1] 0.48214799 0.39204477 0.37424865 0.30111249 0.27718006 0.19968578 [7] 0.19933059 0.17981972 0.04870542 -0.95063877 Largest eigenvalues: [1] 64958122 59814991 57656939 55931689 54641361 53469264 52223894 51709642 [9] 51491801 50804445 Smallest eigenvalues: [1] 0.34432973 0.33329624 0.26655716 0.25276806 0.21523261 0.21465369 [7] 0.16558935 0.09561748 -0.20705440 -0.78292764 Largest eigenvalues: [1] 62475151 60265280 57299132 55650530 55076418 53513444 52320094 52193170 [9] 51463215 50825775 Smallest eigenvalues: [1] 0.22849935 0.18694592 0.18098389 0.16741839 0.07950545 0.06576836 [7] -0.09110808 -0.30732187 -1.42761057 -1.49394263 Largest eigenvalues: [1] 63628570 59499789 56996636 54843240 54713184 53246776 51625543 51142830 [9] 51003266 50462528 Smallest eigenvalues: [1] 0.35787283 0.35011015 0.24563930 0.20501641 0.17293359 0.10539791 [7] 0.02451984 -0.04600245 -0.27117584 -3.61089959 Largest eigenvalues: [1] 64993769 59728540 56948551 56312540 54900219 53180784 52474433 52270809 [9] 51783391 51276052 Smallest eigenvalues: [1] 0.31604271 0.19673866 0.15549241 0.13863547 -0.02487789 -0.06897950 [7] -0.08343397 -0.21110623 -1.12848267 -2.62019299 Largest eigenvalues: [1] 65900523 59804408 57078015 56628833 54590583 53078528 52673395 52198791 [9] 51430489 51405360 Smallest eigenvalues: [1] 0.45523176 0.35999222 0.22123303 0.19836564 0.16940852 0.15057724 [7] 0.12738629 -0.06692745 -0.36537776 -1.64320673 Largest eigenvalues: [1] 63838185 59446151 56371291 55103399 54663391 52965884 51742312 51303359 [9] 51148867 50390962 Smallest eigenvalues: [1] 0.39787487 0.35098284 0.25080461 0.21356840 0.06106247 0.02017161 [7] 0.00824589 -0.05994448 -0.06769519 -0.61758956 Largest eigenvalues: [1] 63377372 59462491 56783258 54808869 54550405 53042371 51706114 51281312 [9] 51090453 50666183 Smallest eigenvalues: [1] 0.48339463 0.40487813 0.39380319 0.37767780 0.31110870 0.29576419 [7] 0.28300147 -0.04288057 -0.04937407 -2.30489085 Largest eigenvalues: [1] 64330203 60638336 57010518 55710863 55589969 53647643 52214285 52008904 [9] 51837158 51149013 Smallest eigenvalues: [1] 0.255264366 0.254990769 0.217688954 0.035840286 0.004374647 [6] -0.135924345 -0.439217037 -0.712485014 -1.004096669 -1.462425588 Largest eigenvalues: [1] 65916877 59557708 56872477 56268542 54426004 53022054 52329167 51769053 [9] 51385268 50961594 Smallest eigenvalues: [1] 0.31873412 0.31250610 0.21958598 0.19047078 0.12456352 0.04217012 [7] -0.31752076 -0.84956313 -1.54931113 -1.85553762 Largest eigenvalues: [1] 66480855 60451398 58477588 56962582 55166767 53218412 52907259 52235169 [9] 51819266 51494708 Smallest eigenvalues: [1] 0.398368541 0.375293894 0.353760776 0.348714132 0.324237684 [6] 0.297573747 0.259491607 0.190384594 0.188742215 -0.007200348 Largest eigenvalues: [1] 64560412 60759659 58180807 55842189 55725554 54407633 52470706 52086613 [9] 51948297 51214153 Smallest eigenvalues: [1] 0.09924339 0.09212016 -0.07674742 -0.11192897 -0.11770956 -0.30974467 [7] -0.32442439 -0.41295500 -0.75624235 -1.25053246 Largest eigenvalues: [1] 66174916 60425722 58000364 57270357 54879815 53398413 53127546 52816238 [9] 51907206 51546062 Smallest eigenvalues: [1] 0.39169404 0.35807565 0.34137348 0.30946762 0.30397442 0.20935081 [7] 0.10948453 -0.08906589 -0.16411154 -1.18168583 Largest eigenvalues: [1] 63649704 60295657 57417707 56285869 55031440 53359681 52534598 52075870 [9] 51845050 51345187 Smallest eigenvalues: [1] 0.49899881 0.44947993 0.44740584 0.41504017 0.32800306 0.28183749 [7] 0.23949415 0.20376783 0.06009082 -0.05709857 Largest eigenvalues: [1] 66277567 60079407 57790439 57107823 54888753 53599572 53206689 51950193 [9] 51774331 51002716 Smallest eigenvalues: [1] 0.38366071 0.34406182 0.32912277 0.28789686 0.27037455 0.21597467 [7] 0.19302749 0.06957620 -0.01169218 -0.39114228 Largest eigenvalues: [1] 64975846 60161970 57064134 56596868 54936164 53341354 52572077 52522065 [9] 52017910 51569705 Smallest eigenvalues: [1] 0.20658819 0.20612932 0.16018438 0.13353185 -0.08180843 -0.25074857 [7] -0.49105292 -1.44979331 -1.64269705 -1.80304536 Largest eigenvalues: [1] 65304738 60312398 57707210 56519668 54775305 53442200 52649438 52170833 [9] 51628495 51359821 Smallest eigenvalues: [1] 0.5460028 0.5302948 0.5084107 0.4437580 0.3605250 0.3539121 [7] 0.1820593 0.1637137 0.1177607 -0.2146693 Largest eigenvalues: [1] 64230436 59313733 56643170 55582984 54401178 52349863 51640310 51166093 [9] 51136973 50298500 Smallest eigenvalues: [1] 0.54698461 0.50663764 0.44033516 0.41707953 0.35626267 0.29646196 [7] 0.26599981 0.04527109 -0.35341494 -4.01554427 Largest eigenvalues: [1] 65509740 59852530 56857360 56455643 54578768 52577185 52279191 51489216 [9] 51446201 50655796 Smallest eigenvalues: [1] 0.21512081 0.14906591 0.11011256 -0.02687004 -0.04432804 -0.11844368 [7] -0.12821064 -0.75861408 -1.07331104 -1.88364080 Largest eigenvalues: [1] 66346754 60430127 57394352 57201277 55015751 53289194 53142123 52837674 [9] 51867902 51817783 Smallest eigenvalues: [1] 0.3710866 0.3508347 0.3330107 0.2301228 0.1937342 0.1514765 [7] 0.1155636 -0.1839370 -0.3467024 -0.9801734 Largest eigenvalues: [1] 64161091 59907824 56932779 55163755 54732640 53146760 51799713 51708517 [9] 51315252 51075084 Smallest eigenvalues: [1] 0.40675491 0.39034868 0.37854384 0.31899379 0.24789933 0.21148566 [7] 0.18662655 0.06834084 0.04751032 -1.39155705 Largest eigenvalues: [1] 64636119 60346324 56880739 56056506 55420205 53660458 51922999 51808036 [9] 51730717 50887629 Smallest eigenvalues: [1] 0.37560935 0.32417452 0.28600191 0.17181566 0.16361341 0.10896189 [7] 0.07418611 0.04317457 0.01693225 -1.98185328 Largest eigenvalues: [1] 64017903 60209294 57307816 55527122 55100499 53941130 52052588 51609549 [9] 51137565 50816590 Smallest eigenvalues: [1] 0.23822468 0.15785225 0.07970109 0.03502709 -0.02867249 -0.03180909 [7] -0.04859561 -0.14190216 -0.35951790 -0.80680108 Largest eigenvalues: [1] 66185362 60797860 58203730 56379951 55293550 53795333 52608526 52301710 [9] 51941995 51468308 Smallest eigenvalues: [1] 0.45419461 0.44368857 0.43370536 0.34804360 0.27836663 0.25406331 [7] 0.05162261 0.03380550 -0.05274366 -2.24685353 Largest eigenvalues: [1] 65335127 60115805 57124621 56485791 55228878 53740399 52397571 52154837 [9] 51986445 51282511 Smallest eigenvalues: [1] 0.48826024 0.44528091 0.39528801 0.37821865 0.37242237 0.31592848 [7] 0.29375195 0.18116860 0.12910893 -0.07278919 Largest eigenvalues: [1] 64465138 59851261 56568612 55876383 54725508 53134958 51928974 51899398 [9] 51459432 50812873 Smallest eigenvalues: [1] 0.34388338 0.31470295 0.28232951 0.22163303 0.21047650 -0.05258964 [7] -0.09257466 -0.17995696 -0.55886801 -2.94081634 Largest eigenvalues: [1] 65528265 60800537 57441141 55909013 55398441 53481114 52024662 51925550 [9] 51660791 51175536 Smallest eigenvalues: [1] 0.42191337 0.40200855 0.38913334 0.34370348 0.31553045 0.31497820 [7] 0.27415048 0.25952143 0.22060993 -0.07022526 Largest eigenvalues: [1] 64195125 60152331 57304196 55463690 55434272 53799107 51926986 51583696 [9] 51343087 50445553 Smallest eigenvalues: [1] 0.4103166 0.3596281 0.3257396 0.2889494 0.2519206 0.1794170 [7] 0.1181834 -0.0274441 -0.1130602 -0.1458673 Largest eigenvalues: [1] 65764229 60379872 57456948 56463180 55395999 53968774 52502043 52023538 [9] 51853948 50636427 Smallest eigenvalues: [1] 0.30003658 0.27514071 0.17844680 0.15536466 0.12801314 0.11383686 [7] 0.03036235 -0.76134313 -1.02306789 -1.02501568 Largest eigenvalues: [1] 65345324 59863669 57682632 55964107 55052907 53777348 52565652 52048010 [9] 52036139 51682016 Smallest eigenvalues: [1] 0.47415951 0.37584902 0.36955926 0.36509014 0.34253408 0.28984457 [7] 0.26700710 0.23295508 0.17400323 -0.03047848 Largest eigenvalues: [1] 65451957 60215216 57924912 56724194 54828496 53211681 52742956 52001688 [9] 51813755 51223775 Smallest eigenvalues: [1] 0.142281911 0.101247008 0.058590347 -0.001330423 -0.018051874 [6] -0.165937088 -0.235156334 -0.324502851 -0.873190654 -1.518822952 Largest eigenvalues: [1] 63612917 60497610 57801040 55150393 54997608 53777524 51966738 51895853 [9] 51181740 50962162 Smallest eigenvalues: [1] 0.44430905 0.42370743 0.39945639 0.38466041 0.31193506 0.28184779 [7] 0.26945890 0.19909868 0.08485923 -0.02049831 Largest eigenvalues: [1] 65151204 60334609 58049947 55760301 55419529 53694643 52455348 52100206 [9] 51983032 51506661 Smallest eigenvalues: [1] 0.35826086 0.24687905 0.24497400 0.18758641 0.13949461 0.04921253 [7] 0.02583006 -0.04954255 -0.18359965 -0.53091826 Largest eigenvalues: [1] 66211298 60601066 57991016 56631218 55032931 53636523 52696588 52642256 [9] 51961725 51793681 Smallest eigenvalues: [1] 0.36911374 0.36687346 0.35853611 0.27108959 0.23069233 0.16791281 [7] 0.16721935 0.10432921 0.02927506 -0.42260927 Largest eigenvalues: [1] 66573956 61037979 57893578 57292566 56070603 54380361 53325296 53235505 [9] 52422433 52016380 Smallest eigenvalues: [1] 0.4190735 0.4070922 0.3405512 0.3072790 0.2964792 0.2503843 [7] 0.1807682 0.1407221 0.1123483 -0.6553671 Largest eigenvalues: [1] 65495821 59565246 57296642 56802713 54631670 53355384 52744751 51886134 [9] 51510542 51004241 Smallest eigenvalues: [1] 0.56463874 0.48159187 0.47784485 0.41365549 0.37551443 0.26991481 [7] 0.25479935 0.22357007 -0.07050388 -3.82438333 Largest eigenvalues: [1] 64843447 60121967 57418202 56099220 55146568 53460555 52210715 51970094 [9] 51943783 50976876 Smallest eigenvalues: [1] 0.45303443 0.44804797 0.41963693 0.39024844 0.34455935 0.25551341 [7] 0.24148828 0.09942670 0.06185218 -3.53302476 Largest eigenvalues: [1] 63805044 60644696 57912325 56030931 55706527 54414673 52713698 52670737 [9] 51886899 51591819 Smallest eigenvalues: [1] 0.4578711 0.3773066 0.3653459 0.3542151 0.3523558 0.3166131 [7] 0.2718408 0.2593948 0.1147047 -0.4169546 Largest eigenvalues: [1] 64253743 60372200 57746910 55665604 55563209 54205803 52588849 52325706 [9] 51650457 51142665 Smallest eigenvalues: [1] 0.44713283 0.42137137 0.38632405 0.29865266 0.20458295 0.18679541 [7] 0.09734140 0.05745541 0.01992097 -1.39667907 Largest eigenvalues: [1] 63035420 60100239 56982329 55403538 54676248 53660700 51811384 51729271 [9] 50947612 50846655 Smallest eigenvalues: [1] 0.51203841 0.46721205 0.43036363 0.38347410 0.36912243 0.35571560 [7] 0.34827207 0.14763799 0.10701455 -0.06605479 Largest eigenvalues: [1] 65203605 61313877 57696881 56611895 56318921 54595251 53459840 52595437 [9] 52313518 51842000 Smallest eigenvalues: [1] 0.44892974 0.42565504 0.38195828 0.37610479 0.33296835 0.28640749 [7] 0.26135775 -0.03768478 -0.18366181 -0.77853612 Largest eigenvalues: [1] 64156328 60460528 57654175 56136977 55415842 53872704 52373780 52179905 [9] 51819921 51193054 Smallest eigenvalues: [1] 0.31731585 0.21097395 0.20436093 0.18989051 0.12797501 [6] 0.08474374 0.02840311 -0.22049051 -0.29987531 -22.45608441 Largest eigenvalues: [1] 65886530 59829752 57773321 56119051 54976959 53811668 52505007 52310217 [9] 52004167 51444084 Smallest eigenvalues: [1] 0.4421756 0.4001940 0.3461679 0.2436915 0.2121544 0.1651616 [7] 0.1135466 -0.2049093 -0.2953542 -0.7346995 Largest eigenvalues: [1] 65775083 60449279 57675268 56924751 54877346 52924646 52865527 52450857 [9] 51750396 51548305 Smallest eigenvalues: [1] 0.5660133 0.5591972 0.4488088 0.4276763 0.3074990 0.2735265 [7] 0.2437631 0.2436161 -0.2092905 -0.2403396 Largest eigenvalues: [1] 65518084 60770237 57694984 56663045 55505105 53769933 52798593 52618856 [9] 51982966 51418190 Smallest eigenvalues: [1] 0.39201828 0.36607785 0.35204663 0.32680014 0.28956974 0.22437456 [7] 0.14268699 0.12509449 0.03413339 -2.99073803 Largest eigenvalues: [1] 63731433 59913220 57537649 55585139 54967054 53503923 51893813 51760078 [9] 51578795 50913673 Smallest eigenvalues: [1] 0.34244869 0.24713111 0.22917031 0.21855827 0.12267815 0.02799559 [7] -0.09435156 -0.25574024 -0.63660542 -1.31597273 Largest eigenvalues: [1] 65188942 60609757 57885515 56226885 55318100 53900123 52354358 52096839 [9] 51809490 51127977 Smallest eigenvalues: [1] 0.41227613 0.40870052 0.33616820 0.33362906 0.28079421 0.23104931 [7] 0.19895556 0.12086652 0.05272953 -0.39137290 Largest eigenvalues: [1] 65176525 60286508 57729669 56397156 55140153 53515113 53259637 52595000 [9] 51885942 51641438 Smallest eigenvalues: [1] 0.5008149 0.4216607 0.3996957 0.3841024 0.3261405 0.3150002 [7] 0.2412383 0.2055896 -0.1503619 -0.1628951 Largest eigenvalues: [1] 64503744 60436940 57293888 55935278 55144083 53420476 51923137 51838316 [9] 51810506 50910026 Smallest eigenvalues: [1] 0.6144951 0.5285018 0.5217817 0.5196151 0.4470148 0.3437827 [7] 0.2999062 0.2523786 0.2484838 -0.6737067 Largest eigenvalues: [1] 64546214 59863211 57068038 55710816 55048166 53609544 52170113 51846223 [9] 51643171 50809190 Smallest eigenvalues: [1] 0.37222354 0.37165058 0.31668573 0.28685235 0.27794986 0.18920346 [7] 0.18072816 0.17747899 0.13493871 -0.06034644 Largest eigenvalues: [1] 65832347 60698452 58366800 56387753 55512010 53945062 52598967 52453114 [9] 52357428 51818851 Smallest eigenvalues: [1] 0.35770525 0.33293579 0.32768492 0.30300358 0.25719724 0.20680826 [7] 0.19959926 0.09582846 -0.49196518 -3.15240362 Largest eigenvalues: [1] 65449561 59860469 57142189 56774543 54882509 52878486 52661818 52447356 [9] 51871090 51498949 Smallest eigenvalues: [1] 0.4517968 0.4144365 0.3300266 0.3087105 0.2581300 0.2437867 [7] 0.2334273 0.1675006 0.1075077 -0.5933252 Largest eigenvalues: [1] 61990273 59495261 56169635 54830368 54810776 53084656 51980907 51963983 [9] 50881904 50687090 Smallest eigenvalues: [1] 0.3506319230 0.2758619363 0.2657261017 0.2395028654 0.1649213441 [6] 0.0811668969 0.0003459881 -0.1449473441 -0.5231058413 -0.8660665085 Largest eigenvalues: [1] 65291053 61470136 58265204 57253097 55376675 53682057 53391601 52686558 [9] 52297482 51450792 Smallest eigenvalues: [1] 0.4793136 0.4583449 0.4146647 0.3706613 0.3250721 0.2587679 [7] 0.2264628 0.1974565 0.1659534 -0.5557488 Largest eigenvalues: [1] 62927075 59428130 56917992 54832712 54746405 53274805 51958205 51216053 [9] 50862840 50480673 Smallest eigenvalues: [1] 0.2412614 0.2390749 0.1992416 0.1908809 0.1331087 0.0116919 [7] -0.1018362 -0.2505629 -0.3093319 -1.0932292 Largest eigenvalues: [1] 64095374 59974165 57551797 55743796 54854443 53577597 51806523 51776650 [9] 51717979 50834386 Smallest eigenvalues: [1] 0.41544694 0.37910818 0.23492621 0.07291494 0.07267453 0.04956870 [7] -0.05042230 -0.06958034 -0.30108024 -2.05870162 Largest eigenvalues: [1] 63849817 60299918 57457323 55643758 55519229 53803956 52656806 51852855 [9] 51754879 51311383 Smallest eigenvalues: [1] 0.2246526516 0.1942011844 0.1937623025 0.1659102309 0.1623246554 [6] 0.1610865035 0.0879658289 -0.0009876474 -0.2353104174 -0.3403656520 Largest eigenvalues: [1] 63603903 59327103 56393229 55541008 54790499 53096645 51785774 51502903 [9] 50837448 50204772 Smallest eigenvalues: [1] 0.50770215 0.39444190 0.37925689 0.37911256 0.33363794 0.29753137 [7] 0.20674451 0.17236082 -0.08702109 -0.34161654 Largest eigenvalues: [1] 64556946 60777383 57801352 55956468 55380047 53784533 52804492 52188723 [9] 52119033 51895624 Smallest eigenvalues: [1] 0.3858945 0.3357381 0.3322148 0.2991350 0.2648856 0.2166075 [7] 0.2097733 0.1959674 -0.1248980 -1.5621686 Largest eigenvalues: [1] 64988000 60744097 58054952 55793758 55714057 54257483 52254240 52026348 [9] 51952737 51354732 Smallest eigenvalues: [1] 0.22561415 0.16207596 0.15719959 0.07536898 0.03632150 -0.06279389 [7] -0.35865122 -0.37470584 -1.38351044 -1.73710540 Largest eigenvalues: [1] 64611910 59590608 56910221 55998848 54675695 53070642 52256865 52004935 [9] 51630179 51039778 Smallest eigenvalues: [1] 0.44767823 0.40929841 0.31800547 0.29323309 0.24793446 0.23712671 [7] 0.17928678 0.16993373 -0.04305723 -1.19057602 Largest eigenvalues: [1] 64459967 60581001 57233205 56274291 55618530 53983003 52254222 52103640 [9] 51949071 51065380 Smallest eigenvalues: [1] 0.29175891 0.23391803 0.17408246 0.15674499 0.13489617 0.03069871 [7] -0.08542268 -0.29960155 -0.49240463 -1.15718716 Largest eigenvalues: [1] 65011155 60446753 57391949 56561354 54868283 53567535 52497609 52424645 [9] 51804319 51659271 Smallest eigenvalues: [1] 0.28625032 0.23514710 0.20044846 0.12233990 0.07800716 -0.17761160 [7] -0.25776908 -0.35657178 -0.52667098 -1.41482632 Largest eigenvalues: [1] 64139926 59265630 57053193 55480737 54299754 53206194 51861387 51672562 [9] 51475812 50955437 Smallest eigenvalues: [1] 0.22936969 0.21020719 0.17412006 0.16857077 0.14773110 -0.04124600 [7] -0.04524443 -0.13908801 -0.19386815 -1.60214300 Largest eigenvalues: [1] 64827179 60849185 57772424 56091366 55686590 54345296 52699600 52619501 [9] 52033152 51844209 Smallest eigenvalues: [1] 0.412687187 0.378728427 0.329309738 0.315846639 0.309482282 [6] 0.260399031 0.258287998 0.004449181 -0.127375454 -10.241339447 Largest eigenvalues: [1] 64424604 59948334 57293836 55663979 55086637 53523884 52232847 51767244 [9] 51558272 50970216 Smallest eigenvalues: [1] 0.36599217 0.35035789 0.33298055 0.24896675 0.20065789 0.16959265 [7] 0.13564926 0.13228616 0.07244268 -0.05980429 Largest eigenvalues: [1] 62703934 60077912 57137338 55468784 55142718 53363255 52450982 52300059 [9] 51319769 51097271 Smallest eigenvalues: [1] 0.3801999 0.3482936 0.2911245 0.2376649 0.2114886 0.2042119 [7] 0.1396087 -0.1238492 -0.3356010 -1.5960486 Largest eigenvalues: [1] 65509902 60152591 57115971 56687346 55225618 53671732 52595198 52389513 [9] 52049240 51614870 Smallest eigenvalues: [1] 0.40036700 0.34391822 0.33329054 0.27999331 0.18251816 0.15645880 [7] 0.04867742 -0.37491944 -0.43668209 -5.08273853 Largest eigenvalues: [1] 65539086 60222540 57388358 56269213 55131641 53232074 52490064 52041479 [9] 51631253 51249262 Smallest eigenvalues: [1] 0.1954337 0.1900241 0.1856947 -0.1009354 -0.1317049 -0.2657994 [7] -0.3685551 -0.3867340 -0.4988534 -1.0059088 Largest eigenvalues: [1] 65078229 61302853 57667033 56408164 56335387 54364814 53902332 52580335 [9] 52210065 51853661 Smallest eigenvalues: [1] 0.4477225 0.3848476 0.3436877 0.3162659 0.2796636 0.2688860 [7] 0.2687305 0.1863084 -0.1544271 -0.4701790 Largest eigenvalues: [1] 64188783 60775878 58101977 56181014 55269762 53746974 52018781 51951917 [9] 51867480 50942808 Smallest eigenvalues: [1] 0.29422165 0.19777063 0.10466091 0.09802734 0.08529111 -0.01484967 [7] -0.03153301 -0.07522498 -0.08202590 -2.15647362 Largest eigenvalues: [1] 65018490 59874004 57597808 56494080 55166656 53943434 52963395 52339654 [9] 52293857 51909023 Smallest eigenvalues: [1] 0.4571294 0.4331764 0.3556075 0.3295324 0.3015585 0.2531303 [7] 0.1890027 -0.0762550 -0.2423593 -2.0077737 Largest eigenvalues: [1] 65594600 59761014 56750503 56303172 54397133 52641892 52325120 51402736 [9] 51157988 50646589 Smallest eigenvalues: [1] 0.4646382 0.4500035 0.4326764 0.3553120 0.3421914 0.2759485 [7] 0.2269887 0.1665191 0.1383409 -0.3495080 Largest eigenvalues: [1] 64765642 59847766 57466185 55416579 55326091 53851506 51752952 51621365 [9] 51513030 50756216 Smallest eigenvalues: [1] 0.54077236 0.45580438 0.39245221 0.36618302 0.32701812 0.25522995 [7] 0.17374478 0.09220614 0.02697602 -0.18929149 Largest eigenvalues: [1] 64297809 60192559 57326812 55886898 55741257 54169291 52391068 52339491 [9] 51817913 51719604 Smallest eigenvalues: [1] 0.28795199 0.27277850 0.20074329 0.18314525 0.07810581 [6] 0.07390435 -0.14078310 -0.23773276 -0.81091645 -19.99259512 Largest eigenvalues: [1] 63386915 60157856 57630136 55396973 55059110 53740049 52612356 51764476 [9] 51217132 50971375 Smallest eigenvalues: [1] 0.44495994 0.43756862 0.40479803 0.36700433 0.29030394 0.28358212 [7] 0.20101780 0.16501665 0.06417002 -0.60855837 Largest eigenvalues: [1] 65777865 59744112 57271941 56758633 54656306 53142956 52658067 52156304 [9] 51650234 51153478 Smallest eigenvalues: [1] 0.5600320259 0.5197066362 0.4716906350 0.4274944451 0.3802579594 [6] 0.3145297440 0.1539205452 0.0993539107 0.0449715190 -0.0008183772 Largest eigenvalues: [1] 64622130 60260555 57568973 55499532 55270147 53859864 52528099 52187523 [9] 51608209 51386552 Smallest eigenvalues: [1] 0.38680342 0.38043602 0.29153600 0.24563297 0.23429306 0.18889191 [7] 0.01685479 -0.06894029 -0.25638247 -0.99896044 Largest eigenvalues: [1] 64469025 59751953 56836436 56087082 54973882 53396839 52174809 52118878 [9] 51635719 51052704 Smallest eigenvalues: [1] 0.46791424 0.42696534 0.40733922 0.29847974 0.27113267 0.26420213 [7] 0.22380461 0.19868696 0.03986304 -1.18350445 Largest eigenvalues: [1] 63467451 59614210 57326320 55294604 54774928 53569594 52225269 51868355 [9] 51462107 51049675 Smallest eigenvalues: [1] 0.43702356 0.42604157 0.39079303 0.34412615 0.33467068 0.30929347 [7] 0.21153955 0.05084477 -0.07964505 -0.36445304 Largest eigenvalues: [1] 62826830 59678675 57072272 55577700 54873055 53217787 51617413 51517158 [9] 51454822 50419893 Smallest eigenvalues: [1] 0.48176879 0.47590168 0.45135691 0.35256321 0.29979562 0.24374336 [7] 0.18477920 0.15047625 0.04436969 -0.31178165 Largest eigenvalues: [1] 64051732 60470592 57314570 55920693 55677193 53961064 52688454 52333781 [9] 52084407 51491467 Smallest eigenvalues: [1] 0.5016051 0.4968539 0.4371616 0.3619396 0.2849206 0.2823763 [7] 0.2764347 0.2168504 -0.4795734 -0.9207457 Largest eigenvalues: [1] 63668237 59487438 56679394 55383196 54760833 52965982 52505702 51419262 [9] 51258260 50827519 Smallest eigenvalues: [1] 0.41912095 0.41569188 0.38103989 0.35351037 0.32666803 0.15140703 [7] 0.10824039 0.04329408 0.01489731 -0.63925734 Largest eigenvalues: [1] 65886826 59762903 57373163 56081924 54784273 53253947 52266660 51992319 [9] 51872940 50786459 Smallest eigenvalues: [1] 0.43595765 0.39682051 0.39075055 0.33381001 0.29843423 0.27807291 [7] 0.08690499 0.06523444 -0.02987169 -0.15160563 Largest eigenvalues: [1] 64742431 59808026 57082245 55931053 55223080 53601270 51979427 51713581 [9] 51200746 50160068 Smallest eigenvalues: [1] 0.40488521 0.33661461 0.31488626 0.30953580 0.20523401 0.19087398 [7] 0.12114293 -0.04880466 -0.21783977 -1.20261650 Largest eigenvalues: [1] 63223035 60261246 57197895 55536047 54634545 53602041 51867519 51650129 [9] 51020678 50782355 Smallest eigenvalues: [1] 0.4849433275 0.4841665497 0.3777428439 0.3416971499 0.2464414420 [6] 0.1714379744 0.1662778665 0.1268239945 0.0005470483 -0.7292119221 Largest eigenvalues: [1] 62227487 59472121 56301950 54810892 54627139 52990412 51981668 51350084 [9] 50758495 50592550 Smallest eigenvalues: [1] 0.56944125 0.56092355 0.53088372 0.38999585 0.37768531 0.33125085 [7] 0.14577636 0.07204877 -0.01303944 -0.08134181 Largest eigenvalues: [1] 65509212 59707801 56930931 56801415 54693907 52846224 52825664 51613132 [9] 51241242 50563950 Smallest eigenvalues: [1] 0.45139495 0.33014890 0.32141809 0.24491037 0.20517283 0.06123890 [7] 0.05308619 -0.11056516 -0.41556868 -1.78319977 Largest eigenvalues: [1] 65090916 61286284 57576899 57017512 56036583 54061194 53642363 52598580 [9] 52562384 52037266 Smallest eigenvalues: [1] 0.37826796 0.26562021 0.22840776 0.21147742 0.10750055 0.08870933 [7] -0.07661383 -0.57303159 -0.72562523 -1.43752797 Largest eigenvalues: [1] 66099606 59632397 56959965 56639559 54271809 52790293 52774600 51948815 [9] 51194509 51138006 Smallest eigenvalues: [1] 0.49795328 0.48946833 0.37090172 0.34569614 0.34364666 0.24733095 [7] 0.23063347 0.03688379 -0.06018632 -0.07092340 Largest eigenvalues: [1] 64304716 59211940 56646151 55378824 54553727 52950678 51749212 51337080 [9] 51010538 50350073 Smallest eigenvalues: [1] 0.57828218 0.43946131 0.43929519 0.43191753 0.32229192 0.26328218 [7] 0.25870389 0.15465279 -0.01163865 -0.17573346 Largest eigenvalues: [1] 63856256 59434670 56599109 55565201 54294527 52741153 51592902 51416187 [9] 50854223 49980333 Smallest eigenvalues: [1] 0.32262618 0.28155888 0.26583075 0.25263305 0.18970866 0.18448297 [7] 0.14260862 0.06096392 0.02455327 -0.61564965 Largest eigenvalues: [1] 65520186 60717282 58313241 56814197 55276033 54077777 52758127 52422198 [9] 52209834 51323013 Smallest eigenvalues: [1] 0.26260530 0.21686847 0.19140481 0.18325633 0.15980163 0.06528655 [7] 0.03317500 -0.01989466 -0.02473640 -1.32647737 Largest eigenvalues: [1] 65137609 59739526 56861443 55352361 54609599 53063802 51844055 51464858 [9] 51354641 50984481 Smallest eigenvalues: [1] 0.49605156 0.47801544 0.38649387 0.32656970 0.29630198 0.29523228 [7] 0.27247007 0.23548578 -0.01054134 -4.59470119 Largest eigenvalues: [1] 65458625 60933445 58171282 56502806 55889848 54203623 52785493 52380574 [9] 52298581 51335343 Smallest eigenvalues: [1] 0.46684321 0.36387549 0.27705717 0.25738809 0.18158818 0.17546580 [7] 0.11212597 0.09262325 -0.04820603 -2.14074394 Largest eigenvalues: [1] 64472340 59723600 56643172 55327342 54632084 53111796 51594997 51417633 [9] 51103578 50351645 Smallest eigenvalues: [1] 0.12619207 0.11150809 -0.02642782 -0.11883213 -0.20232777 -0.26620876 [7] -0.29929589 -0.33377198 -0.40606544 -2.12884828 Largest eigenvalues: [1] 65215394 60451497 57823944 55590231 55242169 53697723 52268919 51749697 [9] 51616911 51551837 Smallest eigenvalues: [1] 0.5134272 0.4424175 0.4241758 0.4106739 0.2890797 0.2725983 [7] 0.2428147 0.1979289 0.1501808 -0.3316823 Largest eigenvalues: [1] 65618110 60382275 57637651 56388302 54993976 53577224 52547187 51891132 [9] 51701511 51075420 Smallest eigenvalues: [1] 0.59023219 0.58918366 0.47027725 0.45783010 0.32727309 0.31447231 [7] 0.26417584 0.23580021 0.09613169 -0.19109745 Largest eigenvalues: [1] 66106226 60462707 57873612 56510852 55256661 53910668 52629003 52425409 [9] 51906728 51459859 Smallest eigenvalues: [1] 0.45392489 0.37648662 0.36913566 0.34349880 0.27966157 0.22471334 [7] 0.19231751 0.15185063 -0.04310512 -0.54915024 Largest eigenvalues: [1] 65138793 60799831 58083511 56522591 55289786 54000798 52439949 52299768 [9] 52066025 51152576 Smallest eigenvalues: [1] 0.4809745 0.4590980 0.4387196 0.3687736 0.3483114 0.3247535 [7] 0.2592652 0.2098659 0.1649771 -0.2093161 Largest eigenvalues: [1] 64917145 59591691 56585076 56403815 54415806 52955504 52227002 51755799 [9] 51457858 50476682 Smallest eigenvalues: [1] 0.5524188 0.5253289 0.5077754 0.4161437 0.3520868 0.3513292 [7] 0.2103284 0.2087082 0.1859932 -0.1284037 Largest eigenvalues: [1] 63837922 60245945 57035962 55380949 55326319 53792924 52322533 52050087 [9] 51476482 51299291 Smallest eigenvalues: [1] 0.34254222 0.33927761 0.31655651 0.28933653 0.25041960 0.14760181 [7] 0.14038325 0.10272106 0.09726858 -0.04434161 Largest eigenvalues: [1] 62043686 60363468 57442009 55964839 55030812 54198462 52667039 52376837 [9] 51524088 51024495 Smallest eigenvalues: [1] 0.5968017 0.5715338 0.5118664 0.4725151 0.4217953 0.4008595 [7] 0.3050661 0.2051502 0.1252929 -0.6374712 Largest eigenvalues: [1] 64160435 60688682 57059963 55706722 55619054 54010276 52354304 52204999 [9] 51551473 51087770 Smallest eigenvalues: [1] 0.43921422 0.42016738 0.35638344 0.30966081 0.26502777 0.24474031 [7] 0.18751967 0.10361093 0.09089492 -0.24473658 Largest eigenvalues: [1] 65926783 60097564 57534009 57235572 54874892 53467654 53210909 52079431 [9] 52018865 51148221 Smallest eigenvalues: [1] 0.4080132 0.3844416 0.3041990 0.2304309 0.1596702 0.1284254 [7] 0.1103804 -0.1029656 -0.4918004 -6.7413261 Largest eigenvalues: [1] 65643124 60330007 57714685 56891546 55069589 53498821 52869298 52499837 [9] 52343252 51841262 Smallest eigenvalues: [1] 0.41389349 0.40761232 0.40226160 0.31894818 0.22299817 0.21388907 [7] 0.16096874 0.03526162 -0.25323135 -0.37868853 Largest eigenvalues: [1] 63486960 60336516 56992318 55336170 54965194 53270669 52033524 51574922 [9] 51378816 51136791
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.279887 | 0.7437776 | 16.15451 | 0.025 | 2.603456 | 2.992705 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + speed + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
speed = speed_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_speed_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 20. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 552 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.4871369 0.4371022 0.3969283 0.3897641 0.3730379 0.2673980 [7] 0.2008282 0.1900299 0.1361075 -0.3468347 Largest eigenvalues: [1] 68059266 64101840 60644122 58736466 58716578 57068833 55627800 54815286 [9] 54654377 54536680 Smallest eigenvalues: [1] 0.31626973 0.26059966 0.23993168 0.21653830 0.19324014 0.10787567 [7] 0.08651189 -0.28053069 -0.30436903 -0.42319472 Largest eigenvalues: [1] 68770392 64169545 60674221 59601290 58063150 56494814 55448851 55198213 [9] 54695329 54499491 Smallest eigenvalues: [1] 0.43298209 0.39065054 0.32038564 0.31580052 0.27135299 0.23095625 [7] 0.20945298 0.19700370 0.08325258 -0.41730796 Largest eigenvalues: [1] 67770450 63208445 60343961 58687915 58280158 56793741 55070711 54572301 [9] 54536838 53659641 Smallest eigenvalues: [1] 0.43237843 0.39038460 0.34811747 0.33055939 0.31228261 0.25721830 [7] 0.14359522 0.08298407 -0.13808340 -0.62250939 Largest eigenvalues: [1] 67811971 62987753 59541897 59247626 57265095 55165720 54978367 54645876 [9] 54120743 53559691 Smallest eigenvalues: [1] 0.4404208 0.3973378 0.3768946 0.2737752 0.2050022 0.1869457 [7] 0.1405393 0.1161547 0.1069949 -0.1166931 Largest eigenvalues: [1] 67137597 63620292 60580274 58578451 58299324 56627449 55069595 54935718 [9] 54450249 53882219 Smallest eigenvalues: [1] 0.4361153 0.4326552 0.3869301 0.3522986 0.3027189 0.2735660 [7] 0.1994096 0.1946225 -0.1716368 -0.8596436 Largest eigenvalues: [1] 68084219 63736704 60353725 59617447 58281549 56405027 55941119 55218463 [9] 54652844 54529492 Smallest eigenvalues: [1] 0.38927997 0.37610068 0.35684531 0.34063844 0.31202250 0.27494319 [7] 0.27244318 0.23238277 0.16768573 -0.02078581 Largest eigenvalues: [1] 67387409 63146916 60185673 58730138 58419765 56802746 54846634 54774673 [9] 54583931 53767885 Smallest eigenvalues: [1] 0.45607174 0.41654925 0.35855495 0.33982063 0.29229437 0.21420155 [7] 0.18843033 0.11117026 0.01735056 -0.36860044 Largest eigenvalues: [1] 68361349 63183905 60546176 59889133 57425627 55737221 55510477 54616628 [9] 54518969 53666258 Smallest eigenvalues: [1] 0.49811625 0.46528024 0.43474154 0.36427775 0.35894018 0.33293173 [7] 0.28401616 0.26487715 0.10022111 -0.06254842 Largest eigenvalues: [1] 68064710 62670534 59709023 58503314 57846340 56015128 54596787 54425121 [9] 54202304 53272207 Smallest eigenvalues: [1] 0.3593228887 0.3433896281 0.3369084233 0.3132160259 0.2576256241 [6] 0.1771936430 0.0555107639 0.0002109515 -0.0042069481 -1.7101748456 Largest eigenvalues: [1] 68395305 62396380 59498750 59466638 57367625 55769806 55239370 54171465 [9] 54091163 52995028 Smallest eigenvalues: [1] 0.51350430 0.51159491 0.47357855 0.39443796 0.37486979 0.35960475 [7] 0.35264703 0.35242619 0.01385313 -0.10981068 Largest eigenvalues: [1] 68858102 63357473 60530783 59180159 57635973 55961754 55123054 54263050 [9] 54161199 53137821 Smallest eigenvalues: [1] 0.53093655 0.51995572 0.48821032 0.47648058 0.46355993 0.31445682 [7] 0.31291593 0.23488736 -0.03642857 -0.34042996 Largest eigenvalues: [1] 68424485 63190125 59891761 58884313 57566614 55831695 54697181 54461233 [9] 54276996 53538246 Smallest eigenvalues: [1] 0.5174449 0.5021500 0.4412483 0.3880284 0.3130337 0.2963612 [7] 0.2473445 0.2330143 0.1785020 -0.2004829 Largest eigenvalues: [1] 67645049 63634076 60086272 58794605 58313547 56647524 54851828 54824342 [9] 54603160 53441398 Smallest eigenvalues: [1] 0.4665770015 0.4069988808 0.3895608957 0.3856017392 0.2619467891 [6] 0.2502397556 0.2181061500 0.0007206708 -0.0504037136 -0.1134290527 Largest eigenvalues: [1] 66632318 63520905 60254586 58655310 57823329 56068446 54601011 54391995 [9] 54350224 53388102 Smallest eigenvalues: [1] 0.45818700 0.37136770 0.29148577 0.27702628 0.24315137 0.21055155 [7] 0.19510489 0.01871583 0.01108419 -0.72363063 Largest eigenvalues: [1] 69183118 64459976 61163657 60194874 58849131 57346541 55796547 55683673 [9] 55507089 54488472 Smallest eigenvalues: [1] 0.47726477 0.46309090 0.43523194 0.39681253 0.28294893 0.20860649 [7] 0.19858134 0.17230710 -0.02344266 -0.57905785 Largest eigenvalues: [1] 69363412 64124990 60920367 60247435 58125390 56259240 56042633 54948944 [9] 54526296 53691877 Smallest eigenvalues: [1] 0.45139613 0.43086785 0.41039084 0.35391708 0.34869672 0.32162403 [7] 0.27304407 0.18773427 0.07331108 -0.12103944 Largest eigenvalues: [1] 66963884 63545029 60317747 58632379 58325131 56537075 54772232 54415200 [9] 54369365 53375125 Smallest eigenvalues: [1] 0.43709837 0.38000027 0.34314821 0.32264968 0.32256152 0.29458365 [7] 0.27292184 0.14086888 -0.05545111 -0.15267781 Largest eigenvalues: [1] 67072042 62650767 59544403 58387544 57213244 55349123 54186067 54158601 [9] 53816704 52846055 Smallest eigenvalues: [1] 0.422189092 0.404023271 0.383861175 0.317653503 0.316002243 [6] 0.294476889 0.092847498 0.049750875 0.008568628 -1.148264890 Largest eigenvalues: [1] 68199451 62355141 59796309 58810834 57084186 55633965 54676434 54473218 [9] 53890661 53565731 Smallest eigenvalues: [1] 0.36601341 0.34884508 0.32397289 0.30520595 0.22180805 0.20022794 [7] 0.19795086 0.02900890 -0.08856656 -0.55525858 Largest eigenvalues: [1] 68551210 63238500 60182506 59475762 57766437 55928747 55276650 54688690 [9] 54346976 53404496 Smallest eigenvalues: [1] 0.5236764 0.5192387 0.5022011 0.4842300 0.4085521 0.3715304 [7] 0.3193392 0.3005085 0.2890489 -0.2175593 Largest eigenvalues: [1] 67928828 63663113 60863678 59257439 58003601 56485819 55303790 55043862 [9] 54898748 54170244 Smallest eigenvalues: [1] 0.48284305 0.45986782 0.36174236 0.35885619 0.31053144 0.25346649 [7] 0.21006018 0.19946098 -0.06829768 -0.29319774 Largest eigenvalues: [1] 68103616 62978338 60173316 59292523 57509879 55866911 55020144 54497332 [9] 54141711 53538661 Smallest eigenvalues: [1] 0.4950097 0.4636102 0.4341808 0.3521315 0.2925940 0.2902679 [7] 0.2731803 0.2567635 0.1783970 -0.1862945 Largest eigenvalues: [1] 68172085 62937912 60183781 59824308 57500008 55959923 55500437 54658056 [9] 54407035 53536824 Smallest eigenvalues: [1] 0.39768985 0.39122856 0.37494588 0.33651524 0.26772258 0.19871315 [7] 0.16946260 0.08006802 0.02121582 -0.34346341 Largest eigenvalues: [1] 65940319 62344604 59691727 58142836 57630444 55823040 54544779 54469383 [9] 53818081 53290574 Smallest eigenvalues: [1] 0.4365127 0.3614570 0.2775098 0.2773886 0.2513917 0.2427106 [7] 0.1893908 0.1661593 0.1588374 -0.2544476 Largest eigenvalues: [1] 67122286 63509849 60780775 58325872 58055733 56501379 54870908 54419206 [9] 54139163 53607976 Smallest eigenvalues: [1] 0.420597619 0.410745867 0.368259699 0.310143784 0.227328357 [6] 0.204441963 0.039067837 -0.008790068 -0.328413604 -0.346530671 Largest eigenvalues: [1] 66037014 64224088 60699255 58555412 58153110 56617827 55225662 54783167 [9] 54331770 53885360 Smallest eigenvalues: [1] 0.52748599 0.46638658 0.45179256 0.42314000 0.40293589 0.36212396 [7] 0.27969146 0.27198076 -0.07221661 -2.62416503 Largest eigenvalues: [1] 66513698 63278026 59855593 58213011 57996845 55829530 54336266 54132971 [9] 54067279 53109153 Smallest eigenvalues: [1] 0.45634931 0.44209161 0.41576289 0.35035815 0.32261647 0.30067384 [7] 0.30023702 0.19512978 0.11790271 -0.04748266 Largest eigenvalues: [1] 65878907 62898650 59728870 58297646 57719713 55993283 54640176 54230520 [9] 53822797 53075670 Smallest eigenvalues: [1] 0.50510552 0.48768840 0.46010217 0.44683777 0.31004613 0.24806864 [7] 0.22691530 0.14519283 -0.05051331 -0.35949256 Largest eigenvalues: [1] 67498749 64060536 60110675 59531468 58726183 56835254 55162004 55064940 [9] 54728857 53538259 Smallest eigenvalues: [1] 0.3094222 0.2595862 0.2541490 0.2522295 0.1958157 0.1856597 [7] 0.1216368 -0.1725698 -0.3185201 -0.3619991 Largest eigenvalues: [1] 67300507 62096933 59508524 58926534 56793849 55251736 54585475 54136001 [9] 53513805 52672732 Smallest eigenvalues: [1] 0.5033218 0.4783948 0.4262774 0.4234277 0.3057034 0.3038685 [7] 0.2768524 0.2434997 -0.1691813 -0.3278553 Largest eigenvalues: [1] 66518757 63269474 60191380 58260125 58206584 56574526 54827894 54489678 [9] 53923445 53540435 Smallest eigenvalues: [1] 0.48918706 0.47462820 0.42909671 0.39800639 0.33585951 0.33112584 [7] 0.27284565 0.07943919 -0.11571926 -0.92037649 Largest eigenvalues: [1] 69222807 64030303 60448521 59222388 58384903 56699450 55126458 55021546 [9] 54838160 54105682 Smallest eigenvalues: [1] 0.416985886 0.378743453 0.345784576 0.330311833 0.200104660 [6] 0.174274331 0.148573109 0.065419697 0.005920638 -1.084810571 Largest eigenvalues: [1] 68318679 63736977 60757475 58951832 58752474 56951645 55566161 55182307 [9] 54919181 54481657 Smallest eigenvalues: [1] 0.3744231 0.3733671 0.3553443 0.3411885 0.2518314 0.2415413 [7] 0.2252323 0.1888753 0.1035058 -2.9700488 Largest eigenvalues: [1] 67099045 63272366 60170863 58372070 58290558 56543802 54743651 54509254 [9] 54340226 53270275 Smallest eigenvalues: [1] 0.4203994 0.3446973 0.3410058 0.3307456 0.2955211 0.2714684 [7] 0.2323524 0.2140012 0.1143990 -0.2032699 Largest eigenvalues: [1] 68156692 63357485 60278084 59227975 57812680 56098633 55203506 55077256 [9] 54354781 54129890 Smallest eigenvalues: [1] 0.5906458 0.5873059 0.5847440 0.5490714 0.5127235 0.5012821 [7] 0.4849396 0.4395064 0.3227387 -1.8935748 Largest eigenvalues: [1] 68256622 63370189 60222910 59017165 57862824 55976164 54783492 54743614 [9] 54087691 53621602 Smallest eigenvalues: [1] 0.42976933 0.39700879 0.37356246 0.27685748 0.24309946 0.17745138 [7] 0.15359435 0.11145381 0.09396638 -1.23292036 Largest eigenvalues: [1] 68328598 62888364 60037456 59129174 57488789 56159645 55030792 54555726 [9] 54525131 53890837 Smallest eigenvalues: [1] 0.55004545 0.50210387 0.48044303 0.42128365 0.39004892 0.33616378 [7] 0.31727410 0.23817137 0.08922346 -0.01835973 Largest eigenvalues: [1] 68283398 63863469 60994535 59810602 57589428 55697948 55405464 54616766 [9] 54224875 53503845 Smallest eigenvalues: [1] 0.44027896 0.43283983 0.38029104 0.36565636 0.33521763 0.27004087 [7] 0.24172554 0.23630925 0.17518938 -0.06797854 Largest eigenvalues: [1] 66241033 63553237 60238572 58838239 57768728 56908731 55221327 54618512 [9] 53860584 53717247 Smallest eigenvalues: [1] 0.55314140 0.49808467 0.48119124 0.36321582 0.34659613 0.28693376 [7] 0.24198914 0.09408923 -0.02784464 -0.28214494 Largest eigenvalues: [1] 69018227 64128690 60998433 59808183 58279589 56333682 55690260 55181213 [9] 55090343 54206642 Smallest eigenvalues: [1] 0.4726470 0.4269587 0.4037764 0.3664048 0.3500020 0.2975436 [7] 0.1772066 0.1757382 0.1420796 -0.8633437 Largest eigenvalues: [1] 68040339 63681881 60855726 59001226 58357501 56717739 54947036 54628022 [9] 54489538 53852312 Smallest eigenvalues: [1] 0.34868348 0.32606343 0.31571882 0.27297998 0.23888565 0.14540253 [7] 0.03916881 0.03131517 -0.13332400 -0.41710638 Largest eigenvalues: [1] 65314961 63401131 60103251 58095865 57531950 56113046 54588320 54360131 [9] 53671897 53061319 Smallest eigenvalues: [1] 0.45496708 0.45452662 0.43290031 0.37788800 0.31918824 0.24126342 [7] 0.18284014 0.11407919 -0.02109173 -0.05402286 Largest eigenvalues: [1] 68081190 62822194 59940799 58848160 57844185 55881097 55357211 54602444 [9] 54046184 53943930 Smallest eigenvalues: [1] 0.53875611 0.49638694 0.41383932 0.38415113 0.36157461 0.32026101 [7] 0.31343084 0.26991871 0.24705935 -0.03186374 Largest eigenvalues: [1] 69001612 63164956 60726358 59677718 57398271 55411495 55386894 54665716 [9] 53788714 53391130 Smallest eigenvalues: [1] 0.48073317 0.42625166 0.42333368 0.36812326 0.34516524 0.32162632 [7] 0.25500258 0.23415890 0.14881881 -0.09277153 Largest eigenvalues: [1] 66989365 63625402 60341405 58491793 58176755 56548718 54937409 54680466 [9] 54376037 53990071 Smallest eigenvalues: [1] 0.4843283 0.4585012 0.3983035 0.3808898 0.3084147 0.3023291 [7] 0.2436740 0.2001448 0.1122935 -0.1753386 Largest eigenvalues: [1] 67029232 63198647 60164788 58287771 58247208 56586577 54931100 54339653 [9] 54196997 53487574 Smallest eigenvalues: [1] 0.4834365 0.3988858 0.3403165 0.3177665 0.2802590 0.2531752 [7] 0.2239748 0.2084495 0.1905648 -0.4318380 Largest eigenvalues: [1] 69301709 63929047 61231528 60135504 57879806 56589298 55746805 54905347 [9] 54612772 54084649 Smallest eigenvalues: [1] 0.592315926 0.572323127 0.468126026 0.408312690 0.361957586 [6] 0.357558641 0.197612349 0.192047716 -0.001285125 -0.034488330 Largest eigenvalues: [1] 67217736 62820734 60044831 58419511 57804653 56175814 54647397 54571362 [9] 54249515 53643527 Smallest eigenvalues: [1] 0.5201938 0.4894251 0.4531740 0.4039184 0.3455898 0.3265580 [7] 0.3225675 0.2822306 0.2317851 -1.5090775 Largest eigenvalues: [1] 68071045 62771423 59977836 59051581 57525083 56035625 54797724 54063812 [9] 53729617 52613633 Smallest eigenvalues: [1] 0.50513942 0.44915861 0.37602448 0.33991175 0.32276343 0.24378112 [7] 0.20372369 0.13740468 0.07695445 -0.92755240 Largest eigenvalues: [1] 69115278 63621572 60675863 58967918 58352685 56793236 55486177 54945916 [9] 54824275 54522138 Smallest eigenvalues: [1] 0.36663659 0.36649950 0.34293067 0.26896848 0.22819671 0.20576198 [7] 0.19777934 0.19599314 -0.09180112 -1.02862132 Largest eigenvalues: [1] 68868587 63716566 60727672 59626044 58191992 56840329 55426208 54928084 [9] 54575558 53713146 Smallest eigenvalues: [1] 0.37785008 0.36373303 0.30286342 0.27407066 0.26981205 0.26946474 [7] 0.24734828 0.20137140 0.05640455 -0.05977492 Largest eigenvalues: [1] 69574215 63520521 60786643 59687911 58117146 56592206 55504509 54738375 [9] 54547611 53827033 Smallest eigenvalues: [1] 0.43409418 0.42218964 0.35141293 0.34250855 0.27221329 0.27099634 [7] 0.22145390 0.02206452 -0.04109297 -6.00719540 Largest eigenvalues: [1] 67808576 64202059 60482193 59399268 58548623 56436186 55644613 55188764 [9] 54320223 53789302 Smallest eigenvalues: [1] 0.3442454230 0.3376436772 0.3197629749 0.3160097179 0.2390944073 [6] 0.1229629268 0.1128499044 -0.0007692301 -0.5166756526 -0.6933854505 Largest eigenvalues: [1] 67748172 63422645 60256715 59469845 57416920 55997381 55164768 54641503 [9] 54574920 53541980 Smallest eigenvalues: [1] 0.412677630 0.339258553 0.310752531 0.263551865 0.226463623 [6] 0.219127498 0.193101447 0.181948708 0.006700095 -0.397420613 Largest eigenvalues: [1] 66238531 62217525 59573641 58105371 57310025 55599109 53930816 53928528 [9] 53806505 52648330 Smallest eigenvalues: [1] 0.5489729 0.5071630 0.4302460 0.4207504 0.3020158 0.2796464 [7] 0.2681556 0.2107831 0.1066990 -0.8239525 Largest eigenvalues: [1] 67568552 64139242 60504948 59421811 58595022 56700774 55282716 54966169 [9] 54835593 53904665 Smallest eigenvalues: [1] 0.51088162 0.48506500 0.38909132 0.33015270 0.31119151 0.26728222 [7] 0.19934615 0.14503639 0.05533713 -0.11641848 Largest eigenvalues: [1] 66461710 64442104 60786409 58715408 58338083 56802141 55110712 55083895 [9] 54540940 54118942 Smallest eigenvalues: [1] 0.5138599 0.4419077 0.4138884 0.3804675 0.3782512 0.3487442 [7] 0.3478423 0.2303019 -0.1612810 -3.4902104 Largest eigenvalues: [1] 68691678 63525039 59755017 59479030 58325403 56226754 55319968 54788780 [9] 54502533 53705743 Smallest eigenvalues: [1] 0.4891512 0.4788613 0.4436544 0.3933629 0.3898036 0.3063964 [7] 0.3001360 0.2847364 0.2757718 -0.5226982 Largest eigenvalues: [1] 67435567 62794678 59867014 59112816 56957478 55138808 54709138 53869882 [9] 53655681 52875429 Smallest eigenvalues: [1] 0.36259907 0.35417442 0.30301563 0.26373907 0.23797479 0.21026581 [7] 0.19887019 0.19604302 0.02928042 -0.05492904 Largest eigenvalues: [1] 68587333 63293933 60630711 59375226 57943250 56001434 55374620 55091061 [9] 54138537 53947498 Smallest eigenvalues: [1] 0.59517572 0.54654609 0.53926798 0.46474824 0.37709382 0.32447032 [7] 0.30067989 0.27527320 -0.07630564 -0.09355798 Largest eigenvalues: [1] 68456935 64160158 60954533 58868578 58596662 56813391 55452523 54924358 [9] 54839387 54358757 Smallest eigenvalues: [1] 0.47018455 0.43618346 0.34724248 0.34407028 0.31301957 0.13881482 [7] 0.13161609 0.08359004 -0.03143958 -0.05128687 Largest eigenvalues: [1] 68167649 63262086 60546633 58653525 57437255 55762432 54507266 54180272 [9] 54088867 53321232 Smallest eigenvalues: [1] 0.5624139 0.4773664 0.4147852 0.4048095 0.4011495 0.3813351 [7] 0.2762676 0.2732593 0.2420925 -0.4028556 Largest eigenvalues: [1] 67494281 63288147 59985830 59263398 57709501 55991989 54621552 54579444 [9] 54440505 53439909 Smallest eigenvalues: [1] 0.48987627 0.45855660 0.41213000 0.32369859 0.28594498 0.23581489 [7] 0.20627680 0.03657812 -0.00553368 -0.12320354 Largest eigenvalues: [1] 68743350 64198814 60864391 59241318 58602183 56754061 55461578 55070750 [9] 54941056 54471558 Smallest eigenvalues: [1] 0.51390023 0.48430507 0.45595817 0.44183864 0.39999669 0.39393468 [7] 0.34396878 0.25019694 0.20905366 -0.03458746 Largest eigenvalues: [1] 66549646 63156820 59869802 58547853 57996506 56095636 54541956 54474939 [9] 54326771 53281674 Smallest eigenvalues: [1] 0.23579131 0.19797926 0.16348135 0.12675588 0.06501839 0.04211488 [7] 0.02641495 -0.10843971 -0.26184509 -2.61208018 Largest eigenvalues: [1] 68414965 63715588 60853508 58941952 58452414 57158519 55347011 55132302 [9] 54650319 54300148 Smallest eigenvalues: [1] 0.5507021 0.4952098 0.4530175 0.4346892 0.3841613 0.3242088 [7] 0.3039139 0.1624287 -0.1888110 -3.6390781 Largest eigenvalues: [1] 69471437 63077083 60005960 59427265 57527032 55693380 55253195 54745026 [9] 54559209 54080556 Smallest eigenvalues: [1] 0.42502247 0.39646002 0.38823320 0.36176840 0.33014068 0.32227665 [7] 0.31464403 0.01439214 -0.02400790 -0.06026872 Largest eigenvalues: [1] 67949595 63196962 60457910 58595311 57566260 56193568 54572674 54190056 [9] 54152649 53368084 Smallest eigenvalues: [1] 0.46865458 0.43429456 0.32142795 0.28741370 0.26576764 0.11121914 [7] 0.10182332 0.07441637 -0.01045278 -0.03944125 Largest eigenvalues: [1] 66942469 63505685 60665260 58294776 58233816 56730174 55047953 54697459 [9] 54269623 53972202 Smallest eigenvalues: [1] 0.3740484 0.3026676 0.2790268 0.2637559 0.2370925 0.2157886 [7] 0.2036167 0.1749273 0.1554799 -0.7774389 Largest eigenvalues: [1] 67399605 62789251 59958220 58497737 57564868 55983800 54482127 54233563 [9] 53621660 52467550 Smallest eigenvalues: [1] 0.36378565 0.31921817 0.30553080 0.28393074 0.27513078 0.03152577 [7] 0.03149619 -0.03901565 -0.15937589 -2.13047391 Largest eigenvalues: [1] 67016536 63680093 60575587 58663041 58497538 57071723 55415775 54773926 [9] 54341155 54149353 Smallest eigenvalues: [1] 0.55302651 0.45022239 0.37309786 0.36430415 0.33107637 0.31883252 [7] 0.28099918 0.23378306 0.16817241 -0.02547947 Largest eigenvalues: [1] 67277337 63179174 60205816 58697082 57873336 56218961 54538533 54489877 [9] 54257981 53389249 Smallest eigenvalues: [1] 0.61041244 0.59586829 0.54510813 0.50578135 0.44193619 0.40141562 [7] 0.36415673 0.33638829 0.29494625 -0.05460051 Largest eigenvalues: [1] 68167338 63860055 60495694 59697066 57814700 56072107 55331137 55148906 [9] 54304412 54079808 Smallest eigenvalues: [1] 0.4376435 0.4049017 0.3787041 0.3223802 0.2171088 0.2151866 [7] 0.1585135 0.1442549 0.1206910 -0.4251732 Largest eigenvalues: [1] 68184531 63667509 60623166 59712027 57955988 56503627 55424063 55226090 [9] 54617339 53973308 Smallest eigenvalues: [1] 0.37390983 0.36285367 0.35459864 0.27937323 0.20137449 0.18593865 [7] 0.18167535 0.07005072 0.03350012 -1.23029729 Largest eigenvalues: [1] 65423518 62099073 59592072 57851324 57446447 55362180 54455760 54438164 [9] 53522444 53218576 Smallest eigenvalues: [1] 0.44359425 0.42939751 0.34020097 0.30385384 0.20538030 0.10849466 [7] 0.04643053 -0.01631910 -0.38642925 -0.88464119 Largest eigenvalues: [1] 67708789 63534685 60681200 58907560 58495488 56751640 55652641 55256451 [9] 54749033 54422734 Smallest eigenvalues: [1] 0.4662827 0.4510253 0.3861807 0.2878057 0.2210033 0.2192955 [7] 0.1654335 0.1385009 0.1301377 -2.5833472 Largest eigenvalues: [1] 68955976 64378731 61037748 60113421 58598958 57120552 55959259 55535063 [9] 55102042 54680941 Smallest eigenvalues: [1] 0.40304525 0.38922916 0.37960931 0.31481611 0.31065750 0.26681945 [7] 0.09155275 0.07165704 0.02106968 -0.42524862 Largest eigenvalues: [1] 68180980 63172381 59864587 58943633 57585141 56092622 54806168 54600239 [9] 54280325 53451268 Smallest eigenvalues: [1] 0.53020409 0.46862655 0.43102286 0.33622462 0.26806288 0.24654839 [7] 0.21547387 0.19878633 0.17243970 -0.06501671 Largest eigenvalues: [1] 68191452 64073179 61012483 59480633 58318972 56513983 55709349 55139905 [9] 54673376 54521249 Smallest eigenvalues: [1] 0.454399678 0.368957238 0.361311930 0.344483347 0.309491776 [6] 0.222550549 0.105645979 -0.009634668 -0.283283940 -1.350372683 Largest eigenvalues: [1] 67865449 63461592 60926667 59305856 58166427 56834269 55057311 54828865 [9] 54701708 53644860 Smallest eigenvalues: [1] 0.385489074 0.339088948 0.337854291 0.323149018 0.229454991 [6] 0.207186884 0.114152561 0.068643349 -0.006851919 -0.344605356 Largest eigenvalues: [1] 68214176 63199159 60348321 59418587 58028890 56340267 55290403 55070394 [9] 55061825 54019966 Smallest eigenvalues: [1] 0.31946836 0.30438363 0.29937308 0.26339950 0.22114627 0.21299499 [7] 0.21186254 0.19713965 0.09901826 -0.06406513 Largest eigenvalues: [1] 65103446 62167472 59747186 57724216 57064933 56013837 54352832 53791164 [9] 52828173 52790421 Smallest eigenvalues: [1] 0.49466537 0.47530245 0.47448685 0.46329900 0.38954014 0.26461205 [7] -0.03224441 -0.16083733 -0.21264541 -1.52598581 Largest eigenvalues: [1] 68682833 63500509 60367217 59650131 57719444 55751671 55331398 54641935 [9] 54407742 53684650 Smallest eigenvalues: [1] 0.38816449 0.34084715 0.29729645 0.28189568 0.25817663 0.19675391 [7] 0.16909634 -0.03988069 -0.18518397 -1.30201892 Largest eigenvalues: [1] 68558799 63417656 60643518 60346566 57416310 56071488 55807297 54730713 [9] 54342711 53481197 Smallest eigenvalues: [1] 0.41356748 0.41283024 0.37793226 0.35407525 0.24610008 0.19083224 [7] 0.07852834 0.06874451 0.05868728 -0.15215231 Largest eigenvalues: [1] 64973706 63507134 60225300 58644948 57370591 56861049 55393714 54754736 [9] 53672061 53434798 Smallest eigenvalues: [1] 0.52853457 0.51067878 0.41846842 0.39989648 0.37170678 0.30852560 [7] 0.08824105 0.04665996 -0.01549561 -0.12295605 Largest eigenvalues: [1] 65169538 62863778 59811828 57797566 57246051 55991193 54376681 54363859 [9] 53239029 53047793 Smallest eigenvalues: [1] 0.4383703 0.4111223 0.3452179 0.2534708 0.2198715 0.2110006 [7] 0.1684109 0.1371931 -0.3066051 -0.3522867 Largest eigenvalues: [1] 67488654 64168456 60293962 59057188 58758893 56901662 55728262 54814559 [9] 54612011 54484284 Smallest eigenvalues: [1] 0.09077574 0.07985318 0.07161046 -0.06546924 -0.12357081 -0.16574267 [7] -0.21544949 -0.48774375 -0.83137836 -1.98341432 Largest eigenvalues: [1] 66195681 64278486 60842737 58947202 58620138 56907207 55835488 55177032 [9] 54779117 54593055 Smallest eigenvalues: [1] 0.4749992 0.4588567 0.4417316 0.3748957 0.3720367 0.3162966 [7] 0.3140249 0.2632057 -0.0280806 -2.0185636 Largest eigenvalues: [1] 68978953 64357723 60924403 60487418 58066529 56268462 56176150 55668085 [9] 54406992 53989675 Smallest eigenvalues: [1] 0.3630992 0.3002337 0.2967818 0.2834526 0.2188619 0.2176326 [7] 0.1361318 0.0295708 -0.1960163 -3.0776484 Largest eigenvalues: [1] 67324951 63763746 60236085 59100481 58484849 56469610 55154252 55036454 [9] 54423842 53840466 Smallest eigenvalues: [1] 0.4393979 0.4335799 0.3535523 0.3416898 0.3262382 0.3198756 [7] 0.2599242 0.2244695 0.2188060 -0.3704628 Largest eigenvalues: [1] 69389725 63379986 60416549 59945552 57850181 56166456 55908720 54662160 [9] 54479225 53752139 Smallest eigenvalues: [1] 0.5088960 0.4617664 0.4360174 0.3913409 0.3876926 0.3313498 [7] 0.2930483 0.2128162 0.1721470 -0.3028481 Largest eigenvalues: [1] 67548263 62922130 59965643 58899477 57449254 55952148 54783006 54624333 [9] 54236373 53645519 Smallest eigenvalues: [1] 0.521842376 0.520011459 0.497703415 0.478549456 0.326143515 [6] 0.291596374 0.260953709 0.194431572 0.027887885 -0.007009047 Largest eigenvalues: [1] 66771614 63725955 60100392 58829551 57896168 56108666 55124980 54572437 [9] 54513456 53914225 Smallest eigenvalues: [1] 0.4313105 0.3445489 0.3442898 0.2853614 0.2807683 0.2501643 [7] 0.1619296 0.1004652 -0.8247342 -7.2402608 Largest eigenvalues: [1] 67131179 63154484 59929993 58892666 57761317 55989821 54759196 54373410 [9] 53828908 52983938 Smallest eigenvalues: [1] 0.37640735 0.36416540 0.29618411 0.21635469 0.20268014 0.17298621 [7] 0.13174738 0.05457955 -0.18058773 -0.21500361 Largest eigenvalues: [1] 68609531 64134758 60414755 60234951 58115936 56284038 55834964 55082088 [9] 54911624 53600040 Smallest eigenvalues: [1] 0.50247460 0.47260993 0.38647617 0.36478648 0.36288107 0.30084449 [7] 0.25583464 0.24388533 0.08722445 -0.33180412 Largest eigenvalues: [1] 68531566 63888273 60130973 59667500 58693034 56660728 55541734 55177951 [9] 54660654 53924702 Smallest eigenvalues: [1] 0.4928859 0.4831381 0.4545999 0.4173196 0.3830974 0.2714029 [7] 0.2088009 0.1708331 0.1314161 -0.8384515 Largest eigenvalues: [1] 67826879 63397132 60822273 59282953 57974316 56742458 55057886 54898142 [9] 54868155 53958399 Smallest eigenvalues: [1] 0.20543543 0.16406222 0.13946428 0.13155527 0.01737225 -0.04304625 [7] -0.12514565 -0.22232352 -1.03993087 -2.18440288 Largest eigenvalues: [1] 65918912 61917774 59546108 57733513 57663878 55908569 54218269 53742805 [9] 53539442 52857183 Smallest eigenvalues: [1] 0.4933460 0.4516526 0.4407941 0.4010209 0.3965264 0.3463170 [7] 0.3341390 0.1981114 0.1618570 -0.4107189 Largest eigenvalues: [1] 68014649 63020138 59777877 59393790 57196425 55288574 55022353 54149971 [9] 53671496 52608983 Smallest eigenvalues: [1] 0.4550006 0.4235911 0.3334757 0.3229685 0.2805139 0.2758863 [7] 0.2751037 0.2352111 0.1790599 -3.4237993 Largest eigenvalues: [1] 67948630 62608888 59981010 59039138 57814452 56067304 54870319 54209206 [9] 53740478 52912651 Smallest eigenvalues: [1] 0.40014581 0.36849807 0.30293426 0.28140058 0.23684477 0.13934769 [7] 0.06755045 -0.02203300 -0.10866453 -0.18224245 Largest eigenvalues: [1] 67876387 63134415 59976381 58919291 58412697 56716895 55282204 54996769 [9] 54744138 53999243 Smallest eigenvalues: [1] 0.5033202 0.4097102 0.3990640 0.3883469 0.3517175 0.2437599 [7] 0.2431688 0.1988100 0.1392137 -0.4830344 Largest eigenvalues: [1] 67044114 63213891 60130967 58860348 57627075 56179643 54488399 54321776 [9] 54197509 53350164 Smallest eigenvalues: [1] 0.45060840 0.42807831 0.30089375 0.29628542 0.29603247 0.29542166 [7] 0.15964715 0.14897590 -0.01336732 -0.25958192 Largest eigenvalues: [1] 68413752 63601725 60822801 59808151 58036723 56607045 56015639 55492248 [9] 54960583 54658739 Smallest eigenvalues: [1] 0.5904692 0.4976456 0.4702491 0.3976988 0.3738093 0.3645971 [7] 0.3240381 0.3184169 0.2746071 -0.2363938 Largest eigenvalues: [1] 68362988 63671482 60460396 59788598 57546347 56181868 55450546 54608953 [9] 54336991 53479769 Smallest eigenvalues: [1] 0.5710800 0.5640956 0.5442517 0.4381953 0.4163381 0.4114387 [7] 0.4016177 0.2740346 0.2240140 -0.5849995 Largest eigenvalues: [1] 67517055 63211161 59963090 59216642 57716013 56118148 54780751 54403143 [9] 54351313 53122785 Smallest eigenvalues: [1] 0.5144350 0.4717993 0.3905050 0.3899166 0.2978297 0.2316817 [7] 0.2020666 0.1547138 0.0225471 -0.7302839 Largest eigenvalues: [1] 66894031 63944070 60013529 58857412 58483601 57074872 55154840 54865255 [9] 54229713 53585708 Smallest eigenvalues: [1] 0.44725665 0.44573068 0.43751959 0.42946557 0.33754621 0.29625245 [7] 0.26160239 0.23080588 0.20363386 -0.06763161 Largest eigenvalues: [1] 66918101 63491317 59858200 59013190 57495495 55998288 54491613 54277216 [9] 54028111 52879966 Smallest eigenvalues: [1] 0.4425354 0.3690194 0.3584283 0.3528590 0.3514590 0.3355940 [7] 0.3000671 0.1211724 0.1082390 -0.6851168 Largest eigenvalues: [1] 66528197 63166261 60377521 58705088 57827724 56148189 55677762 54492141 [9] 54209331 54147771 Smallest eigenvalues: [1] 0.3953901 0.3540681 0.2987046 0.2740494 0.2271158 0.1969634 [7] 0.1546901 0.1240115 -0.3236322 -0.5011239 Largest eigenvalues: [1] 69023359 63184524 60399164 59359283 57600309 55734814 55266961 54521889 [9] 54342755 53310978 Smallest eigenvalues: [1] 0.45563190 0.37823123 0.33830151 0.33148410 0.30596916 0.25124252 [7] 0.22863720 0.14232750 0.12419326 -0.08990773 Largest eigenvalues: [1] 66043011 63222739 60234088 58235574 57967486 56423212 54673119 54554982 [9] 53879930 53246138 Smallest eigenvalues: [1] 0.24604180 0.21493893 0.20040227 0.09773293 -0.02546299 -0.04815794 [7] -0.05146104 -0.78119750 -1.31136695 -1.69888129 Largest eigenvalues: [1] 67683422 62380245 59673150 58290138 57526124 55897587 54851571 54304464 [9] 54152766 53388444 Smallest eigenvalues: [1] 0.55078292 0.51338187 0.50589985 0.41717784 0.33959169 0.31521354 [7] 0.21719589 0.12176297 -0.07072099 -0.37853862 Largest eigenvalues: [1] 69139029 63693011 60114237 59691291 58146325 56002469 55567959 55524284 [9] 54508372 54364076 Smallest eigenvalues: [1] 0.4351992 0.3987839 0.3824598 0.3378732 0.2606060 0.2508343 [7] 0.2151245 0.1898829 0.1023967 -0.6948539 Largest eigenvalues: [1] 68733663 64134850 60727968 59915740 57962986 56407405 55630953 55312853 [9] 54297335 54258940 Smallest eigenvalues: [1] 0.53484588 0.42556523 0.41570369 0.39366101 0.38426783 0.36058011 [7] 0.25899550 0.25342828 0.19805837 -0.05033832 Largest eigenvalues: [1] 67122253 63358040 60485393 58986995 57363422 55971787 54592712 54527424 [9] 54323654 53760752 Smallest eigenvalues: [1] 0.46508605 0.40510691 0.29925393 0.27044472 0.23636723 0.23429491 [7] 0.22232868 0.13777595 0.06874249 -0.77713298 Largest eigenvalues: [1] 68180216 63197853 60579100 59476964 57527674 56175957 55326442 54706216 [9] 54512863 53698090 Smallest eigenvalues: [1] 0.43334345 0.41197094 0.37364522 0.34752942 0.30926025 0.27936114 [7] 0.20318198 0.19349993 -0.03850194 -0.18890380 Largest eigenvalues: [1] 68235858 63641755 61109297 60028696 57442462 55652697 55589629 54667081 [9] 54187876 53549769 Smallest eigenvalues: [1] 0.6197192 0.5443604 0.4970049 0.4502359 0.4325619 0.3099852 [7] 0.3037181 0.2719893 0.2187992 -4.3173235 Largest eigenvalues: [1] 68741002 63389623 60732652 59074596 58047664 56450568 54987006 54756860 [9] 54650662 53974077 Smallest eigenvalues: [1] 0.50637323 0.49061049 0.43122512 0.43080375 0.28762009 0.28469532 [7] 0.26850906 -0.01901069 -0.14258580 -0.20492768 Largest eigenvalues: [1] 68349894 62941431 59769307 59015252 57570044 55898782 54866580 54716095 [9] 54611928 53774586 Smallest eigenvalues: [1] 0.38204869 0.34709909 0.33077802 0.32353933 0.30607034 0.21910549 [7] 0.18169733 0.15562452 -0.04396911 -0.84144077 Largest eigenvalues: [1] 69978042 62940249 60083432 60072850 57324308 55931636 55782780 54740508 [9] 54342107 53974136 Smallest eigenvalues: [1] 0.3724431 0.3455962 0.3414101 0.3114556 0.3009087 0.2945569 [7] 0.2011349 0.1404208 0.1375942 -1.5617201 Largest eigenvalues: [1] 70255071 63776450 61399597 60899760 58027722 56292554 56017732 55570819 [9] 54615887 54437528 Smallest eigenvalues: [1] 0.39604516 0.39351708 0.32995606 0.26447135 0.25137016 0.18067785 [7] 0.15859488 0.14919848 -0.04081838 -0.20996525 Largest eigenvalues: [1] 68492762 64198715 61251004 59567579 58458310 56978995 55330504 55272862 [9] 55110370 54201685 Smallest eigenvalues: [1] 0.42853376 0.40284336 0.36222066 0.31929266 0.25211957 0.20408867 [7] 0.13287602 0.07981155 0.04949470 -1.07206364 Largest eigenvalues: [1] 70149479 63623083 60875447 59604711 57572748 55818266 55625866 54758699 [9] 54225160 54132430 Smallest eigenvalues: [1] 0.4134856 0.3272312 0.2795836 0.2554193 0.2108288 0.1440820 [7] -0.1641066 -0.4342838 -2.1496383 -2.4938596 Largest eigenvalues: [1] 66811542 63366094 60431009 59121716 57488377 55650388 54744204 54525253 [9] 53771403 53075530 Smallest eigenvalues: [1] 0.41257337 0.38604746 0.34035932 0.30968326 0.29953331 0.26542595 [7] 0.11580983 0.06510327 0.02043763 -0.06679304 Largest eigenvalues: [1] 68676446 63157113 60525932 59653409 57624309 56220373 55536444 54439066 [9] 54291899 53264470 Smallest eigenvalues: [1] 0.40979146 0.37910311 0.36331590 0.34947441 0.31481149 0.26545673 [7] 0.25635612 0.03800147 -0.07982756 -0.09810509 Largest eigenvalues: [1] 66973152 62751168 59555968 58342374 57528375 55803141 54255639 54202246 [9] 53431692 52518936 Smallest eigenvalues: [1] 0.47739111 0.42157482 0.40364665 0.35183985 0.34761427 0.34046791 [7] 0.23104382 -0.02181021 -0.06972688 -0.08068021 Largest eigenvalues: [1] 66965675 62079761 59356953 58068905 57120695 54815450 53894385 53587637 [9] 53362247 52417503 Smallest eigenvalues: [1] 0.46215341 0.41857618 0.41177900 0.40378570 0.33789643 0.30447158 [7] 0.01017379 -0.13362746 -0.31025824 -1.40944793 Largest eigenvalues: [1] 68732522 63335363 59860942 59579664 57404224 55369431 55287669 54171420 [9] 53940059 53018396 Smallest eigenvalues: [1] 0.3095818 0.2778032 0.2545463 0.2197349 0.1953447 0.1852127 [7] 0.1472302 -0.1423292 -0.1739088 -7.7728334 Largest eigenvalues: [1] 67334819 62941735 60102184 58869760 57340064 55814185 54706507 54674878 [9] 54641267 53415065 Smallest eigenvalues: [1] 0.50115690 0.48429533 0.44553863 0.40515728 0.34452359 0.30252002 [7] 0.27072430 0.08791954 0.06078579 -0.80934514 Largest eigenvalues: [1] 68672614 63395526 59991608 59129944 58140288 56482990 54858718 54695680 [9] 54461345 53753595 Smallest eigenvalues: [1] 0.3860044 0.3824185 0.3206108 0.2997718 0.2540411 0.2315155 [7] 0.1360335 -0.2639487 -0.5670442 -0.7219225 Largest eigenvalues: [1] 67282238 63562389 60128636 58625375 58517712 56931965 54997354 54555117 [9] 54185018 53635801 Smallest eigenvalues: [1] 0.30325056 0.29874419 0.23979320 0.20915818 0.20475933 0.17085431 [7] 0.11078222 0.09518855 -1.80241987 -2.32152462 Largest eigenvalues: [1] 69949807 64121589 61201566 59557393 58314949 56754865 55518420 55232282 [9] 54786552 54360565 Smallest eigenvalues: [1] 0.5656168 0.5459389 0.5307897 0.5071578 0.4788590 0.4242468 [7] 0.2676424 0.1972563 0.1701764 -0.1489015 Largest eigenvalues: [1] 69666734 63432673 60377362 60127470 57885457 56487122 55792032 55080301 [9] 54688257 54145775 Smallest eigenvalues: [1] 0.5263281 0.4612386 0.4441120 0.4208742 0.3836335 0.2636897 [7] 0.2454053 0.2242008 0.1952285 -0.3667273 Largest eigenvalues: [1] 67887378 63084368 59704785 59171495 57341098 55716494 54895080 54373154 [9] 54259558 53490263 Smallest eigenvalues: [1] 0.44011677 0.41593644 0.40595178 0.37867142 0.31194354 0.29370175 [7] 0.26200139 0.17180736 0.09959999 -0.08855659 Largest eigenvalues: [1] 69132237 63959573 60198890 59909500 58147258 56127210 55574416 55200340 [9] 54329539 54222982 Smallest eigenvalues: [1] 0.49582636 0.48170465 0.45545788 0.41535396 0.31666443 0.29850157 [7] 0.23190553 0.05164566 -0.01182284 -0.87743788 Largest eigenvalues: [1] 68830882 63416373 60488564 59737195 57641430 56116078 55500207 54338978 [9] 54214870 53182409 Smallest eigenvalues: [1] 0.38370556 0.35542697 0.30085070 0.26385480 0.25050507 0.24841977 [7] 0.22510366 0.17700562 -0.07308743 -2.36891544 Largest eigenvalues: [1] 68707693 63730190 60768678 59825413 58441912 56974564 55420380 55035742 [9] 54914929 53976469 Smallest eigenvalues: [1] 0.3332730 0.3156874 0.3089196 0.2948094 0.2923146 0.2672954 [7] 0.1809407 0.1010079 0.0764179 -0.5716010 Largest eigenvalues: [1] 67311033 63228047 59675813 58754173 58158345 56392368 54518937 54508048 [9] 53829478 52778975 Smallest eigenvalues: [1] 0.46599774 0.46389302 0.43408618 0.34884094 0.34790297 0.30601859 [7] 0.24181956 0.23707329 0.20018916 -0.08858747 Largest eigenvalues: [1] 67160353 63173780 59973832 59054165 57924193 56125013 54971145 54673344 [9] 54209699 53723958 Smallest eigenvalues: [1] 0.39410693 0.35767248 0.35460259 0.28428720 0.23976973 0.18395171 [7] 0.11804654 0.04405101 -0.15458088 -0.79080988 Largest eigenvalues: [1] 66872622 62380480 59279307 57980076 57539566 55897162 54393556 53901042 [9] 53845919 53136358 Smallest eigenvalues: [1] 0.323264964 0.309539847 0.294746452 0.258753508 0.258534033 [6] 0.254078357 0.193114427 0.120513092 0.017501962 -0.006173376 Largest eigenvalues: [1] 67342453 63754033 60881660 58716735 57926063 56536263 55011066 54656585 [9] 54516927 53935285 Smallest eigenvalues: [1] 0.387625408 0.362205506 0.257718358 0.247279385 0.206357377 [6] 0.195219648 0.188117232 0.045500866 0.003735276 -1.262557776 Largest eigenvalues: [1] 68854102 63530864 60778998 59356633 58323291 56404055 55715708 55279950 [9] 54741653 54625630 Smallest eigenvalues: [1] 0.41296135 0.38172985 0.35421380 0.34992552 0.33355387 0.31326266 [7] 0.27215212 0.16163363 -0.04750187 -0.13886336 Largest eigenvalues: [1] 69230303 63705965 60894754 59507015 57739908 56248699 55373937 54827714 [9] 54457926 53885244 Smallest eigenvalues: [1] 0.36513525 0.36193873 0.34250046 0.33617873 0.33064104 0.26574666 [7] 0.14706563 0.11578097 0.09993230 -0.08604741 Largest eigenvalues: [1] 64456429 62837209 59534654 57840833 57251885 56114038 54669652 53717257 [9] 52983381 52782008 Smallest eigenvalues: [1] 0.48485933 0.42069863 0.40256858 0.35026141 0.31637754 0.31356426 [7] 0.30505936 0.05131425 -0.95163903 -2.04058040 Largest eigenvalues: [1] 69570851 64228249 60759833 59722423 58920403 57145768 55752327 55566770 [9] 55069884 54404837 Smallest eigenvalues: [1] 0.47194590 0.41309073 0.40014234 0.30010011 0.29816836 0.29024273 [7] 0.27052271 0.21007136 0.16463066 -0.06046053 Largest eigenvalues: [1] 68282255 64054315 60937099 59102480 58833402 57000556 55213628 55015420 [9] 54758449 54153609 Smallest eigenvalues: [1] 0.537597484 0.492863763 0.464689635 0.428751814 0.368095968 [6] 0.355371242 0.353818236 0.096839378 0.051521737 -0.007289211 Largest eigenvalues: [1] 68736655 63339851 60293118 59380859 57924835 56079712 55257034 54652647 [9] 54476647 53445724 Smallest eigenvalues: [1] 0.52023083 0.40615967 0.31544967 0.30963637 0.17914254 0.16709164 [7] 0.08086812 -0.03036284 -0.15910660 -1.27972192 Largest eigenvalues: [1] 68186444 64078137 61082381 59142149 58684496 57354949 55562564 55510046 [9] 54835038 54619162 Smallest eigenvalues: [1] 0.32733711 0.31082986 0.20455389 0.16333363 0.12632839 0.06093062 [7] -0.01848520 -0.11618604 -0.18585931 -0.26415818 Largest eigenvalues: [1] 67899617 63297020 60679025 58375123 58252942 56802139 55165285 55050192 [9] 54316920 53845937 Smallest eigenvalues: [1] 0.49579345 0.46459471 0.43557574 0.29234085 0.26424607 0.25963971 [7] 0.19443362 0.14473023 0.05374592 -0.72163710 Largest eigenvalues: [1] 67890755 64452171 60561760 59327590 59107234 57495625 56225733 54928055 [9] 54882863 54310321 Smallest eigenvalues: [1] 0.29852432 0.28351856 0.26586747 0.26402343 0.25586058 0.17655433 [7] 0.09652747 0.09495147 0.04924579 -0.11484047 Largest eigenvalues: [1] 67176787 63092420 60105910 58462954 57801828 56379539 54925036 54616274 [9] 54313983 53835274 Smallest eigenvalues: [1] 0.32836460 0.30499321 0.28355256 0.15258405 0.08491753 0.04164644 [7] -0.03807749 -0.08645150 -0.31818180 -0.60286359 Largest eigenvalues: [1] 67059557 62783770 60072832 58359237 58099412 56733309 55503191 54400056 [9] 54074523 53550498 Smallest eigenvalues: [1] 0.5257537 0.4932001 0.4632578 0.4131117 0.3733560 0.3715883 [7] 0.3697265 0.1941975 0.1067847 -0.3125859 Largest eigenvalues: [1] 68245429 63676309 60691629 58838523 58231211 56609586 54765110 54725448 [9] 54443838 53699365 Smallest eigenvalues: [1] 0.49046269 0.43748772 0.43342034 0.39623538 0.33814282 0.30552026 [7] 0.26359161 0.23405429 0.05289384 -0.13666884 Largest eigenvalues: [1] 69342463 63610162 60345885 60276266 57528439 55826900 55415827 54705205 [9] 54245417 53804470 Smallest eigenvalues: [1] 0.50868109 0.45056586 0.40874208 0.38956552 0.29551761 0.27297426 [7] 0.27077064 0.15408753 0.07846835 -0.01533921 Largest eigenvalues: [1] 69087481 64070081 61056296 59878754 58356241 56597491 55790881 55671557 [9] 54620406 54301427 Smallest eigenvalues: [1] 0.42850410 0.36611559 0.33661665 0.31296854 0.26844534 0.23802056 [7] 0.18473688 0.17913251 0.04415692 -0.02595416 Largest eigenvalues: [1] 67781283 63135575 60337201 58872838 57957242 56478162 54875613 54624185 [9] 54429774 53746833 Smallest eigenvalues: [1] 0.4108388 0.4003424 0.3775023 0.3625002 0.3052690 0.2909786 [7] 0.1950105 0.1336236 0.1032076 -0.4821160 Largest eigenvalues: [1] 68976083 63873456 61226796 59859088 58056251 56486218 55790005 55228703 [9] 54987220 54315881 Smallest eigenvalues: [1] 0.37882266 0.34028489 0.28705626 0.26170249 0.24619553 0.17425355 [7] 0.16158144 0.11732694 -0.04609683 -1.10893350 Largest eigenvalues: [1] 67749864 63616492 60111534 59026426 58182680 56305287 55448915 54968516 [9] 54279533 54019571 Smallest eigenvalues: [1] 0.4798319 0.4454601 0.3938914 0.3606507 0.3057518 0.2902040 [7] 0.2477077 0.2428912 0.1587395 -2.7392064 Largest eigenvalues: [1] 68044711 63274631 60667276 58839697 57836413 55999262 54582860 54362046 [9] 54326062 53505627 Smallest eigenvalues: [1] 0.46417098 0.43023522 0.42322877 0.40789499 0.36801713 0.21655523 [7] 0.16262262 0.10214514 0.05279603 -0.15676510 Largest eigenvalues: [1] 65712904 63717841 59689605 58626942 57841128 56553391 54756752 54320370 [9] 53704723 52984965 Smallest eigenvalues: [1] 0.55106524 0.54802720 0.50303284 0.44560899 0.34724666 0.33847477 [7] 0.31636077 0.30070953 0.21958703 -0.01086172 Largest eigenvalues: [1] 69221438 63380157 60330865 59337338 57836217 55564543 55231978 54676586 [9] 54179991 53677315 Smallest eigenvalues: [1] 0.43012514 0.41874317 0.39875714 0.34869051 0.31249787 0.29565942 [7] 0.22504537 0.20714737 0.04095898 -0.08909213 Largest eigenvalues: [1] 66441008 62507192 59569895 58727718 57046833 55532876 54601424 54320194 [9] 54169040 53495582 Smallest eigenvalues: [1] 0.40916664 0.36614031 0.30417047 0.29798446 0.26853259 0.24112690 [7] 0.22265145 0.02821519 -0.33540255 -0.83608679 Largest eigenvalues: [1] 67482497 64304200 60871376 59604191 57979890 56399350 55363758 54980386 [9] 54889828 53684091 Smallest eigenvalues: [1] 0.4547845 0.4300995 0.4189329 0.3504711 0.3441597 0.3419499 [7] 0.3155616 0.2645905 0.1773215 -0.3105974 Largest eigenvalues: [1] 68213336 63662094 60163718 60110510 57418897 55691108 55628095 54332052 [9] 54166569 53192626 Smallest eigenvalues: [1] 0.48390015 0.42550764 0.42173499 0.39036001 0.35219322 0.27956112 [7] 0.21300613 0.19468117 0.06588118 -1.76354249 Largest eigenvalues: [1] 69639245 63716058 61190746 60264969 57942840 56544018 56022362 55360739 [9] 54931729 54489852 Smallest eigenvalues: [1] 0.5298590 0.5069894 0.4662907 0.4047080 0.3812657 0.2823521 [7] 0.2457399 0.2298946 0.0538540 -0.1068527 Largest eigenvalues: [1] 67888953 63530478 60194116 59087938 58257303 56498519 55072814 54652178 [9] 54642283 53888628 Smallest eigenvalues: [1] 0.4566794 0.4446798 0.3696830 0.3068844 0.2957746 0.2673373 [7] 0.2383926 0.1906433 0.1005098 -0.1087566 Largest eigenvalues: [1] 68696523 63781110 61156342 60096574 58406416 56793309 56197309 55791804 [9] 54928720 54785650 Smallest eigenvalues: [1] 0.25249009 0.23245851 0.22627027 0.18396258 0.01163844 -0.07939703 [7] -0.09495438 -0.58986388 -0.66825005 -1.70776729 Largest eigenvalues: [1] 69485490 62924798 60607100 59499719 57273861 56176941 55635130 54463270 [9] 54436525 53405039 Smallest eigenvalues: [1] 0.50272694 0.40052646 0.37716362 0.35186956 0.29382745 0.21145639 [7] 0.19738354 0.18916578 -0.02930844 -0.43794715 Largest eigenvalues: [1] 66900119 64026035 60284963 58804417 58524095 56805535 55409122 54693253 [9] 54533074 54264585 Smallest eigenvalues: [1] 0.63739465 0.57175472 0.55022995 0.50560296 0.44949819 0.39750131 [7] 0.35224521 0.34635449 0.07455013 -3.22365343 Largest eigenvalues: [1] 68852866 63350712 60343595 59684610 57920927 56247034 55294411 54765593 [9] 54572809 53855816 Smallest eigenvalues: [1] 0.5207391 0.5142735 0.4861362 0.4029976 0.3511577 0.3455516 [7] 0.2927575 0.1394520 0.1170988 -0.7762447 Largest eigenvalues: [1] 69889954 63881345 60843346 60006099 58474527 56689224 55982669 55163124 [9] 55091285 54106856 Smallest eigenvalues: [1] 0.46135243 0.42983944 0.42809203 0.36286342 0.28613569 0.22629540 [7] 0.21359433 0.16522174 0.05703338 -0.59080377 Largest eigenvalues: [1] 67994672 64291231 60864099 59518830 57955202 56463691 55335853 55208964 [9] 54532483 54335958 Smallest eigenvalues: [1] 0.5213761 0.5207476 0.5128386 0.4979757 0.4749098 0.4695813 [7] 0.4001223 0.3385715 0.1582069 -0.1607803 Largest eigenvalues: [1] 69167679 63324840 60634900 59608886 57250170 55517239 55401924 54769634 [9] 54149388 54007453 Smallest eigenvalues: [1] 0.25856838 0.24665044 0.24489504 0.23235943 0.19930672 0.15852512 [7] 0.13717906 0.01666857 -0.02776673 -0.50285010 Largest eigenvalues: [1] 65986973 62143773 59465511 57755233 57506666 56218883 54879872 53946852 [9] 53365903 53226171 Smallest eigenvalues: [1] 0.58714210 0.47006647 0.34736291 0.34421435 0.34005165 0.19490583 [7] 0.17862964 0.15453040 0.01972939 -0.11823883 Largest eigenvalues: [1] 66552103 62658163 59908456 57889779 57555281 56115107 54572919 54339424 [9] 53874322 53495371 Smallest eigenvalues: [1] 0.5302539 0.5223155 0.4865758 0.4796674 0.3714350 0.3429008 [7] 0.2921189 0.1653057 0.1246505 -0.1421293 Largest eigenvalues: [1] 67206999 63986993 60655200 58667163 58406358 57064499 55221359 55039279 [9] 54207721 54021999 Smallest eigenvalues: [1] 0.43097740 0.36119222 0.35838787 0.28543899 0.27788424 0.21188469 [7] 0.18678654 0.08748722 0.01695237 -0.05088439 Largest eigenvalues: [1] 66617876 63924570 60584731 58779846 58212317 57034539 55294458 54808089 [9] 54062145 53805637 Smallest eigenvalues: [1] 0.47416793 0.44683285 0.40797109 0.33429500 0.26514514 0.23089591 [7] 0.19579139 0.08867551 -0.20059096 -0.48923356 Largest eigenvalues: [1] 66466941 63774615 60616645 58536259 58286395 56652530 55324124 55017871 [9] 54287375 53796901 Smallest eigenvalues: [1] 0.4432598 0.4253506 0.4041308 0.3716867 0.3505375 0.3274370 [7] 0.1997087 0.1666967 0.1479205 -2.4286655 Largest eigenvalues: [1] 68211517 62942820 59945834 59031554 57586094 55651543 54828102 54401591 [9] 54258548 53568387 Smallest eigenvalues: [1] 0.5044178 0.4773572 0.4551132 0.3889971 0.3423413 0.3131601 [7] 0.2767880 0.2192109 0.1183464 -0.0288965 Largest eigenvalues: [1] 67859339 63739809 60699298 59192003 58429059 56986299 55249817 55036646 [9] 54884982 54099007 Smallest eigenvalues: [1] 0.58036095 0.56370544 0.50840478 0.45951838 0.37749878 0.30823749 [7] 0.29143405 0.18325271 0.08676596 -0.04918784 Largest eigenvalues: [1] 68221607 64100266 60397961 59601221 58770486 56798370 56085484 55384020 [9] 54930181 54530510 Smallest eigenvalues: [1] 0.56334307 0.42905597 0.39833222 0.37102248 0.31738319 0.31435292 [7] 0.29634007 0.19169255 0.03645459 -0.62273629 Largest eigenvalues: [1] 69274645 64097060 60563961 59517089 58599951 56519908 55811457 55581030 [9] 54561710 54529193 Smallest eigenvalues: [1] 0.4627699 0.4295349 0.3676500 0.3326736 0.2583977 0.2157022 [7] 0.1785384 0.1710148 -0.1107456 -0.1404629 Largest eigenvalues: [1] 66685059 64050620 60533397 59359343 58519099 57440118 55913902 55364086 [9] 54458645 54263029 Smallest eigenvalues: [1] 0.31768345 0.31519332 0.24220521 0.23307781 0.17096665 0.13534950 [7] 0.02486383 -0.09316573 -0.15928319 -0.85290381 Largest eigenvalues: [1] 68939046 64548078 61671751 60419034 58333971 56774926 56008016 55679848 [9] 55058223 54504138 Smallest eigenvalues: [1] 0.40452432 0.34448307 0.28112042 0.23524077 0.15734818 0.14537830 [7] 0.13758854 0.05135597 -0.21189954 -3.52815528 Largest eigenvalues: [1] 66756008 62872871 60374397 58027024 57595475 56590070 54984280 54443287 [9] 53711410 53458626 Smallest eigenvalues: [1] 0.5210834 0.4889263 0.4083012 0.3784572 0.3563570 0.3036359 [7] 0.2738420 0.2694066 -0.1280490 -0.3505927 Largest eigenvalues: [1] 70237578 63605156 60827521 60062509 57655145 55983684 55850525 55149277 [9] 54377280 54173550 Smallest eigenvalues: [1] 0.5204368 0.5194599 0.5033069 0.4891839 0.4806208 0.4400889 [7] 0.2759457 0.2096628 0.1496838 -0.0593476 Largest eigenvalues: [1] 68136620 63159699 59482451 59326600 57198409 55205953 54939704 54379928 [9] 53815445 53375852 Smallest eigenvalues: [1] 0.38969161 0.38315464 0.36131414 0.34546239 0.33726275 0.27192500 [7] 0.03590317 -0.19033606 -0.69665955 -0.98629475 Largest eigenvalues: [1] 69127822 62617158 60247437 59253959 57788972 56368379 55060311 54407406 [9] 54188420 53370453 Smallest eigenvalues: [1] 0.34593493 0.30201249 0.29565687 0.29215138 0.25012501 0.19698128 [7] 0.17561478 0.07455176 -0.03460790 -1.31420064 Largest eigenvalues: [1] 67926262 63820612 60472580 59447779 58856238 57209177 56077264 55339617 [9] 54864131 54599225 Smallest eigenvalues: [1] 0.40966603 0.37720460 0.36806271 0.31562833 0.30590466 0.28104597 [7] 0.21621038 0.19218372 -0.09152827 -0.14372583 Largest eigenvalues: [1] 67632840 63462449 60435860 59326959 58221857 56478398 55437687 55078080 [9] 54884132 54053719 Smallest eigenvalues: [1] 0.36027296 0.32639957 0.31594191 0.29757818 0.29337772 0.27743922 [7] 0.17998490 0.16819169 0.05842588 -0.19578529 Largest eigenvalues: [1] 67124105 63790202 60644324 59343422 58073543 56650578 54996738 54942811 [9] 54638317 53462731 Smallest eigenvalues: [1] 0.486770243 0.420912309 0.413817556 0.376600861 0.344528465 [6] 0.340294688 0.329593280 0.269510305 0.002281095 -0.004255621 Largest eigenvalues: [1] 66111632 62849630 59951962 57973663 57331027 56123645 54713321 53881129 [9] 53341270 53125909 Smallest eigenvalues: [1] 0.3883417489 0.3491045749 0.3067350792 0.2550572622 0.2265003420 [6] 0.2199862098 0.1553286948 0.0944263835 0.0008516599 -0.0638146778 Largest eigenvalues: [1] 66710781 63364037 60030581 58623604 57397682 56775190 54946210 54786644 [9] 53842643 53490967 Smallest eigenvalues: [1] 0.5637528 0.5419897 0.4428667 0.4052040 0.3920259 0.3795125 [7] 0.3319619 0.2212743 0.2018714 -0.4536793 Largest eigenvalues: [1] 67394205 62967051 60004731 58415027 57965492 56338287 54606630 54558045 [9] 54393535 53694973 Smallest eigenvalues: [1] 0.50889819 0.50369422 0.46528257 0.39200883 0.38769059 0.26292213 [7] 0.22940326 0.16108537 0.07277549 -0.14992666 Largest eigenvalues: [1] 67668353 63392549 60736805 59060604 57668846 56301989 55021685 54888573 [9] 54477546 53594814 Smallest eigenvalues: [1] 0.331786777 0.319749116 0.295548008 0.221645425 0.069216329 [6] 0.068289592 -0.006212043 -0.088377661 -0.341037488 -0.657373652 Largest eigenvalues: [1] 66966124 62073207 59971408 58686235 56824330 55470968 54421775 54054261 [9] 53909143 53196207 Smallest eigenvalues: [1] 0.30590336 0.28922804 0.10887320 0.09883375 0.05815187 0.05679819 [7] 0.02731384 -0.23627284 -0.35662313 -7.93883679 Largest eigenvalues: [1] 67240229 63723331 60637707 58604015 58562130 56715067 55386736 54744412 [9] 54712574 53862751 Smallest eigenvalues: [1] 0.55174974 0.53528330 0.53228765 0.46254542 0.41690105 0.39356970 [7] 0.36313971 0.32095499 0.26018024 -0.08127162 Largest eigenvalues: [1] 67404684 63163572 59827497 58974898 57900966 56223716 54729504 54556207 [9] 54117681 53059642 Smallest eigenvalues: [1] 0.43075575 0.39124024 0.32650863 0.29738639 0.23100032 0.16361357 [7] 0.12570836 0.09121337 0.03889566 -0.12293219 Largest eigenvalues: [1] 66480973 62450578 59377719 57906683 57901375 56120410 54868064 54093249 [9] 53705747 53078279 Smallest eigenvalues: [1] 0.3333896 0.2936180 0.2833411 0.2768416 0.2739611 0.2350702 [7] 0.1751081 0.0591253 -0.1704813 -0.5133930 Largest eigenvalues: [1] 67500055 62932190 59801651 58406708 58231666 56561117 54788438 54326507 [9] 53816784 52926055 Smallest eigenvalues: [1] 0.43979422 0.42807794 0.40683904 0.34816100 0.32690375 0.27245654 [7] 0.25250254 0.15518672 0.09406743 -0.25774783 Largest eigenvalues: [1] 69053542 63695355 60709179 59919692 58039180 56399379 55695709 55307966 [9] 54650301 54282431 Smallest eigenvalues: [1] 0.485980102 0.461631430 0.431649288 0.336399157 0.322719495 [6] 0.315954722 0.291855992 0.119460054 -0.003092713 -1.478181867 Largest eigenvalues: [1] 66015547 62561504 59757316 57760920 57398464 56001216 54654940 54188613 [9] 53656815 53302225 Smallest eigenvalues: [1] 0.4779414 0.4559354 0.4332499 0.3491799 0.3285141 0.2913935 [7] 0.2784286 0.2572038 0.1390236 -0.4300199 Largest eigenvalues: [1] 68887680 63229451 60326789 59821294 57507402 55639506 55337575 54602750 [9] 53977024 53448250 Smallest eigenvalues: [1] 0.49978400 0.49573154 0.49325425 0.36725057 0.28500298 0.27938672 [7] 0.17906587 0.09536708 0.01228579 -1.07660768 Largest eigenvalues: [1] 67745428 63773297 60124556 59871277 57945368 55964544 55237248 54997079 [9] 54620604 53778960 Smallest eigenvalues: [1] 0.47488027 0.45723033 0.43219627 0.33945542 0.32413592 0.31755705 [7] 0.25362649 0.14262922 -0.09124982 -3.69536574 Largest eigenvalues: [1] 69125412 63355495 60005174 59769902 57502985 55639155 55536923 55318360 [9] 54459464 54028735 Smallest eigenvalues: [1] 0.3356955 0.3280880 0.2647143 0.2372037 0.1697187 0.1693662 [7] 0.1498740 0.1486174 -0.1842534 -0.3377884 Largest eigenvalues: [1] 69216772 62757763 60465658 59781037 57255711 55690319 55533579 54220016 [9] 54066408 53324171 Smallest eigenvalues: [1] 0.47580857 0.45699867 0.43824024 0.36566893 0.34206670 0.30629217 [7] 0.25846419 0.20816451 0.03757381 -0.63351762 Largest eigenvalues: [1] 67834927 62774763 59447134 59165436 57153056 55638065 54799999 54349132 [9] 53957783 52992106 Smallest eigenvalues: [1] 0.346771178 0.316619816 0.287468248 0.219000071 0.206334503 [6] 0.192261995 0.130587622 0.073194629 0.040934389 -0.005896099 Largest eigenvalues: [1] 66232252 63351333 60660963 58299984 58202038 56786341 54989687 54473253 [9] 54051326 53414650 Smallest eigenvalues: [1] 0.4912986 0.3952202 0.3814746 0.3488784 0.2959755 0.2849064 [7] 0.2793402 0.1879415 -0.4514353 -1.9625740 Largest eigenvalues: [1] 69056905 63857148 60819086 60015951 58689176 57023941 55787217 55280506 [9] 55024017 54181478 Smallest eigenvalues: [1] 0.4445259 0.4026287 0.3803546 0.3427683 0.2856042 0.2466100 [7] 0.1583362 0.1428188 -0.1360472 -1.4697316 Largest eigenvalues: [1] 69261232 63408985 60406547 59322023 58008720 56470992 55321070 55034576 [9] 54567249 54403317 Smallest eigenvalues: [1] 0.4591023 0.4479664 0.4125607 0.3818001 0.3524783 0.3408688 [7] 0.3404251 0.3223423 0.1867043 -0.0276775 Largest eigenvalues: [1] 68295806 63531261 60667153 59155443 58097175 56599858 54966039 54688705 [9] 54520366 53663393 Smallest eigenvalues: [1] 0.4709050 0.4213692 0.3380607 0.2978260 0.2740392 0.2646879 [7] 0.2214487 0.1148222 0.0240219 -0.1503111 Largest eigenvalues: [1] 65108933 63545497 60397690 58762416 57265915 56710340 55513448 54495293 [9] 53944267 53343764 Smallest eigenvalues: [1] 0.4659294 0.4509652 0.4467306 0.3837532 0.3815056 0.2303242 [7] 0.1827741 0.1626047 0.1445543 -0.2696805 Largest eigenvalues: [1] 68762246 63285103 60373690 59612562 57299987 55896714 55443082 54278679 [9] 53991150 53176194 Smallest eigenvalues: [1] 0.4130568 0.3937870 0.3540565 0.3334333 0.3153374 0.2656520 [7] 0.2142584 0.2043796 0.1956920 -0.4876508 Largest eigenvalues: [1] 67851308 63309761 59892240 58764935 58118804 56243355 54976757 54554690 [9] 54245116 53881182 Smallest eigenvalues: [1] 0.45316964 0.43292136 0.39861938 0.37706568 0.35216640 0.33946179 [7] 0.28631334 0.11490725 -0.06549247 -0.22008776 Largest eigenvalues: [1] 67332033 62548035 59512894 58558878 57261798 55680329 54397932 54227645 [9] 53533525 52608895 Smallest eigenvalues: [1] 0.5746084 0.5682279 0.5399228 0.4946502 0.4557642 0.4391461 [7] 0.3905207 0.3149719 0.2419134 -0.6311985 Largest eigenvalues: [1] 68151008 63470656 59643043 59505941 57728660 55577923 55188416 54840522 [9] 54012822 53435845 Smallest eigenvalues: [1] 0.3768203 0.3434568 0.3126892 0.2950423 0.2544676 0.2255260 [7] 0.1743748 0.1322102 0.1145547 -0.0961093 Largest eigenvalues: [1] 65712751 62698276 59831129 57728718 57610849 56089067 54497838 54022855 [9] 53395013 52868310 Smallest eigenvalues: [1] 0.4852878 0.4304419 0.4118543 0.3411607 0.3038525 0.2995367 [7] 0.2914871 0.1188802 0.1060944 -1.3614202 Largest eigenvalues: [1] 68698349 63559586 60137020 59527629 58468102 56630664 55393651 55019879 [9] 54408631 53559306 Smallest eigenvalues: [1] 0.40513875 0.32228698 0.20760785 0.08278121 0.07702146 -0.11317236 [7] -0.11620439 -0.21119055 -0.22898326 -0.78761168 Largest eigenvalues: [1] 69539785 63706416 60579101 59917096 57744039 56123245 55772537 55163401 [9] 54940126 54247446 Smallest eigenvalues: [1] 0.44740360 0.41517168 0.34890028 0.31478864 0.31055619 0.30083396 [7] 0.18983695 0.16786851 0.03759635 -0.11236091 Largest eigenvalues: [1] 68242810 64109695 60999037 58471536 58103312 56620391 54818470 54690284 [9] 54457817 54089293 Smallest eigenvalues: [1] 0.50054299 0.46327774 0.42029263 0.30535303 0.28293509 0.27114140 [7] 0.25601392 0.25529800 0.14855946 -0.08291632 Largest eigenvalues: [1] 68900162 63133721 60207133 59639781 57448509 55841760 55421997 54651878 [9] 54535198 53809789 Smallest eigenvalues: [1] 0.293757386 0.276471050 0.275218610 0.269484817 0.236108237 [6] 0.224047966 0.138025746 0.004741941 -0.036013199 -0.353486436 Largest eigenvalues: [1] 66165437 62315372 59500547 58598045 57156983 55461878 54231739 54036165 [9] 53945915 52624723 Smallest eigenvalues: [1] 0.4850139 0.4514526 0.4437194 0.4253488 0.3793953 0.3006255 [7] 0.2667503 0.2557637 0.0299274 -0.1443655 Largest eigenvalues: [1] 67513769 63372692 60105520 59184759 57382971 55785918 54909098 54523552 [9] 54202915 53553967 Smallest eigenvalues: [1] 0.46381824 0.46247489 0.40969333 0.36169458 0.34140814 0.32574838 [7] 0.32124210 0.30876319 0.07176867 -0.25426278 Largest eigenvalues: [1] 68353520 62943922 60224341 59346588 57701510 56120219 55048774 54580258 [9] 54200269 53504580 Smallest eigenvalues: [1] 0.46517982 0.44353266 0.42161907 0.41404655 0.38660814 0.34034229 [7] 0.28858964 0.25333331 0.06548184 -0.03590323 Largest eigenvalues: [1] 67631864 62609567 59563041 59442309 56682136 55006488 54700611 53950109 [9] 53220431 52800842 Smallest eigenvalues: [1] 0.49972925 0.41066026 0.37879492 0.37387974 0.32384214 0.28792519 [7] 0.24825119 0.22821467 -0.09198361 -0.25175615 Largest eigenvalues: [1] 66485856 63453702 59946325 58190615 58138205 56331349 54857692 54257828 [9] 54042639 53589507 Smallest eigenvalues: [1] 0.38236950 0.36252778 0.35518183 0.32109615 0.31132048 0.12973617 [7] 0.06858247 0.05588445 0.01891915 -1.54063118 Largest eigenvalues: [1] 67640788 63113247 60357375 59537122 57211823 55513741 55020230 54576960 [9] 54342418 53637604 Smallest eigenvalues: [1] 0.37626169 0.37454948 0.34151930 0.33883409 0.22495147 0.17039998 [7] 0.09780854 -0.01694977 -0.03569648 -0.07035893 Largest eigenvalues: [1] 68825265 63944158 61224766 59872223 57912496 56360597 55451368 54831289 [9] 54579134 54048424 Smallest eigenvalues: [1] 0.4028121 0.3654165 0.3442723 0.3251275 0.2734337 0.2619761 [7] 0.1808446 0.1716327 0.1350898 -0.2098837 Largest eigenvalues: [1] 67044132 63573216 60060729 58849598 57824055 56318506 54778629 54704382 [9] 54438820 53551248 Smallest eigenvalues: [1] 0.37152193 0.33571232 0.33042411 0.30923594 0.28258308 0.27769724 [7] 0.20850121 0.09408740 0.02577425 -1.21695942 Largest eigenvalues: [1] 68871626 63371527 60425725 58927158 57895211 56213067 54769140 54695561 [9] 54109213 53671082 Smallest eigenvalues: [1] 0.5677888 0.5536590 0.4428736 0.4323306 0.4280742 0.3636788 [7] 0.2196662 0.1740491 0.1077036 -0.6101697 Largest eigenvalues: [1] 67937695 63314232 60171600 58781868 58138257 56413155 54756651 54701341 [9] 54570676 53518915 Smallest eigenvalues: [1] 0.49809300 0.44337765 0.42807016 0.41802416 0.34540485 0.33412024 [7] 0.31144208 0.23798913 0.18562467 -0.05492108 Largest eigenvalues: [1] 68062421 63697796 60593136 59552228 58234918 56506804 55299233 55133074 [9] 54950037 54059247 Smallest eigenvalues: [1] 0.530591237 0.437449000 0.374083324 0.370243806 0.326711207 [6] 0.310179887 0.274516916 0.242786647 0.004471943 -0.238329279 Largest eigenvalues: [1] 67968475 62832019 59973366 58829103 57978083 56366358 54748601 54636909 [9] 54520714 53413307 Smallest eigenvalues: [1] 0.32599051 0.31399632 0.28705203 0.27001397 0.26717055 0.25506547 [7] -0.08922359 -0.15344583 -0.62533560 -1.35547096 Largest eigenvalues: [1] 68987267 63274815 60374122 58473577 57658601 56222886 55061467 54340630 [9] 54032886 53980107 Smallest eigenvalues: [1] 0.42160650 0.35904724 0.33444561 0.32658770 0.26567538 0.24531821 [7] 0.24250461 0.14482566 0.06342946 -0.13186043 Largest eigenvalues: [1] 67791964 62743910 60137863 58548149 57284572 56087195 54318484 54205844 [9] 54186618 53530986 Smallest eigenvalues: [1] 0.6836037 0.6217672 0.5978494 0.5498190 0.5083277 0.4399588 [7] 0.4095982 0.3863816 0.0622130 -1.1377070 Largest eigenvalues: [1] 68652716 63570369 60406762 59669134 57551189 55869989 55543487 54534804 [9] 54244071 53530981 Smallest eigenvalues: [1] 0.5047807 0.4994762 0.4122991 0.4029489 0.3798612 0.3150421 [7] 0.3134479 0.0657160 0.0108828 -0.6921051 Largest eigenvalues: [1] 68358978 62742148 59501161 59430063 57141470 55241072 55172982 54676178 [9] 53821392 53740363 Smallest eigenvalues: [1] 0.3763180 0.3507675 0.3493824 0.2961508 0.2739005 0.1557431 [7] 0.1302856 0.1261891 -0.2716968 -0.4572453 Largest eigenvalues: [1] 67180795 62911076 60073112 58386807 58112446 56674710 55161103 54807199 [9] 54282991 54180180 Smallest eigenvalues: [1] 0.51825678 0.50858523 0.42941099 0.42306856 0.39313864 0.22992365 [7] 0.22205427 0.19883580 0.19600634 -0.02382812 Largest eigenvalues: [1] 68181934 63145992 59659215 58919826 57725549 55927573 54839037 54640696 [9] 54068664 53756894 Smallest eigenvalues: [1] 0.4633487 0.4089110 0.3756067 0.3143089 0.3023882 0.1936310 [7] 0.1726981 -0.1575451 -0.4906537 -0.5769257 Largest eigenvalues: [1] 64955854 62161712 58988272 57262286 57254612 55405918 54277190 53296123 [9] 53026158 52479693 Smallest eigenvalues: [1] 0.39552453 0.37047145 0.36670792 0.24629472 0.23971954 0.14586112 [7] 0.13673154 -0.04348396 -0.15668267 -0.56399889 Largest eigenvalues: [1] 68298698 63929417 61040720 60052672 57819846 55931852 55771931 55236090 [9] 54607004 54270295 Smallest eigenvalues: [1] 0.42446653 0.39159520 0.35423284 0.34430443 0.29714359 0.25938481 [7] 0.25180424 0.14552813 0.09512778 -0.11624616 Largest eigenvalues: [1] 66032737 62563711 59881113 57503525 57406172 55800232 54184552 53762312 [9] 53352452 52950988 Smallest eigenvalues: [1] 0.3832133 0.3489829 0.3068655 0.3048139 0.3000095 0.2789882 [7] 0.1540770 0.1416989 -0.2099711 -0.9700794 Largest eigenvalues: [1] 69517741 64405677 61410171 60407288 58116706 56294448 56093023 55293185 [9] 55015539 54576537 Smallest eigenvalues: [1] 0.2836505 0.2547205 0.2507809 0.2224711 0.2145461 0.1984757 [7] 0.1615289 0.1440709 -0.3590197 -0.4561003 Largest eigenvalues: [1] 68651131 62321621 59771441 58764079 57191412 55822610 54611615 54390949 [9] 54094265 53366955 Smallest eigenvalues: [1] 0.3708670 0.3635761 0.3495319 0.2979047 0.2372318 0.1643570 [7] 0.1465032 -0.1035248 -0.1314490 -0.2417842 Largest eigenvalues: [1] 67694000 64053819 60958185 58740855 58541042 57108237 55440717 54945849 [9] 54360874 54250904 Smallest eigenvalues: [1] 0.44880820 0.42050503 0.31156625 0.26309513 0.23900131 0.20363458 [7] 0.19989044 0.11729259 -0.07132550 -0.09552985 Largest eigenvalues: [1] 66653118 62878353 60197566 58079952 57874826 55943823 54964024 54326527 [9] 53833988 53738221 Smallest eigenvalues: [1] 0.448244881 0.404920565 0.362042597 0.307030662 0.301790021 [6] 0.258899783 0.160408036 0.043616490 -0.003838654 -0.530364133 Largest eigenvalues: [1] 69203780 63421071 60736407 59956557 57971693 56633540 55646901 54851995 [9] 54646063 53799205 Smallest eigenvalues: [1] 0.30832109 0.30290703 0.29744492 0.28623086 0.24144231 0.17139600 [7] 0.15012809 0.08034095 0.04922354 -0.24868645 Largest eigenvalues: [1] 67646850 63156763 60201264 58451285 58445884 56754989 55088177 54791549 [9] 54261161 54138415 Smallest eigenvalues: [1] 0.45065556 0.43737500 0.38831661 0.35646101 0.29493733 0.18030761 [7] 0.12602206 0.09632597 -0.11693194 -0.18091574 Largest eigenvalues: [1] 67624081 63637872 60533553 59485109 58297720 56598346 55453947 55253931 [9] 54955942 54048958 Smallest eigenvalues: [1] 0.41784367 0.32521033 0.31102864 0.26715289 0.26584775 0.22800509 [7] 0.22498055 0.10782533 0.04786251 -0.12939108 Largest eigenvalues: [1] 70302812 64179176 61383662 60838684 58293156 56571291 56280951 55912332 [9] 54649619 54607514 Smallest eigenvalues: [1] 0.393649688 0.372842841 0.354945582 0.349008816 0.328542169 [6] 0.317043129 0.184946141 0.007390064 -0.783130531 -1.948406149 Largest eigenvalues: [1] 67450969 62758798 59591944 58830869 57704911 55553369 54877964 54530648 [9] 54102733 53680829 Smallest eigenvalues: [1] 0.46860713 0.46239686 0.45295201 0.44201698 0.44193431 0.43672782 [7] 0.26643439 0.21654264 0.21229470 -0.04520859 Largest eigenvalues: [1] 68102872 62937716 60344309 58652360 57371733 55660525 54646250 54384382 [9] 54351567 53517245 Smallest eigenvalues: [1] 0.49758394 0.45560524 0.37870836 0.34423149 0.34030691 0.34000913 [7] 0.33840585 0.30264441 0.08925985 -0.16088976 Largest eigenvalues: [1] 68725625 63612653 60563425 59669488 58395371 56827968 55361537 55215632 [9] 54941235 54031188 Smallest eigenvalues: [1] 0.425125954 0.387635306 0.341521915 0.311202876 0.239901374 [6] 0.231726547 0.085294774 0.006931304 -0.311120142 -2.225111217 Largest eigenvalues: [1] 68863164 63826591 60708603 59172030 58490436 56756964 55487968 55158893 [9] 55065146 54368408 Smallest eigenvalues: [1] 0.5416901 0.5271960 0.4258205 0.4202488 0.3494735 0.3213776 [7] 0.2880699 0.2575588 0.2019687 -0.2598267 Largest eigenvalues: [1] 67939891 62739597 60119727 59434790 57423568 55695307 55135217 54633227 [9] 54026657 53419061 Smallest eigenvalues: [1] 0.31225383 0.30544928 0.26850826 0.17986269 0.14336040 0.13030417 [7] 0.06201104 -0.03830613 -0.15659227 -0.29048895 Largest eigenvalues: [1] 67163772 63473914 60601418 58575514 58135691 56890375 55143402 54745048 [9] 54113053 53746479 Smallest eigenvalues: [1] 0.4727472 0.4691994 0.4501722 0.4028427 0.3858024 0.3290316 [7] 0.2674321 0.1979201 0.1811703 -0.2418189 Largest eigenvalues: [1] 65197422 62373019 58780215 57690399 56944712 55100278 53747463 53617162 [9] 53296019 52525406 Smallest eigenvalues: [1] 0.5063383 0.4704246 0.4204252 0.4197903 0.3184487 0.2387832 [7] 0.1757686 -0.1409839 -0.3207694 -0.6494330 Largest eigenvalues: [1] 65689191 62984871 59245209 58221885 57632471 56117723 54857213 54022418 [9] 53486398 52974100 Smallest eigenvalues: [1] 0.44124369 0.40868116 0.40222964 0.39687547 0.33409267 0.28605030 [7] 0.22890833 0.07327806 -0.06400052 -0.22477040 Largest eigenvalues: [1] 68195237 63531696 60932280 58926731 58223147 56637479 55280356 54885106 [9] 54874861 54260226 Smallest eigenvalues: [1] 0.454254871 0.329592826 0.301647363 0.271155425 0.255158375 [6] 0.244713836 0.233237724 0.199850360 -0.005549621 -0.467316118 Largest eigenvalues: [1] 67656981 63468181 60716410 59040325 58306341 57292780 55333416 54503824 [9] 54281491 53684607 Smallest eigenvalues: [1] 0.50613606 0.50381202 0.45803082 0.41468776 0.34529966 0.29451282 [7] 0.28436838 0.12874275 0.09821892 -0.47573820 Largest eigenvalues: [1] 67759726 63343574 59947532 58707569 57979512 56250118 54949616 54663768 [9] 54227219 53606373 Smallest eigenvalues: [1] 0.372309844 0.351216404 0.334377786 0.263121217 0.198661172 [6] 0.179596051 0.128893817 -0.002515832 -0.050900013 -0.254004209 Largest eigenvalues: [1] 66970250 63162098 59753706 59008547 57310481 55864711 54578655 54502447 [9] 54153270 53412254 Smallest eigenvalues: [1] 0.47426332 0.46430120 0.45889123 0.40811858 0.23946386 0.21502667 [7] 0.15522436 0.13121184 -0.02172012 -0.15090394 Largest eigenvalues: [1] 66571748 63732176 60472004 58630965 58312718 56695047 55283922 54756135 [9] 54523643 53671557 Smallest eigenvalues: [1] 0.396596029 0.336302539 0.303739109 0.300955582 0.295736212 [6] 0.260966197 0.236422764 0.001843176 -0.057501008 -0.074746393 Largest eigenvalues: [1] 66819605 63459343 60573301 59194679 57569448 57284109 55236684 54508792 [9] 53589348 53385769 Smallest eigenvalues: [1] 0.51552605 0.43666436 0.30035377 0.29591066 0.29208691 0.26076158 [7] 0.24058473 0.18602721 0.02476071 -0.23402836 Largest eigenvalues: [1] 69770509 64361611 61057088 59995823 58377931 56428145 55894330 55785766 [9] 54654906 54555726 Smallest eigenvalues: [1] 0.56470572 0.50588077 0.47947149 0.43431331 0.34032455 0.31899979 [7] 0.29135479 0.17363892 -0.03550081 -0.28290935 Largest eigenvalues: [1] 68455299 63004133 59723327 58719955 57858247 56128182 54663313 54553178 [9] 54225166 53671462 Smallest eigenvalues: [1] 0.53744992 0.51559164 0.43617141 0.40549472 0.39952799 0.35042383 [7] 0.29227735 0.26250785 0.08102647 -0.06432642 Largest eigenvalues: [1] 67391163 63194894 60062440 58089671 58081414 56383140 54877747 54588991 [9] 54216561 53565979 Smallest eigenvalues: [1] 0.5018316 0.4918023 0.4339991 0.4157014 0.3986044 0.3506516 [7] 0.2807431 0.2291521 0.0934334 -0.0584853 Largest eigenvalues: [1] 67300709 63823405 60183360 58692884 58078821 56252441 54614957 54560685 [9] 54522041 53636039 Smallest eigenvalues: [1] 0.47207251 0.36469351 0.32309107 0.26178794 0.23794596 0.23186462 [7] 0.19870700 0.05662681 -0.37153384 -0.44245137 Largest eigenvalues: [1] 68793872 63426624 60587469 59162963 58454774 56774403 55205037 55090901 [9] 54975605 54234976 Smallest eigenvalues: [1] 0.5255225 0.4883308 0.4551543 0.4514007 0.4337803 0.3867593 [7] 0.3433901 0.3216794 0.2508531 -2.9569345 Largest eigenvalues: [1] 69347666 63397312 60514697 59833624 57652962 55942988 55664629 54540927 [9] 54273996 53242716 Smallest eigenvalues: [1] 0.560753792 0.547886828 0.510229081 0.356931321 0.306964763 [6] 0.274470833 0.250072836 0.182874705 -0.001990526 -0.141899379 Largest eigenvalues: [1] 67979265 63023992 60276003 59206151 57469953 55744508 54946029 54450801 [9] 54423329 53510800 Smallest eigenvalues: [1] 0.39640059 0.38156982 0.37859740 0.34502951 0.14118752 0.13238061 [7] 0.05070692 0.03636033 -0.09169851 -0.14404358 Largest eigenvalues: [1] 67895997 62661851 60275114 58999771 57765170 55874360 54880441 54662662 [9] 54438562 53743481 Smallest eigenvalues: [1] 0.33355124 0.30084792 0.24421787 0.17078673 0.12672063 0.09061280 [7] 0.07342554 0.01751195 -0.53350167 -0.89030732 Largest eigenvalues: [1] 69108501 62890224 60229127 59963547 57767422 56345601 55697523 55112006 [9] 54752032 53900508
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.340348 | 0.677209 | 15.52464 | 0.095 | 2.288869 | 2.013395 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + steps + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
steps = steps_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_steps_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 538 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.582138894 0.534270824 0.513420139 0.471838431 0.454178749 [6] 0.452357755 0.393288732 0.113200758 -0.006292351 -0.133889058 Largest eigenvalues: [1] 65148070 60331692 57513833 56575966 54963080 53273464 52536849 51999059 [9] 51763132 50909537 Smallest eigenvalues: [1] 0.46398058 0.39857378 0.39331619 0.37421683 0.36338730 0.32369954 [7] 0.32296612 0.15405775 -0.01615417 -0.18726688 Largest eigenvalues: [1] 65365443 59982211 57005455 56300591 54952863 53026541 52524947 52464909 [9] 51458872 51418732 Smallest eigenvalues: [1] 0.61684261 0.56821037 0.47210371 0.44629476 0.41884613 0.40352989 [7] 0.35217761 0.25119561 -0.01777933 -0.02260171 Largest eigenvalues: [1] 64122964 60205133 57641181 55742245 55138462 53481183 52205342 51782133 [9] 51754441 51215694 Smallest eigenvalues: [1] 0.51802920 0.44278317 0.41322929 0.39435893 0.27396285 0.24895037 [7] 0.15988356 0.12814283 -0.02027725 -1.02468671 Largest eigenvalues: [1] 63430096 61116951 57769770 55940737 55403638 54005666 52794869 52490549 [9] 51932366 51680794 Smallest eigenvalues: [1] 0.504300412 0.459567766 0.375101290 0.285114588 0.271590294 [6] 0.249079905 0.190424226 0.004701724 -4.305062954 -21.397355310 Largest eigenvalues: [1] 63439869 59701325 56726978 55426873 54994492 53721540 52006049 51663306 [9] 51107182 50744442 Smallest eigenvalues: [1] 0.35979152 0.23292737 0.16802264 0.10782127 0.08170898 -0.35660917 [7] -0.85496108 -0.95355993 -4.62522331 -9.86603748 Largest eigenvalues: [1] 65283344 59961148 57436028 56133285 54867695 53301782 52223246 52091618 [9] 51563510 51245435 Smallest eigenvalues: [1] 0.44183621 0.40462111 0.35524045 0.30993226 0.24503424 0.22476122 [7] 0.12210689 0.09114042 0.05777706 -1.96546590 Largest eigenvalues: [1] 64463560 60747596 57381735 56142060 55769820 53970691 52847121 52108864 [9] 51826902 51528514 Smallest eigenvalues: [1] 0.49726825 0.40720772 0.35411498 0.33787783 0.32780184 0.32227653 [7] 0.22797604 0.01210434 -0.40294898 -1.17102763 Largest eigenvalues: [1] 65366604 60578524 58145310 56790936 55198690 53971974 52688634 52494451 [9] 52266766 51859224 Smallest eigenvalues: [1] 0.4920397 0.4383502 0.4284378 0.3534792 0.3144894 0.2845287 [7] 0.2798502 0.2204291 0.2004139 -1.9568552 Largest eigenvalues: [1] 65244776 60233986 57325326 56361126 55401399 53859713 52441787 52411283 [9] 52280202 51408821 Smallest eigenvalues: [1] 0.40962955 0.37548295 0.30511974 0.29634871 0.25324465 0.19755470 [7] -0.07159127 -1.07562920 -1.29689904 -2.51595934 Largest eigenvalues: [1] 64955628 59937525 56601139 56562623 54588278 52787426 52548497 52250312 [9] 51766836 51318097 Smallest eigenvalues: [1] 0.5026986 0.4713707 0.3848784 0.3323492 0.2938468 0.2310180 [7] 0.2201860 0.2159269 -0.2715102 -0.4560355 Largest eigenvalues: [1] 63971864 59877286 57293862 55884049 54757521 53247516 52297372 51843815 [9] 51716600 51110906 Smallest eigenvalues: [1] 0.45536481 0.32896107 0.29719832 0.24224524 0.22137155 0.21727199 [7] 0.09774093 0.08624682 -0.09241553 -3.87359645 Largest eigenvalues: [1] 64619204 60527206 58122772 55730758 55443362 54197920 52821484 52213299 [9] 51976204 51801919 Smallest eigenvalues: [1] 0.55306088 0.53278941 0.51247437 0.46124527 0.40592721 0.29763718 [7] 0.29088174 0.21484414 -0.02570754 -0.07793213 Largest eigenvalues: [1] 64785922 60126556 57323918 55879194 55294659 53081383 52272564 52030897 [9] 51784885 51323664 Smallest eigenvalues: [1] 0.45227127 0.36288271 0.34911706 0.34402992 0.31049747 [6] 0.28662176 0.19562599 -0.03826123 -0.62125560 -11.03690181 Largest eigenvalues: [1] 65111750 60515801 57931089 56540355 55908765 54419429 52607342 52323743 [9] 52209386 51424588 Smallest eigenvalues: [1] 0.47581333 0.43768791 0.37763536 0.31873869 0.31350395 0.30127597 [7] 0.21202479 0.16111747 0.07821737 -0.35123742 Largest eigenvalues: [1] 64325626 61342753 57571151 56351455 56291213 54409813 53980487 52392028 [9] 52174093 52034966 Smallest eigenvalues: [1] 0.5253661 0.4845086 0.3974313 0.3598291 0.2593125 0.2515001 [7] 0.2293299 0.1831083 0.1597757 -5.6348275 Largest eigenvalues: [1] 63402595 59957512 57202232 55295724 54905354 53704976 52228116 52111130 [9] 51426013 51080035 Smallest eigenvalues: [1] 0.4059256 0.4057105 0.3507398 0.2603932 0.2410954 0.2277764 [7] 0.1984418 0.1607915 -1.4570600 -6.1546804 Largest eigenvalues: [1] 64944363 59796905 57230546 56608424 54857074 53384537 52607956 52243509 [9] 51559732 50844034 Smallest eigenvalues: [1] 0.5190173 0.4664545 0.4273429 0.2802843 0.2520270 0.2505320 [7] 0.2303871 0.1175148 -0.6385760 -2.6030769 Largest eigenvalues: [1] 65109952 59585481 56872588 56043457 54997874 53350166 52230234 52026720 [9] 51945870 51294711 Smallest eigenvalues: [1] 0.2420610 0.2255808 0.1831371 0.1809581 -1.2235746 -1.3653772 [7] -3.1410483 -4.1044177 -4.2362828 -28.9074058 Largest eigenvalues: [1] 66371214 59388341 57310200 56728275 54116990 53324108 52626495 51397946 [9] 51190232 50592708 Smallest eigenvalues: [1] 0.5094121 0.4505063 0.4141838 0.3351829 0.1230920 0.0796625 [7] -0.2902778 -1.4702984 -1.6376954 -9.4512125 Largest eigenvalues: [1] 63433418 60169569 56874462 55324326 55065103 53543681 52073229 51447085 [9] 50909756 50599958 Smallest eigenvalues: [1] 0.303186030 0.292375825 0.004067745 -0.113120212 -0.137378876 [6] -0.323482728 -0.832901818 -0.988534255 -1.380347465 -2.243194540 Largest eigenvalues: [1] 66600855 60618822 57946490 57342227 55129390 53458960 53273553 53016655 [9] 51738112 51574550 Smallest eigenvalues: [1] 0.43203119 0.31957562 0.23781789 0.19365725 0.18396453 0.05542385 [7] 0.05058566 -0.01991147 -0.40707677 -3.08390338 Largest eigenvalues: [1] 65853369 60593154 57064085 56842854 55209617 53559969 52804240 52322603 [9] 52101278 51351213 Smallest eigenvalues: [1] 0.457397457 0.320457769 0.242980153 0.207149740 0.149612218 [6] 0.011288135 0.009577169 -2.026699135 -4.616648523 -6.649590643 Largest eigenvalues: [1] 63511584 59974555 57165485 55456214 54970351 53888720 52509155 51886746 [9] 51071567 50969646 Smallest eigenvalues: [1] 0.5108705 0.4763138 0.4498411 0.3954863 0.2899137 0.2800442 [7] 0.2375158 0.2154875 0.2004713 -0.6332202 Largest eigenvalues: [1] 64367888 61559209 58169235 56693481 55732368 54101490 52856923 52594194 [9] 52541862 51853392 Smallest eigenvalues: [1] 0.4384280 0.3981057 0.3757465 0.3625340 0.3061225 0.3012047 [7] 0.2125695 0.1989462 0.1115701 -0.7583390 Largest eigenvalues: [1] 64909383 61174234 58096617 56495606 56491848 54788326 53128603 52664620 [9] 52385494 51783872 Smallest eigenvalues: [1] 0.59479476 0.57035441 0.56250614 0.53616134 0.47446022 0.46023683 [7] 0.43611164 0.24748370 0.06581347 -0.16892236 Largest eigenvalues: [1] 65278986 60361879 57595282 56808569 55013132 53206151 52712570 51855195 [9] 51595625 50817231 Smallest eigenvalues: [1] 0.4270195 0.3747766 0.3380101 0.3298966 0.2549301 0.2512072 [7] 0.2473302 0.1969076 -0.6914395 -0.7782192 Largest eigenvalues: [1] 64836123 60299158 57089401 56008101 54977677 53420146 52058688 52002657 [9] 51640461 50969779 Smallest eigenvalues: [1] 0.3707116 0.3389766 0.3311187 0.2886437 0.1036859 -0.3543006 [7] -1.7384674 -3.2047003 -4.7830826 -24.1133702 Largest eigenvalues: [1] 63309190 60412405 57228517 55767639 54917999 53192534 51992913 51830170 [9] 51750055 50838745 Smallest eigenvalues: [1] 0.5417332 0.4896123 0.4644829 0.4233054 0.4160776 0.3555748 [7] 0.2914740 0.2241525 0.2123182 -0.8281746 Largest eigenvalues: [1] 63994471 59863448 57345239 55277102 54535078 53077700 52014300 51441019 [9] 51209151 51167725 Smallest eigenvalues: [1] 0.50725782 0.41934090 0.41383705 0.27729561 0.26473499 0.23669258 [7] 0.17127266 0.03307805 -0.57878346 -4.67633636 Largest eigenvalues: [1] 65209401 59456049 56827009 55725679 54816956 53240920 51939064 51701773 [9] 51507516 50728759 Smallest eigenvalues: [1] 0.3180695 0.2985033 0.2545072 0.2017825 0.1681180 0.1351658 [7] -3.8766700 -6.7190289 -14.7524683 -22.4548769 Largest eigenvalues: [1] 65861406 60532406 57961349 56826820 55219815 53522510 53087901 52841837 [9] 52092955 51999934 Smallest eigenvalues: [1] 0.38039276 0.34481875 0.25907228 0.25181584 0.24961091 0.20629351 [7] 0.03516675 -0.71212194 -0.98498885 -1.77684346 Largest eigenvalues: [1] 63291128 60576290 57848278 55876190 55127893 54513421 52852185 52534439 [9] 51507267 51205484 Smallest eigenvalues: [1] 0.2935939 0.2815964 0.2526242 0.2324772 0.1792697 -0.2801462 [7] -0.2824761 -0.6372673 -0.8530628 -1.3696133 Largest eigenvalues: [1] 65085877 59958688 57295578 56122876 55159137 53349778 52187254 52153897 [9] 51622367 51249778 Smallest eigenvalues: [1] 0.4636495 0.4241973 0.3813827 0.3650177 0.3357125 0.2721257 [7] 0.2604671 0.1814510 0.1254497 -0.6653157 Largest eigenvalues: [1] 63618500 59215353 57076645 55608960 54538361 52994120 51666115 51566125 [9] 51515881 50645429 Smallest eigenvalues: [1] 0.36652231 0.31603571 0.30783626 0.13851873 0.03389022 [6] -0.01334603 -0.19900935 -0.67484224 -37.53127421 -53.79307327 Largest eigenvalues: [1] 61202534 59118674 56207698 54922278 54195322 53011050 51880984 50910060 [9] 50188861 50018904 Smallest eigenvalues: [1] 0.37641638 0.28160544 0.27859626 0.23586849 0.13527819 0.01134310 [7] -0.04573632 -0.45534468 -2.69101621 -3.28285552 Largest eigenvalues: [1] 64969306 61160124 58300373 55738628 55645285 54314350 52544668 52063148 [9] 51756705 51512001 Smallest eigenvalues: [1] 0.45972451 0.44296116 0.39388481 0.30788031 0.29992387 0.24619009 [7] 0.04157764 -0.34971618 -0.42829049 -7.68965393 Largest eigenvalues: [1] 63054700 60658304 57455065 55580160 55501400 54207960 52569415 52142197 [9] 51433681 51039231 Smallest eigenvalues: [1] 0.39433129 0.36679916 0.31585773 0.21358950 0.21355444 0.20967491 [7] 0.18896538 0.16737422 0.15641722 -0.07897234 Largest eigenvalues: [1] 63117354 60446388 57348222 55529660 55310689 53699526 52854294 52041619 [9] 51677137 51450404 Smallest eigenvalues: [1] 0.53190929 0.52449781 0.50310948 0.42464075 0.35520278 0.33621567 [7] 0.31666149 0.25626923 0.22748197 -0.05643541 Largest eigenvalues: [1] 64921528 61126484 57810905 56702431 55673861 54077357 52841896 52665160 [9] 52439567 51872118 Smallest eigenvalues: [1] 0.44402409 0.42693470 0.29321791 0.26607362 0.25239042 0.14994960 [7] 0.04118788 -0.04611271 -0.39470826 -0.69863187 Largest eigenvalues: [1] 62465018 59542945 56247025 55450127 54488539 52757899 51905864 51575396 [9] 51059429 50281760 Smallest eigenvalues: [1] 0.4905395 0.4679585 0.4323883 0.3402013 0.3265913 0.3046923 [7] 0.2180993 0.1836426 0.1279358 -0.4123913 Largest eigenvalues: [1] 64685935 60047766 57665155 56052304 55401798 53968115 52258216 52202880 [9] 52009997 51523502 Smallest eigenvalues: [1] 0.5808287 0.5181906 0.4884345 0.3982290 0.3938184 0.3780191 [7] 0.3550720 0.3309355 0.3187282 -0.7128785 Largest eigenvalues: [1] 64606963 60711096 57811545 56277666 55802660 54242915 52451850 52276209 [9] 52250244 51371187 Smallest eigenvalues: [1] 0.29573646 0.28548900 0.13631423 0.09101294 0.04886930 0.03415961 [7] -0.02282863 -0.82249094 -1.11838746 -3.33712727 Largest eigenvalues: [1] 64589676 60226187 56738802 56347785 55388184 53393661 52622638 52322757 [9] 52267541 51292064 Smallest eigenvalues: [1] 0.384471971 0.291343405 0.262767255 0.225331121 0.177028896 [6] 0.155569637 0.111332297 -0.009455158 -1.238470055 -7.872201515 Largest eigenvalues: [1] 64109416 58895242 56559304 55894560 54075817 52357987 51815190 51352236 [9] 51100554 50050191 Smallest eigenvalues: [1] 0.4420265 0.4379181 0.4309511 0.4058506 0.3543849 0.3011116 [7] 0.2885254 0.2551085 0.2346812 -0.1523098 Largest eigenvalues: [1] 61903871 59891528 56951910 55140813 54734514 53539882 52175722 51527357 [9] 50791050 50585166 Smallest eigenvalues: [1] 0.4183948 0.4079354 0.3893765 0.3639861 0.2685296 0.2215397 [7] 0.1655500 0.1409848 -0.8635024 -3.6238826 Largest eigenvalues: [1] 66587928 60660483 57483247 56511083 55423761 53772725 52623248 52498535 [9] 51873341 51740835 Smallest eigenvalues: [1] 0.3822995 0.3349637 0.3140252 0.3121702 0.2596931 0.2378911 [7] 0.2081925 0.1764116 -0.5094574 -0.5130824 Largest eigenvalues: [1] 64674264 60844739 58311335 55890716 55696876 54346296 52850263 52536215 [9] 51867134 51617760 Smallest eigenvalues: [1] 0.63910144 0.61685112 0.58942740 0.55083323 0.49200432 0.42708875 [7] 0.37312576 0.25492659 0.07855744 -0.29657984 Largest eigenvalues: [1] 65336058 60461009 57568946 56502202 54941750 53162779 52625073 52213058 [9] 51384393 50977582 Smallest eigenvalues: [1] 0.4857895 0.4292037 0.3959083 0.3657526 0.3458585 0.3435992 [7] 0.3141451 0.1912363 0.1805988 -0.7261910 Largest eigenvalues: [1] 63247401 59893054 57035835 55228200 55061881 53445060 51770939 51733694 [9] 51211704 50961798 Smallest eigenvalues: [1] 0.4487396 0.3845477 0.3725236 0.3365801 0.2878332 0.2565840 [7] 0.2547981 0.1805501 -3.5341140 -6.1643446 Largest eigenvalues: [1] 65317504 60018953 57252415 57202693 54597809 53165302 52921615 52087658 [9] 51973519 51145378 Smallest eigenvalues: [1] 0.604535685 0.486314249 0.442001847 0.435220009 0.414558723 [6] 0.297290354 0.248239666 0.142352946 -0.003398047 -1.114340477 Largest eigenvalues: [1] 65167813 61071672 58152822 56867125 55438591 53496575 53089236 52736231 [9] 51911704 51789930 Smallest eigenvalues: [1] 0.545327466 0.519049578 0.504786705 0.451035254 0.393515566 [6] 0.358569237 0.329280561 0.279436969 0.277642076 -0.006866797 Largest eigenvalues: [1] 64319420 60700234 57722139 56156459 55835862 54557474 52950277 52138403 [9] 52020571 51475996 Smallest eigenvalues: [1] 0.45141749 0.38253218 0.37977975 0.29862668 0.25247099 0.13523288 [7] 0.06372699 -0.26592498 -0.62203637 -1.16139540 Largest eigenvalues: [1] 64946327 60677566 58167003 56495731 55173087 53604556 52799028 52550215 [9] 52175469 51877593 Smallest eigenvalues: [1] 0.5631793 0.5461064 0.4875077 0.4562461 0.3638974 0.3584800 [7] 0.3438786 0.2543562 0.1076786 -0.4530413 Largest eigenvalues: [1] 65311917 59906844 56985900 56476882 54854238 52887579 52450675 52138129 [9] 51639535 51208866 Smallest eigenvalues: [1] 0.5939966 0.5270798 0.5032330 0.4229257 0.3969222 0.3754482 [7] 0.3449907 0.3354566 0.2908666 -0.1194142 Largest eigenvalues: [1] 64259443 60517548 57668439 55916038 55456470 53745249 51805155 51766615 [9] 51643978 50728624 Smallest eigenvalues: [1] 0.4482323 0.4334117 0.3873700 0.3816662 0.3391291 0.2763107 [7] 0.2725865 0.1455238 -0.7910155 -1.2416415 Largest eigenvalues: [1] 62818285 60170130 57027997 55333910 55008869 53317013 52036779 52008368 [9] 51125093 51012129 Smallest eigenvalues: [1] 0.52338930 0.51916634 0.51802720 0.40898895 0.38106018 0.34818961 [7] 0.26314532 0.19972866 0.08942279 -0.12396346 Largest eigenvalues: [1] 62221759 59624694 56743772 55346164 54418424 53507238 51779605 51669336 [9] 50532283 50384938 Smallest eigenvalues: [1] 0.4802773 0.4500428 0.3651332 0.3532638 0.3364786 0.2986449 [7] 0.2825763 0.1524951 0.1286394 -1.6555082 Largest eigenvalues: [1] 63587639 59643610 56854613 55364657 55134545 53461920 52455268 51913882 [9] 51518403 51288009 Smallest eigenvalues: [1] 0.4750561 0.4666026 0.4491465 0.3618929 0.2969885 0.2441727 [7] 0.2265190 -0.0994749 -0.1879190 -3.8971143 Largest eigenvalues: [1] 65611200 60444404 57773103 56950411 54705607 53304939 53015738 52132293 [9] 51514878 51169591 Smallest eigenvalues: [1] 0.4990037 0.4419385 0.4303572 0.4170202 0.2810512 0.2518895 [7] 0.2435805 0.2267070 0.2183130 -0.9566458 Largest eigenvalues: [1] 64323691 60147743 57171880 56096714 55165625 53637034 52493195 52032670 [9] 51999230 51518835 Smallest eigenvalues: [1] 0.40554281 0.39307933 0.35224568 0.29881751 0.25156641 0.21184460 [7] 0.20582112 0.19764824 0.07209213 -5.25581622 Largest eigenvalues: [1] 64909369 61129126 58428614 56188950 55875786 54473679 52532312 52383440 [9] 52091219 51615600 Smallest eigenvalues: [1] 0.3922102 0.3620180 0.3268108 0.2611272 0.2529055 0.2058618 [7] 0.1975627 0.1959268 0.1217729 -2.1681830 Largest eigenvalues: [1] 65571747 60568455 57776239 56659420 55308631 53780616 52566828 52247656 [9] 52071813 51337332 Smallest eigenvalues: [1] 0.485370356 0.310864100 0.307989957 0.296572828 0.220046394 [6] 0.151461521 0.002218544 -0.895487191 -1.530775376 -1.939084785 Largest eigenvalues: [1] 62799527 59710533 56958342 55341016 54909034 53705196 52161778 52126877 [9] 51083987 50906260 Smallest eigenvalues: [1] 0.40943220 0.40923920 0.37720660 0.30750753 0.20546174 [6] 0.15602178 0.08009306 -0.03155124 -1.08163518 -17.64683617 Largest eigenvalues: [1] 65011877 59902886 56763757 56529187 55043132 53415437 52434734 51972918 [9] 51757720 51043243 Smallest eigenvalues: [1] 0.5696885 0.5200058 0.4349116 0.4035829 0.3020217 0.2704845 [7] 0.2684303 0.2512133 0.2419236 -1.4535085 Largest eigenvalues: [1] 65543313 60966032 58067480 56512064 55696669 54193156 52723471 52612508 [9] 52109418 51618272 Smallest eigenvalues: [1] 0.40096058 0.35083143 0.32859303 0.32601818 0.28127811 0.22925439 [7] 0.21195304 0.18646779 0.04865597 -2.01116212 Largest eigenvalues: [1] 65900101 59853999 57187752 56603485 54742607 53457136 52650043 52005321 [9] 51882321 51182385 Smallest eigenvalues: [1] 0.4649486 0.4568153 0.4341013 0.4080081 0.3421340 0.2834149 [7] 0.2537515 0.2349537 0.2327321 -0.3315201 Largest eigenvalues: [1] 65482613 60816554 58048249 56700024 56120910 54524195 52682598 52448386 [9] 52371316 51439683 Smallest eigenvalues: [1] 0.57068226 0.42211693 0.39747428 0.39689597 0.37707957 0.34723472 [7] 0.30803484 0.24994537 -0.01339311 -1.00383665 Largest eigenvalues: [1] 66420032 60787081 58063763 57216759 55177665 53603304 53344990 52405416 [9] 51966515 51598951 Smallest eigenvalues: [1] 0.35043920 0.31639147 0.29461594 0.26699996 0.23734749 [6] 0.14742534 0.10872102 0.08751024 -2.59212710 -12.27370009 Largest eigenvalues: [1] 63968624 60587267 57241963 55858968 55822691 54135264 52990040 52280121 [9] 52026469 51772628 Smallest eigenvalues: [1] 0.4420123 0.4357314 0.3516233 0.3426413 0.3073509 0.1924930 [7] 0.1805966 0.1346656 -0.2101050 -0.8369537 Largest eigenvalues: [1] 64995062 59643408 57089027 56521548 54277184 52755528 52508285 51475254 [9] 51245996 50417057 Smallest eigenvalues: [1] 0.51048804 0.45580278 0.39095756 0.33934288 0.33473126 0.27488713 [7] 0.27409689 -0.08764137 -0.30070317 -0.40846445 Largest eigenvalues: [1] 64662438 60857915 58215130 56351829 55531551 54074757 53011058 52349669 [9] 52283685 52163300 Smallest eigenvalues: [1] 0.52884928 0.50887246 0.44794902 0.38208101 0.36930356 0.36792831 [7] 0.33291083 0.25796138 0.01876542 -0.15594624 Largest eigenvalues: [1] 65348685 60272311 57711004 56410396 55565765 53548089 52669521 52176989 [9] 51818943 51138695 Smallest eigenvalues: [1] 0.5127975 0.4966310 0.4265970 0.4125918 0.3396251 0.2625984 [7] 0.1666105 0.1434122 0.1429262 -0.2603449 Largest eigenvalues: [1] 63718756 61355276 57782812 56375545 55305516 53859789 52852244 52287447 [9] 52261508 51912831 Smallest eigenvalues: [1] 0.4206898 0.3693107 0.3671705 0.3430170 0.3144401 0.3067283 [7] 0.1995124 0.1496485 -1.0483970 -4.6744849 Largest eigenvalues: [1] 66348277 60918782 57312876 57301833 55696792 53855646 53311968 52484686 [9] 52284560 51539900 Smallest eigenvalues: [1] 0.4335716 0.4292870 0.3543884 0.3436370 0.2887624 0.2803902 [7] -0.2580284 -1.5438717 -2.0344285 -3.4414541 Largest eigenvalues: [1] 64464386 59772236 56780844 56401755 54635512 52859047 52177665 52142265 [9] 51642181 51175340 Smallest eigenvalues: [1] 0.47922946 0.39915544 0.31475005 0.30556300 0.22686749 0.21518141 [7] 0.15850637 0.15257790 -0.06018905 -0.54311125 Largest eigenvalues: [1] 66320847 60187470 58003398 55972624 54950478 53151004 52429283 51802356 [9] 51365090 51037974 Smallest eigenvalues: [1] 0.51891681 0.49664889 0.44967162 0.37073948 0.26787808 0.20476697 [7] 0.18228656 0.17300728 0.04872697 -1.41871962 Largest eigenvalues: [1] 65598631 61340935 58159376 56931134 55986208 54373636 53563457 52922123 [9] 52463148 52169973 Smallest eigenvalues: [1] 0.365058229 0.323195797 0.300704524 0.107977260 0.091708186 [6] 0.024732365 -0.006456436 -0.066814925 -3.262360890 -24.195205360 Largest eigenvalues: [1] 63588423 59868185 57053870 55623161 54891888 53290107 52035527 51822195 [9] 51592733 51031827 Smallest eigenvalues: [1] 0.6128888 0.6005414 0.5084246 0.4647590 0.3576826 0.3320714 [7] 0.2924757 0.2352079 0.2192629 -0.0116011 Largest eigenvalues: [1] 63436488 60677069 57270421 55915963 54984756 53995230 52027421 51859383 [9] 51096587 50804366 Smallest eigenvalues: [1] 0.5429188 0.4624436 0.4484672 0.3660855 0.2859350 0.2802123 [7] -0.2252810 -3.2127511 -4.0366510 -5.3848628 Largest eigenvalues: [1] 65541444 60253537 57759824 56620516 54984595 53379433 52452385 52386620 [9] 52035835 51615543 Smallest eigenvalues: [1] 0.49384678 0.47034096 0.43110013 0.41232906 0.34579495 0.27326848 [7] 0.20258560 -0.06413743 -0.15323955 -0.42340140 Largest eigenvalues: [1] 65964400 61049404 58365404 56728603 55751973 54084782 53131516 52679136 [9] 52557385 52283067 Smallest eigenvalues: [1] 0.5178194 0.5068474 0.4966723 0.4001511 0.3682761 0.2510546 [7] 0.1937007 0.1569781 -0.8098995 -6.3224046 Largest eigenvalues: [1] 64696145 59715023 56604277 56306975 54524378 52795171 52360671 51600397 [9] 51158899 50489429 Smallest eigenvalues: [1] 0.4720272 0.4532888 0.4397408 0.3437993 0.2903784 0.2699869 [7] 0.2437427 0.2251591 0.1048481 -0.3145790 Largest eigenvalues: [1] 62874802 59644683 56751587 54942486 54725488 53265018 51928608 51313040 [9] 50887639 50504973 Smallest eigenvalues: [1] 0.201544408 0.177171397 0.144626455 0.091076722 0.004548103 [6] -0.148259185 -0.289884175 -1.575043898 -13.263955105 -79.579311945 Largest eigenvalues: [1] 66433540 60511774 57856772 56895086 55170876 54014777 52720474 52584682 [9] 52453225 51907112 Smallest eigenvalues: [1] 0.46984889 0.40535815 0.38373415 0.31445632 0.30424470 0.20821907 [7] 0.20479267 0.05942211 -0.19443799 -0.46006852 Largest eigenvalues: [1] 66295014 60055206 57477136 56958999 54760055 53148485 52942568 52550470 [9] 51745790 51682275 Smallest eigenvalues: [1] 0.4332651 0.4308242 0.3583716 0.2661786 0.2522003 0.2274065 [7] 0.2265533 0.1934069 -0.3544133 -0.7795985 Largest eigenvalues: [1] 64693328 60433656 57576991 56403901 55390048 53911610 52457037 52451694 [9] 52257789 51384720 Smallest eigenvalues: [1] 0.48280950 0.44458607 0.41297101 0.39655617 0.38245266 0.36329757 [7] 0.32586276 0.27999321 0.06975889 -6.56738212 Largest eigenvalues: [1] 64854384 59736790 57216159 55827698 54986718 53582752 51994993 51922870 [9] 51396962 50504492 Smallest eigenvalues: [1] 0.39820962 0.37804776 0.35628992 0.34829729 0.33528928 0.26461008 [7] 0.23280099 0.21468200 0.21248646 -0.09839829 Largest eigenvalues: [1] 64267814 60678050 57849347 56272576 55681003 54238859 52495499 52198944 [9] 52099877 51544577 Smallest eigenvalues: [1] 0.41887154 0.31343041 0.30939448 0.27154099 0.25444678 0.17239703 [7] 0.15336427 0.09724497 0.03846142 -4.62230843 Largest eigenvalues: [1] 64383814 60560185 57378585 55773472 55580811 53903495 52976999 52062940 [9] 51987916 51724972 Smallest eigenvalues: [1] 0.3321982 0.3099001 0.2951779 0.2923714 0.2593001 0.2387524 [7] 0.1839233 -0.4091854 -2.7724645 -32.5836795 Largest eigenvalues: [1] 62714617 60840721 57265914 55515224 55452445 53767227 52345127 52260058 [9] 51422482 51241427 Smallest eigenvalues: [1] 0.5511623 0.5137978 0.3973151 0.3698572 0.2714385 0.2601094 [7] 0.2599047 0.2129028 -0.6039468 -3.7364834 Largest eigenvalues: [1] 62892615 60256629 57165253 55863827 54884526 54202055 52521761 52276902 [9] 51146891 50914739 Smallest eigenvalues: [1] 0.4482666 0.4132002 0.4043009 0.3446677 0.3057986 0.2371929 [7] 0.2231859 0.1849645 -0.3806293 -1.2192000 Largest eigenvalues: [1] 64912913 60365249 57915971 56245247 55245503 53419182 52538053 52231428 [9] 52175101 51690647 Smallest eigenvalues: [1] 0.5429959 0.5029861 0.4617789 0.3660918 0.3307626 0.3030359 [7] 0.2941898 0.2423092 0.2093103 -1.4799506 Largest eigenvalues: [1] 65310285 61205449 58387605 56788205 56219393 54775783 53121119 52773489 [9] 52719250 52173340 Smallest eigenvalues: [1] 0.5757681 0.5170118 0.3817440 0.3695223 0.3446561 0.2849770 [7] 0.2656549 0.1959019 0.1725764 -0.2854450 Largest eigenvalues: [1] 65604887 60614573 57557609 56305090 55216214 53469352 52454467 52402152 [9] 51998177 51419384 Smallest eigenvalues: [1] 0.36186136 0.22478492 0.21982184 0.20091140 0.15866189 0.05321775 [7] -0.02753659 -0.18814786 -0.73649376 -1.83930125 Largest eigenvalues: [1] 63126554 60013297 57218445 55247689 54841283 53218257 52264101 51445755 [9] 51232175 51009566 Smallest eigenvalues: [1] 0.5889792 0.5325782 0.4799873 0.4081175 0.3822931 0.3360016 [7] 0.3165796 0.2596338 0.1156711 -0.2926909 Largest eigenvalues: [1] 65118790 60088139 57034713 56302051 54940701 53275640 52253927 51582079 [9] 51517645 50753394 Smallest eigenvalues: [1] 0.5462084979 0.4596289757 0.4425864504 0.4092067562 0.3946468524 [6] 0.3602657817 0.2447315615 0.1547394310 0.0193964287 -0.0004436288 Largest eigenvalues: [1] 61796298 59213323 56855892 54938033 54377620 53172281 51519650 51155755 [9] 50459207 50163983 Smallest eigenvalues: [1] 0.5161071 0.4864884 0.3918835 0.3876054 0.3870837 0.3559756 [7] 0.3370716 0.2599319 0.1657500 -0.3115592 Largest eigenvalues: [1] 63609026 59775759 57293552 55094734 55002818 53520016 51926489 51647070 [9] 51198665 51058964 Smallest eigenvalues: [1] 0.3844704 0.2869086 0.2678615 0.2414951 0.1662366 0.1649803 [7] -0.2931335 -1.8512067 -2.2663332 -2.6126528 Largest eigenvalues: [1] 65399203 60358455 58444718 55669337 55604086 54514489 52942546 52772772 [9] 51926528 51626828 Smallest eigenvalues: [1] 0.40034295 0.36388802 0.34484062 0.25063321 0.22174912 0.18652089 [7] 0.17892611 0.17140740 -0.07209435 -1.44236241 Largest eigenvalues: [1] 63763732 59405332 57413034 55948630 54263154 52938941 51853268 51781222 [9] 51477112 50766747 Smallest eigenvalues: [1] 0.4313798 0.4229571 0.3923769 0.3760412 0.3112095 0.3109464 [7] 0.2526391 -0.1554225 -0.8900478 -16.5592499 Largest eigenvalues: [1] 63152583 59993602 57085284 55419122 55064076 53533837 51865233 51627201 [9] 51350229 50770855 Smallest eigenvalues: [1] 0.41276988 0.40321953 0.40185311 0.23765414 0.22292144 0.19771954 [7] 0.16912023 0.08295498 -0.67170684 -1.12303792 Largest eigenvalues: [1] 64139585 59804873 57183976 56051727 54822511 53324425 52168035 51909804 [9] 51898737 51015452 Smallest eigenvalues: [1] 0.53276256 0.46594849 0.43924900 0.39697820 0.31945362 0.29167345 [7] 0.28980983 0.25929236 -0.01086218 -0.13285833 Largest eigenvalues: [1] 63273773 59720686 57231816 54882059 54713773 53247788 51957631 51438734 [9] 50977746 50627827 Smallest eigenvalues: [1] 0.46748942 0.34423002 0.31387525 0.24507436 0.24340465 0.15076138 [7] 0.09617273 -0.69562439 -1.18076695 -4.47359899 Largest eigenvalues: [1] 61526702 59905855 57046257 56146055 54189655 54017569 52814392 51694398 [9] 50826284 50742824 Smallest eigenvalues: [1] 0.4923785 0.3984089 0.3937567 0.3549236 0.3122952 0.3109052 [7] 0.2706105 0.2394305 -0.2794429 -0.9258592 Largest eigenvalues: [1] 62845171 59886485 57063124 55382063 54919764 53291971 51992605 51803111 [9] 51226728 50848565 Smallest eigenvalues: [1] 0.5459344 0.4891997 0.4786678 0.4104942 0.3288842 0.2848951 [7] 0.2847681 0.1815102 0.1424909 -0.3119798 Largest eigenvalues: [1] 65061303 60674413 57479748 55796434 55694628 53880747 52647245 52183251 [9] 52014319 51568813 Smallest eigenvalues: [1] 0.4503516 0.4380780 0.3798042 0.3404305 0.2878967 0.2793281 [7] 0.2346284 0.2103938 -0.1151525 -16.0634542 Largest eigenvalues: [1] 63801784 60786631 57408112 56000477 55902736 54203077 52619103 52096529 [9] 51947571 51564852 Smallest eigenvalues: [1] 0.53132581 0.47939255 0.44143427 0.41821041 0.40036708 0.39283256 [7] 0.26125258 0.25440452 0.04234018 -0.05788324 Largest eigenvalues: [1] 61908991 60921013 57583495 55719933 55087847 53944109 52199272 52187053 [9] 51311269 51051015 Smallest eigenvalues: [1] 0.55633858 0.55459905 0.51682411 0.45409873 0.36279853 0.28371626 [7] 0.27734235 0.24286158 0.16919659 -0.04879497 Largest eigenvalues: [1] 65870742 60146762 57478444 56195525 55011350 53145199 52490917 51801209 [9] 51725161 51007665 Smallest eigenvalues: [1] 0.29941142 0.28255724 0.26899353 0.26408874 0.24559457 0.18665779 [7] 0.03204212 -0.16302223 -0.62465421 -0.77217633 Largest eigenvalues: [1] 64692988 61448493 58366388 56660214 55912037 54073882 53831609 52892771 [9] 52302123 52147463 Smallest eigenvalues: [1] 0.4999409 0.4392076 0.3276502 0.3157298 0.2767293 0.2717452 [7] 0.2070822 -0.2590587 -0.8639667 -1.6282596 Largest eigenvalues: [1] 67366903 60256808 57940051 57564310 55064301 53967328 53436716 52456655 [9] 51710071 51405849 Smallest eigenvalues: [1] 0.5156335 0.4515649 0.3378194 0.3355335 0.3027039 0.2655431 [7] 0.1546276 -0.2241411 -0.6055852 -2.8591961 Largest eigenvalues: [1] 64976128 59853182 57012931 55533646 54739601 53080864 52033152 51713440 [9] 51370904 51200155 Smallest eigenvalues: [1] 0.45290694 0.44925560 0.40351757 0.30919014 0.25459596 0.17384010 [7] 0.17026083 0.11022259 -0.02776676 -0.31821990 Largest eigenvalues: [1] 61432810 59985832 57193901 54767519 54531619 53265460 51504147 51440013 [9] 50665853 50507831 Smallest eigenvalues: [1] 0.52622357 0.50680189 0.46369968 0.38817044 0.25210285 0.20384335 [7] 0.20338961 0.19141173 0.12685740 -0.07178254 Largest eigenvalues: [1] 66202026 60897045 58063314 57194555 55475013 53311879 53307392 52911864 [9] 52169260 52040648 Smallest eigenvalues: [1] 0.52234995 0.45402038 0.43663174 0.41554924 0.40579497 0.28840887 [7] 0.13245821 0.08557838 -0.75062913 -2.86560419 Largest eigenvalues: [1] 65374252 60863355 57518564 57202689 55322858 53729674 52938897 52731382 [9] 52403820 51485447 Smallest eigenvalues: [1] 0.39084695 0.36914184 0.30025457 0.26474489 0.24560916 0.13375087 [7] -0.05033575 -0.05521544 -1.65185785 -4.82023978 Largest eigenvalues: [1] 65400558 61101185 57473590 56295735 56083895 54190276 53128989 52606597 [9] 52276979 51737422 Smallest eigenvalues: [1] 0.5780271 0.5484737 0.4845899 0.4175106 0.3248807 0.3082034 [7] 0.2996564 0.2535816 0.1127043 -1.8725486 Largest eigenvalues: [1] 64195941 60285711 57416563 56098671 55456384 53595903 52126600 52038599 [9] 51843900 50875133 Smallest eigenvalues: [1] 0.4125340 0.3617126 0.3277186 0.3125530 0.2747283 0.2422840 [7] 0.2351366 -0.0112572 -0.1799453 -3.4878682 Largest eigenvalues: [1] 63717076 59716227 57283402 55579766 55459389 53816847 51984241 51458117 [9] 51418582 50617527 Smallest eigenvalues: [1] 0.158950216 0.138747110 0.095224104 -0.003804913 -0.234584077 [6] -0.376242437 -1.934583821 -2.615940916 -11.366270562 -42.885478214 Largest eigenvalues: [1] 62210639 59008470 56523613 54883978 54828048 53128814 52077971 51570901 [9] 50778089 50548099 Smallest eigenvalues: [1] 0.5606641 0.5178252 0.4550787 0.4136515 0.4128867 0.3802478 [7] 0.2519912 0.1598622 0.1547290 -0.8574677 Largest eigenvalues: [1] 64056664 60121490 56752301 55494222 55381324 53671925 52297441 51526186 [9] 51485984 50661714 Smallest eigenvalues: [1] 0.3618078 0.3443411 0.3132744 0.3096701 0.2477763 0.1948330 [7] 0.1731113 0.1549858 -0.1465254 -1.7413840 Largest eigenvalues: [1] 65003619 59255885 56773132 56444943 54675165 53113186 52481697 51687999 [9] 50838184 50270887 Smallest eigenvalues: [1] 0.54426953 0.48562884 0.44388094 0.42821535 0.34888349 0.26731143 [7] 0.23998793 0.12993691 -0.02737212 -0.44424968 Largest eigenvalues: [1] 65550998 60465719 57587850 56121483 55591168 54046566 52740053 52235743 [9] 52054542 51864556 Smallest eigenvalues: [1] 0.42169354 0.39682148 0.39261339 0.33989100 0.32935115 0.22938059 [7] 0.21809042 0.08154989 -0.51332259 -1.69754904 Largest eigenvalues: [1] 62982266 60428341 57530010 55442263 55109750 53755454 52044607 51863246 [9] 51237195 50876446 Smallest eigenvalues: [1] 0.52459098 0.51053602 0.35515245 0.33980637 0.30118029 0.21321678 [7] 0.18689065 0.12651958 -0.08038237 -0.27084950 Largest eigenvalues: [1] 62531812 59705008 56872443 55459454 54529444 53538600 52154088 51877923 [9] 51114746 50752980 Smallest eigenvalues: [1] 0.52171155 0.49562694 0.49447592 0.44617475 0.38149637 0.31870354 [7] 0.29634753 0.25018251 0.24601879 -0.05523009 Largest eigenvalues: [1] 64247196 60702959 57811455 56511277 55326045 53743379 52828963 52591858 [9] 51993151 51674647 Smallest eigenvalues: [1] 0.4856958 0.4851811 0.4698809 0.4536448 0.3643883 0.2650687 [7] -0.6305192 -2.6167447 -6.9863113 -8.5079493 Largest eigenvalues: [1] 65767631 60192997 57414536 56986437 55017791 53821130 52858098 52238089 [9] 52077024 51222271 Smallest eigenvalues: [1] 0.62210840 0.51544880 0.51387347 0.48528008 0.32260528 0.24645020 [7] 0.12895498 -0.07462728 -0.42245680 -1.01614870 Largest eigenvalues: [1] 65192444 60626017 57792212 56461719 55435968 53943961 52519697 52470748 [9] 52090557 51424514 Smallest eigenvalues: [1] 0.6123584 0.5180206 0.4697137 0.4490226 0.3160412 0.2512016 [7] 0.2429981 0.2276873 -0.3757075 -2.4693377 Largest eigenvalues: [1] 64512255 60939379 57510406 55856670 55830455 54158421 52430522 52328012 [9] 51957775 51395342 Smallest eigenvalues: [1] 0.50285305 0.42119011 0.33842476 0.32740418 0.32042739 0.23890470 [7] 0.19142499 0.08581807 -1.07829160 -1.57508291 Largest eigenvalues: [1] 63212056 60557886 56946985 55900077 55025855 53336499 52238259 51773561 [9] 51602547 50807734 Smallest eigenvalues: [1] 0.45464091 0.43894610 0.40747460 0.35503655 0.31265786 0.29094006 [7] 0.23802606 -0.01934277 -0.28903710 -4.57884983 Largest eigenvalues: [1] 65020984 59922993 57531605 56134514 54805829 53182111 52268454 51935433 [9] 51843598 51096607 Smallest eigenvalues: [1] 0.56759586 0.56189578 0.41514216 0.38441990 0.37557169 0.33648270 [7] 0.31638758 0.30483067 0.09840617 -0.14551585 Largest eigenvalues: [1] 63645797 60322326 57525748 55656889 55258278 53726751 52232143 51994825 [9] 51743852 51118727 Smallest eigenvalues: [1] 0.3709913079 0.3575170694 0.3507039142 0.1969533121 0.1864759946 [6] 0.1562555900 0.0005067288 -0.1428596895 -1.4036005271 -4.8821616389 Largest eigenvalues: [1] 64609448 59304612 56830482 54940485 54928090 53223922 52235880 51373447 [9] 51291503 50684140 Smallest eigenvalues: [1] 0.5378951 0.4152804 0.4125642 0.3603796 0.3574761 0.3439116 [7] 0.2817114 0.2490014 -1.1908588 -2.1304555 Largest eigenvalues: [1] 63262192 60140606 57396805 55933981 54780326 53424578 52233240 51771048 [9] 51709538 51262078 Smallest eigenvalues: [1] 0.4139446 0.4003821 0.3210964 0.2948652 0.2792177 0.2462764 [7] 0.1485048 -0.1665783 -0.2396231 -1.1166169 Largest eigenvalues: [1] 65025560 59874668 57719944 55994411 54705952 53532693 52281068 51764539 [9] 51555256 50870097 Smallest eigenvalues: [1] 0.27577537 0.27200639 0.22353516 0.19749033 0.18221636 0.17288771 [7] 0.14576046 0.06904516 0.04295397 -7.41265447 Largest eigenvalues: [1] 62544032 60326473 57361667 55714935 55141761 53576873 52373218 52255801 [9] 51519940 50889022 Smallest eigenvalues: [1] 0.34824419 0.32624775 0.32412938 0.30055734 0.28486927 0.24196818 [7] 0.18425453 0.12732401 0.06721902 -1.14091795 Largest eigenvalues: [1] 63695684 59558522 57054951 54907965 54775839 53308952 51675649 51204229 [9] 51060347 50525826 Smallest eigenvalues: [1] 0.4461087 0.4100242 0.3564076 0.3077360 0.2705415 0.2075168 [7] 0.1856098 -0.2798966 -1.4998011 -1.7307294 Largest eigenvalues: [1] 65060073 59788240 57010817 56374372 54962676 53241951 52533464 52326643 [9] 51834648 51339657 Smallest eigenvalues: [1] 0.4345425 0.3460610 0.3452705 0.3419106 0.2650077 0.1179957 [7] -0.0407012 -0.0478749 -0.6777024 -2.7087721 Largest eigenvalues: [1] 65968492 59864148 57144255 56690856 54655176 53140523 52731877 52259841 [9] 51488220 51465275 Smallest eigenvalues: [1] 0.5542803 0.5512591 0.5228604 0.4515252 0.4155063 0.3076948 [7] 0.2845276 0.2396812 0.1807905 -0.3428144 Largest eigenvalues: [1] 63905137 59502253 56433069 55165699 54726656 53026970 51790581 51360145 [9] 51208848 50453061 Smallest eigenvalues: [1] 0.464282566 0.429567178 0.415205333 0.378129428 0.336070306 [6] 0.259183622 0.216600995 0.033002374 0.006506839 -0.042244432 Largest eigenvalues: [1] 63444504 59522734 56847150 54871722 54615621 53105096 51765857 51333580 [9] 51148670 50729429 Smallest eigenvalues: [1] 0.2372722011 0.2225235054 0.2015075882 0.0929144775 -0.0006222235 [6] -0.2148215623 -0.2224678712 -0.4906172915 -3.0041167833 -3.3593404025 Largest eigenvalues: [1] 65984700 59620554 56934014 56331887 54491746 53085033 52386737 51831911 [9] 51436998 51028028 Smallest eigenvalues: [1] 0.42762804 0.41302478 0.40983814 0.40478580 0.35859747 [6] 0.29442122 0.24534593 -0.08207897 -0.22919430 -10.25323178 Largest eigenvalues: [1] 66549384 60508087 58540776 57026439 55228675 53282403 52964350 52299347 [9] 51874854 51561945 Smallest eigenvalues: [1] 0.43601688 0.43273579 0.35929767 0.23928188 0.20507564 0.17869410 [7] 0.16006524 0.15735591 0.06578892 -0.00884030 Largest eigenvalues: [1] 64630586 60822955 58244976 55906329 55794335 54472403 52524935 52152055 [9] 52006919 51281686 Smallest eigenvalues: [1] 0.40359710 0.29078424 0.28913387 0.24170298 0.13901900 0.09786114 [7] 0.05907958 -0.07789732 -0.62712754 -1.53270335 Largest eigenvalues: [1] 66245908 60488538 58068049 57335231 54946414 53464666 53188835 52880647 [9] 51973737 51603106 Smallest eigenvalues: [1] 0.5617142 0.5599401 0.5083362 0.4206503 0.4119482 0.3668112 [7] 0.3366286 0.2675939 0.0604494 -0.3029912 Largest eigenvalues: [1] 63735402 60132302 56906030 55650046 55220216 53401815 51648460 51633654 [9] 51566797 50685450 Smallest eigenvalues: [1] 0.40801604 0.40389371 0.33990475 0.31620434 0.31242965 [6] 0.29992452 0.19358977 0.05662348 -2.66980776 -16.78142650 Largest eigenvalues: [1] 63715977 60355191 57482558 56348171 55093563 53422203 52593371 52129938 [9] 51897846 51409226 Smallest eigenvalues: [1] 0.4359027 0.3340343 0.3214657 0.3154707 0.2913169 0.2623459 [7] 0.1672228 0.1357154 -0.1990377 -0.6847689 Largest eigenvalues: [1] 66348176 60141875 57861809 57171768 54956008 53665745 53265811 52015686 [9] 51831777 51070947 Smallest eigenvalues: [1] 0.35136998 0.30718827 0.30041682 0.27201388 0.15773403 0.15405150 [7] 0.09808916 -0.05159188 -0.41221943 -2.22285813 Largest eigenvalues: [1] 65043567 60219670 57130463 56659700 55000249 53405129 52629781 52582847 [9] 52067161 51633049 Smallest eigenvalues: [1] 0.51304442 0.50070467 0.46793052 0.27801358 0.24674705 0.23081110 [7] -0.02424976 -0.04756692 -0.45654980 -5.69860578 Largest eigenvalues: [1] 65920403 59915422 57226585 56292137 54626891 53049380 52511637 51598153 [9] 51550425 50591028 Smallest eigenvalues: [1] 0.42857068 0.42233951 0.33428665 0.28511286 0.27304769 0.06738081 [7] 0.06159214 -0.02269885 -0.04753362 -2.62666136 Largest eigenvalues: [1] 65373132 60371013 57772896 56582558 54839576 53505278 52709407 52231512 [9] 51683667 51424207 Smallest eigenvalues: [1] 0.5527861 0.5191890 0.5109496 0.4552053 0.3569596 0.3308421 [7] 0.1655400 -0.2481752 -0.2485755 -14.8087171 Largest eigenvalues: [1] 64298426 59365986 56712783 55646048 54461595 52413836 51695841 51218018 [9] 51195453 50362335 Smallest eigenvalues: [1] 0.5879522 0.5586164 0.4919110 0.4150249 0.3334988 0.3268393 [7] 0.1071417 -0.1503952 -0.3219681 -1.5340869 Largest eigenvalues: [1] 65576323 59905413 56922328 56518290 54638236 52638453 52332864 51549585 [9] 51496916 50719685 Smallest eigenvalues: [1] 0.4452586 0.4253285 0.3897178 0.2382964 0.2189670 0.1750966 [7] 0.1718941 -0.2858584 -0.8273859 -1.8439859 Largest eigenvalues: [1] 66414068 60487398 57456568 57264512 55076190 53346019 53204558 52899585 [9] 51922869 51881458 Smallest eigenvalues: [1] 0.579322470 0.495724326 0.475819493 0.457585349 0.357925325 [6] 0.281455716 0.260275895 -0.001111107 -0.025555299 -0.430857479 Largest eigenvalues: [1] 64228370 59963578 56998759 55226178 54795231 53208368 51859128 51758102 [9] 51371890 51137177 Smallest eigenvalues: [1] 0.5053258 0.4497076 0.3842383 0.2980560 0.2917675 0.1977349 [7] 0.1435539 -0.1076327 -0.1294795 -0.2666228 Largest eigenvalues: [1] 64171263 59863976 57283743 55783843 54713585 53345568 52096852 51865869 [9] 51747188 50845488 Smallest eigenvalues: [1] 0.4874405 0.4831283 0.4762235 0.4539044 0.4132227 0.2655075 [7] 0.2654035 0.1649278 -0.7497195 -3.6836471 Largest eigenvalues: [1] 64703810 60404872 56947943 56118265 55487160 53720828 51980623 51859404 [9] 51791012 50951196 Smallest eigenvalues: [1] 0.53090711 0.52857996 0.40532111 0.31788968 0.29253928 0.28888361 [7] 0.19107938 0.15011937 0.09222173 -0.41676164 Largest eigenvalues: [1] 66256197 60857400 58269889 56445434 55358595 53862156 52668530 52366326 [9] 51998104 51534903 Smallest eigenvalues: [1] 0.5632778 0.5368090 0.4897684 0.4513131 0.3952916 0.3864297 [7] 0.3376703 0.1976449 -0.6951041 -1.5668546 Largest eigenvalues: [1] 65400796 60174958 57188597 56547107 55292785 53800498 52453111 52216088 [9] 52037523 51347479 Smallest eigenvalues: [1] 0.4661901 0.4080849 0.3753071 0.3083683 0.2636065 0.2484938 [7] 0.2471375 0.2301789 0.1823539 -0.7611671 Largest eigenvalues: [1] 64533648 59908454 56634158 55939317 54790492 53195839 51984942 51947753 [9] 51519753 50875168 Smallest eigenvalues: [1] 0.55301142 0.53508523 0.48531364 0.46827562 0.28645905 0.26865378 [7] 0.02387740 0.00851412 -0.04974736 -2.88107699 Largest eigenvalues: [1] 65593782 60854360 57499461 55971282 55457354 53540754 52087735 51980213 [9] 51712925 51238089 Smallest eigenvalues: [1] 0.4606986 0.4150882 0.3895332 0.3698456 0.3016220 0.1967325 [7] -0.2412423 -0.4353416 -4.2177200 -12.4418833 Largest eigenvalues: [1] 66642222 60497163 58211313 57644600 54848392 53687334 53568098 52186766 [9] 51817447 51307454 Smallest eigenvalues: [1] 0.4444366 0.4443511 0.4334750 0.4235253 0.3942360 0.3622654 [7] 0.3180757 0.2967322 0.2288908 -26.3081421 Largest eigenvalues: [1] 64396580 59472323 56986246 56387089 54520198 52437651 52340066 52099638 [9] 51148609 50775198 Smallest eigenvalues: [1] 0.4832095 0.4816598 0.4099703 0.4003063 0.3778948 0.3354794 [7] 0.3217115 0.2173993 0.1108074 -1.8167742 Largest eigenvalues: [1] 64261862 60209997 57363944 55525902 55499370 53860182 51978820 51639716 [9] 51407576 50509109 Smallest eigenvalues: [1] 0.4159491 0.3887005 0.3636342 0.3339376 0.2719207 0.2071950 [7] -0.1554395 -0.1753642 -1.6493714 -3.1613924 Largest eigenvalues: [1] 65831936 60436230 57527128 56524973 55460560 54029766 52557061 52076846 [9] 51920156 50700276 Smallest eigenvalues: [1] 0.4991566 0.4450847 0.3848060 0.3752293 0.2972533 0.2585703 [7] 0.2508491 0.1809243 0.1793704 -0.4216766 Largest eigenvalues: [1] 64369103 60376898 57361903 56147636 55339820 53647877 52442006 52110402 [9] 51926524 51411287 Smallest eigenvalues: [1] 0.3919340 0.3685712 0.2556420 0.2305837 0.2224366 0.1234887 [7] -0.2761569 -0.3616016 -11.4560427 -16.1561883 Largest eigenvalues: [1] 65412366 59923422 57748249 56026030 55116757 53840008 52628318 52101955 [9] 52094337 51747853 Smallest eigenvalues: [1] 0.5405937 0.4704579 0.4415416 0.3790221 0.3078424 0.2719302 [7] 0.2296209 0.0186659 -0.0744638 -0.7226621 Largest eigenvalues: [1] 65520519 60275203 57988226 56788103 54892970 53276053 52799941 52066448 [9] 51868418 51291721 Smallest eigenvalues: [1] 0.57591289 0.53984830 0.44469187 0.40822789 0.35845191 0.26293753 [7] 0.16328850 0.07937359 -0.04800096 -6.00683329 Largest eigenvalues: [1] 64289485 59455696 56834512 55315299 54648085 53056009 51574283 51470745 [9] 51377222 50566365 Smallest eigenvalues: [1] 0.58586685 0.51402486 0.42743002 0.40341103 0.34743473 0.22118159 [7] 0.16053106 0.08174534 0.06713376 -0.40198544 Largest eigenvalues: [1] 63682699 60558805 57862601 55217118 55062996 53841954 52020460 51958573 [9] 51242398 51026267 Smallest eigenvalues: [1] 0.50906806 0.43992522 0.38269723 0.37411904 0.34578560 0.31168999 [7] 0.22278832 0.09681184 -0.08672713 -1.92598298 Largest eigenvalues: [1] 65216969 60390600 58111830 55821549 55480546 53756032 52516394 52155805 [9] 52037381 51570033 Smallest eigenvalues: [1] 0.37125346 0.33622651 0.29554754 0.28392163 0.25954336 0.18204743 [7] 0.10794663 0.07439459 -1.71415284 -1.76398125 Largest eigenvalues: [1] 66281357 60659706 58058772 56696467 55097852 53702741 52758194 52705716 [9] 52016429 51860011 Smallest eigenvalues: [1] 0.4915993 0.4851726 0.4418545 0.4320093 0.4096783 0.3744207 [7] 0.3444420 0.1834299 0.1197684 -0.1764419 Largest eigenvalues: [1] 61917877 59848034 56853819 54935056 54622197 53424167 51985452 51214462 [9] 50675931 50435386 Smallest eigenvalues: [1] 0.44518733 0.41460183 0.32436259 0.31668699 0.29987897 0.19623957 [7] 0.19542040 0.07259145 -2.80552716 -2.92745036 Largest eigenvalues: [1] 66640375 61095951 57961718 57353193 56134267 54440333 53381865 53295039 [9] 52478193 52079181 Smallest eigenvalues: [1] 0.4634656 0.3698625 0.3634382 0.3519396 0.3517787 0.3205757 [7] 0.3197558 0.2100936 0.1818245 -0.3952971 Largest eigenvalues: [1] 64753557 60999215 57910651 56065071 55968898 54252348 52532757 52183472 [9] 52080847 51572769 Smallest eigenvalues: [1] 0.3858889 0.3639822 0.3448909 0.3411816 0.2677283 0.2321544 [7] 0.1140600 -0.1581726 -0.7332295 -1.4332558 Largest eigenvalues: [1] 65565004 59630014 57366436 56865100 54699649 53420088 52803464 51950272 [9] 51565967 51071268 Smallest eigenvalues: [1] 0.4878207 0.4736053 0.4604077 0.4501137 0.4259043 0.2673243 [7] 0.2605347 0.2207386 0.1528024 -0.8640331 Largest eigenvalues: [1] 63872043 60705633 57978116 56097159 55768979 54475466 52770612 52723140 [9] 51950648 51649096 Smallest eigenvalues: [1] 0.4226829 0.4049011 0.3693947 0.3473756 0.2799854 0.2396624 [7] 0.1791423 0.1474199 -4.0729856 -19.3983485 Largest eigenvalues: [1] 64321911 60430367 57812735 55732140 55625407 54268799 52640600 52389440 [9] 51708865 51207869 Smallest eigenvalues: [1] 0.5553300 0.4967537 0.4364663 0.4144603 0.3296271 0.3032553 [7] 0.2884542 0.2636767 0.1265461 -18.7405014 Largest eigenvalues: [1] 63101342 60157442 57042025 55467023 54738047 53721113 51871042 51779396 [9] 51009249 50904160 Smallest eigenvalues: [1] 0.4966046 0.4709479 0.3776067 0.3097582 0.2638198 0.2393345 [7] 0.1111486 -0.1408088 -0.8568489 -1.4758753 Largest eigenvalues: [1] 65270513 61372036 57764697 56673041 56384759 54655131 53518208 52651284 [9] 52366803 51905607 Smallest eigenvalues: [1] 0.44346563 0.42564798 0.34981173 0.31166490 0.29445893 0.25320201 [7] 0.22600226 0.21321413 0.07203382 -1.65710364 Largest eigenvalues: [1] 63898644 59870162 57230832 55478703 54860298 53458313 51864385 51618377 [9] 51568458 50839329 Smallest eigenvalues: [1] 0.46244840 0.38948767 0.37215329 0.26736355 0.19798737 0.16938847 [7] 0.12489110 -0.01901132 -0.76193337 -3.55169477 Largest eigenvalues: [1] 65952490 59884255 57836859 56179865 55038290 53870873 52556097 52365838 [9] 52069754 51507352 Smallest eigenvalues: [1] 0.42999778 0.38555428 0.37323619 0.36471501 0.32681658 0.32183526 [7] 0.15807602 0.05987858 -6.59816174 -7.33697480 Largest eigenvalues: [1] 64034822 60439047 57778130 55756713 55345882 54104653 51944458 51895153 [9] 51443279 50903441 Smallest eigenvalues: [1] 0.6424924 0.6164485 0.5648250 0.4252163 0.3786334 0.3785901 [7] 0.3333032 0.2573348 -0.2328014 -0.3363637 Largest eigenvalues: [1] 65843703 60504600 57741779 56989262 54939473 52987954 52922512 52512440 [9] 51803876 51612969 Smallest eigenvalues: [1] 0.56231586 0.39004207 0.36305529 0.32163075 0.27072760 0.24938666 [7] 0.22502081 0.08064115 -0.35063075 -0.43664614 Largest eigenvalues: [1] 65587673 60830487 57764657 56726586 55570430 53833902 52855569 52680560 [9] 52038380 51483534 Smallest eigenvalues: [1] 0.4295399 0.3392148 0.3266543 0.3067237 0.2652543 0.2038584 [7] 0.1140841 -0.1150886 -0.2993984 -1.2668640 Largest eigenvalues: [1] 65242863 60345619 57795897 56458293 55203857 53578015 53318279 52652814 [9] 51949893 51697251 Smallest eigenvalues: [1] 0.430067710 0.422533650 0.298756962 0.277670314 0.149106526 [6] 0.004114766 -0.151584554 -1.716368655 -14.456496183 -15.246523300 Largest eigenvalues: [1] 64570556 60491679 57362371 55997647 55204651 53481933 51974861 51894203 [9] 51866692 50972864 Smallest eigenvalues: [1] 0.4367080 0.3518828 0.3323773 0.3312061 0.3238202 0.3020763 [7] 0.2846286 0.2665455 -0.1121726 -1.1884098 Largest eigenvalues: [1] 65735735 60835951 58215531 56787345 55486000 54009957 52739215 52403891 [9] 52355074 51511373 Smallest eigenvalues: [1] 0.34953304 0.34263765 0.33106232 0.28835138 0.28621615 0.27790996 [7] 0.24896089 0.20303937 0.08655229 -2.27140333 Largest eigenvalues: [1] 65095325 60085501 57590523 56051404 54770889 53440447 52167452 51943210 [9] 51656173 51275428 Smallest eigenvalues: [1] 0.6592048 0.6404003 0.5166595 0.4033482 0.4028323 0.3708722 [7] 0.3462916 0.2698337 0.2648815 -0.7286708 Largest eigenvalues: [1] 64613077 59920510 57132441 55773065 55111497 53670501 52220693 51902478 [9] 51703973 50873263 Smallest eigenvalues: [1] 0.37891647 0.31123961 0.30510601 0.19230167 0.17716224 0.03259586 [7] -0.17742905 -0.64515518 -2.02278639 -2.28797808 Largest eigenvalues: [1] 65900707 60756964 58434230 56451026 55575079 54007667 52663257 52506551 [9] 52413928 51885792 Smallest eigenvalues: [1] 0.45556575 0.36751171 0.35966646 0.26996310 0.26295304 0.19468767 [7] 0.18823328 -0.03956099 -0.15294538 -0.34344492 Largest eigenvalues: [1] 63440266 61070682 56983675 55922306 55303250 54043908 52022979 51873568 [9] 51411685 50654573 Smallest eigenvalues: [1] 0.4905209 0.4643631 0.4284030 0.4142746 0.2207196 0.1673253 [7] -0.5509606 -1.6271276 -7.1104395 -9.8297614 Largest eigenvalues: [1] 65516259 59914351 57209289 56836790 54941499 52939629 52716622 52506521 [9] 51921697 51562362 Smallest eigenvalues: [1] 0.4106379 0.3301665 0.2167164 0.2040239 0.1352433 0.1261937 [7] -0.1479056 -1.4012180 -1.9481681 -4.5814904 Largest eigenvalues: [1] 62053635 59553829 56229488 54892512 54870917 53141701 52027549 52017605 [9] 50939490 50742460 Smallest eigenvalues: [1] 0.23339206 0.19264821 0.14566220 0.09516121 0.01871251 -0.10373377 [7] -0.28396276 -0.87932007 -1.53954870 -2.86300275 Largest eigenvalues: [1] 65363760 61528790 58337241 57320176 55442653 53749587 53451881 52751825 [9] 52355324 51516724 Smallest eigenvalues: [1] 0.46900975 0.45756721 0.45639449 0.42779764 0.38861220 0.27796359 [7] 0.24700575 0.20415410 0.16402602 -0.02413903 Largest eigenvalues: [1] 62994291 59486543 56982678 54894778 54810845 53335460 52007252 51275553 [9] 50918118 50544221 Smallest eigenvalues: [1] 0.56332150 0.56235172 0.53824983 0.53555934 0.46745360 0.45266697 [7] 0.38544392 0.23974666 0.09397433 -0.07977456 Largest eigenvalues: [1] 63506834 60585083 57685873 55448152 55411504 53919463 52154542 51873020 [9] 51453738 50900873 Smallest eigenvalues: [1] 0.45586335 0.44886781 0.38949076 0.37173644 0.36319228 0.27477958 [7] 0.04376298 0.04111338 -0.18370843 -9.00470598 Largest eigenvalues: [1] 65263619 60764933 57655387 57042414 55057333 53274063 53081235 52058941 [9] 51956356 51192634 Smallest eigenvalues: [1] 0.42942178 0.42424857 0.39652557 0.38896025 0.33227749 0.31281139 [7] 0.26494138 -0.09445423 -0.51650472 -1.42408393 Largest eigenvalues: [1] 64162879 60036713 57612890 55807625 54920771 53641231 51860806 51835422 [9] 51778135 50900906 Smallest eigenvalues: [1] 0.5132643 0.5029630 0.4351605 0.4099295 0.3557336 0.2691699 [7] 0.2262361 0.1695444 0.1412563 -1.3564060 Largest eigenvalues: [1] 63726205 60267131 57125561 55734594 55459744 53931121 52284879 51836487 [9] 51321733 50949508 Smallest eigenvalues: [1] 0.6947738 0.5524289 0.5163589 0.3769426 0.3621315 0.3343969 [7] 0.3005910 0.2647608 0.1340909 -0.1257241 Largest eigenvalues: [1] 63915112 60359994 57515484 55705835 55580355 53864952 52717574 51906035 [9] 51811247 51374724 Smallest eigenvalues: [1] 0.17399293 0.14668297 0.13014329 0.10154982 0.05478427 [6] -0.07858091 -0.08885453 -0.38554795 -2.55661303 -10.46824644 Largest eigenvalues: [1] 63671141 59391123 56451760 55603415 54857795 53157005 51835080 51557921 [9] 50900544 50269519 Smallest eigenvalues: [1] 0.5565602876 0.4412926206 0.3703934677 0.3242838418 0.2929735410 [6] 0.2866446591 0.2326488857 0.0004668943 -0.4870154074 -0.5942967261 Largest eigenvalues: [1] 64621816 60829664 57869410 56017177 55439920 53843014 52863578 52242244 [9] 52173231 51954614 Smallest eigenvalues: [1] 0.4294170 0.2906370 0.2838302 0.2368419 0.2036671 0.1859544 [7] 0.1632616 0.1387046 -1.4531621 -15.6338062 Largest eigenvalues: [1] 64679069 59651279 56971323 56061394 54739390 53132849 52317677 52062137 [9] 51683223 51105237 Smallest eigenvalues: [1] 0.4768358 0.4633440 0.4134908 0.3899816 0.3311158 0.3232596 [7] 0.2825004 -0.6337067 -6.9747085 -26.9398822 Largest eigenvalues: [1] 64526309 60636211 57295159 56336653 55681572 54043629 52302861 52158735 [9] 52010805 51129006 Smallest eigenvalues: [1] 0.44937738 0.41200232 0.38136894 0.26573141 0.22418340 0.18096288 [7] 0.15753976 0.12372860 0.01736977 -0.90399644 Largest eigenvalues: [1] 65485371 61207567 58668150 56571645 55672649 54252856 52769983 52643571 [9] 52480537 51858158 Smallest eigenvalues: [1] 0.4927097 0.3541109 0.3403424 0.3067935 0.3039201 0.2957033 [7] 0.2955304 0.2553524 0.1724951 -0.6452331 Largest eigenvalues: [1] 64363823 59914191 56930183 55718190 54838230 53186891 51957963 51857211 [9] 51396822 51066086 Smallest eigenvalues: [1] 0.4445254 0.4325453 0.4180866 0.3392527 0.3293453 0.2918831 [7] 0.2819983 0.2135124 0.1794837 -0.9750292 Largest eigenvalues: [1] 65079999 60507571 57459036 56624897 54934481 53631010 52558210 52483901 [9] 51857988 51722368 Smallest eigenvalues: [1] 0.35238406 0.30235391 0.28126035 0.23503907 0.23020427 0.01862637 [7] -0.54217517 -0.62257215 -1.66134727 -6.06466464 Largest eigenvalues: [1] 64206520 59327298 57117161 55543154 54364857 53267864 51922715 51723964 [9] 51532529 51021170 Smallest eigenvalues: [1] 0.3727948 0.3474193 0.3254185 0.3116484 0.2841517 0.2740666 [7] 0.2120624 0.1155873 -0.4931777 -3.9524265 Largest eigenvalues: [1] 62045232 59317993 56434316 54636107 54404068 53041601 51763938 51297251 [9] 50613816 50489818 Smallest eigenvalues: [1] 0.3933471 0.3471600 0.3320841 0.3306430 0.2960491 0.2025489 [7] 0.1797307 0.1717850 0.1313368 -3.8661918 Largest eigenvalues: [1] 64896235 60908382 57840302 56154951 55754018 54406921 52751216 52680298 [9] 52092783 51906524 Smallest eigenvalues: [1] 0.58382175 0.46840075 0.43570285 0.39391324 0.38179398 0.33526374 [7] 0.33285675 0.15951703 -0.05347295 -9.23003284 Largest eigenvalues: [1] 64021201 60112179 57377663 55482512 55476044 54003150 52367237 52205834 [9] 51580870 51232105 Smallest eigenvalues: [1] 0.5679771 0.5136341 0.4454096 0.4098713 0.3246302 0.2852869 [7] 0.2810462 0.2742600 0.1594525 -0.9096981 Largest eigenvalues: [1] 62402250 59945731 56876040 55088529 54775174 53395944 51771857 51663222 [9] 50733360 50563583 Smallest eigenvalues: [1] 0.5208800 0.5131013 0.4176284 0.3495412 0.3087863 0.2598037 [7] 0.2594486 0.1430163 0.1112036 -0.1455603 Largest eigenvalues: [1] 64730411 60918235 58019251 56041332 55812023 54316581 52664103 52328449 [9] 52179450 51424259 Smallest eigenvalues: [1] 0.51429120 0.49676158 0.44222096 0.39439018 0.34219113 0.31474323 [7] 0.11792681 0.05927812 -0.03319816 -7.07977194 Largest eigenvalues: [1] 63952055 59936772 57256508 55541418 55167004 53683301 52276794 51994404 [9] 51563416 51075028 Smallest eigenvalues: [1] 0.31044308 0.25629393 0.16914060 0.13848943 0.12932323 0.04998798 [7] -0.53621952 -0.99503219 -1.38720389 -3.18335418 Largest eigenvalues: [1] 62771592 60134043 57204467 55531513 55205386 53424257 52509237 52349368 [9] 51375022 51158186 Smallest eigenvalues: [1] 0.3435085 0.3334230 0.2694998 0.2170939 0.1734174 0.1204316 [7] 0.1135274 -0.7253679 -5.1454549 -29.7942473 Largest eigenvalues: [1] 65575891 60206493 57181444 56748017 55287651 53731993 52651717 52450969 [9] 52098622 51678461 Smallest eigenvalues: [1] 0.54896002 0.53930877 0.52887691 0.32190308 0.27647123 0.23428633 [7] 0.22939166 0.06935047 -0.02291231 -0.05160940 Largest eigenvalues: [1] 63033814 60881869 57725918 56353474 54964041 54488758 52888474 52591832 [9] 51648111 51144277 Smallest eigenvalues: [1] 0.53688674 0.50979492 0.35955751 0.34266514 0.33681509 0.22482783 [7] 0.18510949 0.10494858 0.04029477 -1.21583142 Largest eigenvalues: [1] 63082588 61122435 57922257 56548851 55201858 54717729 52950649 52864058 [9] 51948054 51283083 Smallest eigenvalues: [1] 0.37055333 0.24397796 0.22535539 0.22064736 0.20276503 0.20001838 [7] 0.16633918 0.05716543 -1.93005306 -6.40058671 Largest eigenvalues: [1] 65278890 59918567 57430993 56262550 54734647 53438270 52354384 52071414 [9] 51797266 51290060 Smallest eigenvalues: [1] 0.457640508 0.434488032 0.415186189 0.378885804 0.370192720 [6] 0.294331408 0.156670212 0.151513969 0.002483472 -0.068920470 Largest eigenvalues: [1] 64260653 60839144 58165575 56247786 55338077 53814764 52079468 52014303 [9] 51922844 51010359 Smallest eigenvalues: [1] 0.34855723 0.32653035 0.21678353 0.20444853 0.03070099 [6] -1.47484974 -2.61706685 -9.63598610 -10.65152405 -11.81698325 Largest eigenvalues: [1] 65085852 59936137 57667199 56556491 55233158 54006823 53023309 52398653 [9] 52347806 51973266 Smallest eigenvalues: [1] 0.3381866 0.3227711 0.3098073 0.2812932 0.2717524 0.2368776 [7] 0.1772994 -1.2831674 -2.5541371 -15.3659377 Largest eigenvalues: [1] 64668112 60361693 57195391 56379975 54830152 53255052 52520586 52363800 [9] 51869621 51710322 Smallest eigenvalues: [1] 0.6008290 0.5774503 0.5152635 0.4450602 0.4363860 0.4048657 [7] 0.2738052 0.2437140 0.1016007 -0.2659326 Largest eigenvalues: [1] 65662001 59818585 56814940 56366223 54458983 52704285 52380267 51463555 [9] 51209721 50711322 Smallest eigenvalues: [1] 0.36773786 0.34527390 0.31587361 0.28753809 0.24899620 0.07115531 [7] 0.07013047 0.02301751 -0.29917983 -0.55715220 Largest eigenvalues: [1] 64833014 59910569 57528814 55484897 55387991 53913139 51807501 51686018 [9] 51570911 50822061 Smallest eigenvalues: [1] 0.42114651 0.41012319 0.27469020 0.21575691 0.20137663 0.09823638 [7] 0.03508838 -0.45886452 -0.91304983 -2.30407978 Largest eigenvalues: [1] 64361593 60247304 57389767 55946292 55801165 54225426 52448197 52389107 [9] 51873376 51778606 Smallest eigenvalues: [1] 0.5239711 0.4660117 0.4390764 0.4384642 0.2931430 0.2334313 [7] 0.2302813 0.1873801 0.1763725 -11.2653385 Largest eigenvalues: [1] 63453016 60212635 57687679 55459311 55121073 53799618 52661547 51824672 [9] 51279725 51028949 Smallest eigenvalues: [1] 0.4941352 0.3978747 0.3490921 0.2902397 0.2815614 0.2734541 [7] 0.2595843 0.2544340 -1.5936816 -4.4238888 Largest eigenvalues: [1] 65845680 59805365 57340790 56821329 54719602 53206672 52712707 52219037 [9] 51702344 51220631 Smallest eigenvalues: [1] 0.51356322 0.49695658 0.49159728 0.43954030 0.34125666 [6] 0.23246579 0.20326497 0.14610412 0.02726586 -15.33415248 Largest eigenvalues: [1] 64413183 60109496 56859240 56060069 55029419 53201102 52047343 52006692 [9] 51767086 50956372 Smallest eigenvalues: [1] 0.5355418 0.4460271 0.4436493 0.3404052 0.2988852 0.2740152 [7] 0.2665325 0.2030855 -0.1478093 -0.3066490 Largest eigenvalues: [1] 64688108 60314315 57637293 55560905 55330792 53920476 52587938 52238865 [9] 51664518 51446987 Smallest eigenvalues: [1] 0.50025753 0.44788931 0.37637313 0.34216412 0.28581862 0.27678297 [7] 0.09094782 -0.01622387 -1.34507222 -6.79008198 Largest eigenvalues: [1] 64534920 59809700 56904018 56148298 55038247 53457244 52232116 52175519 [9] 51688107 51115216 Smallest eigenvalues: [1] 0.48890093 0.38292492 0.36992951 0.35624224 0.23811757 0.23788674 [7] 0.18817711 -0.05535112 -0.38692746 -1.37068085 Largest eigenvalues: [1] 63534652 59675338 57395507 55357123 54840424 53632265 52284759 51921644 [9] 51519247 51114186 Smallest eigenvalues: [1] 0.50408815 0.43963425 0.41289794 0.38187241 0.35225835 0.34647649 [7] 0.34299125 0.32091325 0.31336602 -0.02669146 Largest eigenvalues: [1] 62895176 59742572 57136264 55640866 54940740 53281578 51674828 51576426 [9] 51509171 50484428 Smallest eigenvalues: [1] 0.5317972 0.4111299 0.3156682 0.2807998 0.2799069 0.2146495 [7] 0.1659147 0.1238339 -0.6588994 -0.7753490 Largest eigenvalues: [1] 64118211 60527814 57381779 55982082 55740875 54021148 52745121 52385741 [9] 52140453 51552308 Smallest eigenvalues: [1] 0.50709128 0.49099777 0.40388220 0.37044460 0.35276207 [6] 0.05156476 0.03688797 -2.64826461 -3.19911244 -10.65902213 Largest eigenvalues: [1] 63856036 60138867 56921212 55829284 55189170 53515160 51835841 51665493 [9] 51643967 50642379 Smallest eigenvalues: [1] 0.513142749 0.395678723 0.356456868 0.339783740 0.223403441 [6] 0.200601311 0.005595955 -0.353177970 -0.424262348 -1.266350097 Largest eigenvalues: [1] 63734011 59548656 56744384 55444984 54823432 53028764 52564218 51473893 [9] 51308682 50890905 Smallest eigenvalues: [1] 0.41250445 0.36135583 0.23407873 0.12024406 0.02703175 [6] -0.59760540 -1.05935942 -1.15977714 -14.21677087 -25.84205488 Largest eigenvalues: [1] 65953425 59815186 57442187 56142899 54845114 53314603 52321618 52044911 [9] 51935666 50849781 Smallest eigenvalues: [1] 0.36615439 0.31326129 0.28495931 0.21551577 0.19159089 0.13238991 [7] 0.02555591 -1.91107869 -6.16149963 -8.45163422 Largest eigenvalues: [1] 64811459 59869089 57150571 55992868 55291305 53664492 52036887 51766814 [9] 51265665 50214149 Smallest eigenvalues: [1] 0.45007466 0.43451046 0.41871822 0.34876442 0.27131051 0.25260930 [7] 0.17996303 0.13108908 -0.04422398 -3.82919130 Largest eigenvalues: [1] 62928653 59214590 56752903 54675098 54613992 53038678 51411295 51156372 [9] 50814684 50462889 Smallest eigenvalues: [1] 0.49268166 0.48263594 0.41107868 0.40034653 0.37068409 0.26057429 [7] 0.14597205 0.07235150 0.03807847 -2.53513236 Largest eigenvalues: [1] 62292103 59532020 56365181 54874367 54688050 53050250 52035823 51398565 [9] 50818688 50648019 Smallest eigenvalues: [1] 0.5278855 0.4758727 0.4338333 0.4282913 0.4171706 0.3689617 [7] 0.2936994 0.2033135 -0.1243822 -1.4423889 Largest eigenvalues: [1] 65577663 59767918 56997841 56864343 54757559 52901387 52889416 51675037 [9] 51295138 50629651 Smallest eigenvalues: [1] 0.5204820 0.4225804 0.4155447 0.3779917 0.3631986 0.2949551 [7] 0.2277822 -0.1807936 -1.1845013 -1.5216757 Largest eigenvalues: [1] 65648655 60112696 57563338 56832083 54708105 52908926 52670447 52074726 [9] 51670763 51203976 Smallest eigenvalues: [1] 0.39859094 0.34904025 0.31045039 0.26102341 0.12235162 0.09026301 [7] 0.02238457 0.02061492 -4.92707840 -5.92397543 Largest eigenvalues: [1] 65156532 61344783 57639545 57079460 56097183 54121380 53700622 52650893 [9] 52612872 52099386 Smallest eigenvalues: [1] 0.37820033 0.35014782 0.33763113 0.33480218 0.28982951 0.26945971 [7] 0.20797659 0.19721865 0.08415929 -0.95241435 Largest eigenvalues: [1] 66168494 59692238 57024740 56703378 54335689 52848992 52839439 52011249 [9] 51248214 51202882 Smallest eigenvalues: [1] 0.4334646 0.3884285 0.3570164 0.3296284 0.2183761 0.2167296 [7] 0.1806627 0.1454605 -0.8857873 -2.3714396 Largest eigenvalues: [1] 64370625 59268930 56707960 55440157 54615398 53011247 51796337 51390240 [9] 51073100 50413122 Smallest eigenvalues: [1] 0.58426383 0.58321723 0.53197649 0.44854330 0.40623896 0.39575861 [7] 0.36774993 0.17371816 -0.04097231 -0.25655805 Largest eigenvalues: [1] 63924784 59492838 56665637 55629089 54358797 52804916 51649014 51467250 [9] 50915770 50044818 Smallest eigenvalues: [1] 0.3318537 0.2901188 0.2727990 0.2651640 0.2297298 0.1693474 [7] -0.1287857 -0.1425885 -3.0594349 -21.9744984 Largest eigenvalues: [1] 65592052 60782668 58385805 56880154 55344360 54145498 52816661 52488715 [9] 52267393 51392132 Smallest eigenvalues: [1] 0.45676739 0.44932882 0.36923430 0.34882823 0.30920800 0.27799927 [7] 0.12146820 0.07497249 -0.27544281 -1.73156160 Largest eigenvalues: [1] 62977568 60268357 57461357 55734827 55323960 54132613 52305680 52225240 [9] 51333933 51131169 Smallest eigenvalues: [1] 0.37591592 0.34939391 0.28394355 0.22288594 0.02183537 [6] -0.13688291 -0.89638787 -1.87339689 -4.26093626 -33.15763459 Largest eigenvalues: [1] 65204940 59795188 56925205 55414986 54673291 53127366 51908386 51523503 [9] 51404041 51047409 Smallest eigenvalues: [1] 0.4117747 0.4005399 0.3992011 0.3304966 0.3046413 0.2551265 [7] 0.1850499 0.1543968 0.1345448 -0.5482180 Largest eigenvalues: [1] 63981840 59956176 57294991 55683757 55268825 53483755 52624990 51617780 [9] 51583966 51339124 Smallest eigenvalues: [1] 0.54588648 0.54438498 0.46984053 0.43218464 0.41920238 0.28237188 [7] 0.27370193 0.26754378 -0.04608023 -0.24557334 Largest eigenvalues: [1] 64539581 59781570 56704900 55390191 54696216 53173699 51644082 51473733 [9] 51166525 50415484 Smallest eigenvalues: [1] 0.3113205 0.2909393 0.2809136 0.2588262 0.1333198 -1.0004547 [7] -1.4927454 -2.0314479 -2.2647917 -2.7687152 Largest eigenvalues: [1] 65283855 60509423 57883477 55654332 55307358 53762030 52333977 51810699 [9] 51671180 51616296 Smallest eigenvalues: [1] 0.4837935 0.4553574 0.4505911 0.4154184 0.4053612 0.4034359 [7] 0.3928558 0.2583591 0.2003834 -0.3563524 Largest eigenvalues: [1] 64274093 60120534 57524312 55883456 55363625 53796518 52096232 51948413 [9] 51746521 50995978 Smallest eigenvalues: [1] 0.48284963 0.37793857 0.36901334 0.33060318 0.26928105 0.26230950 [7] 0.22734393 0.18096328 0.03577805 -0.62467375 Largest eigenvalues: [1] 63420055 60508344 57049049 55589578 55244582 53565600 52629417 51657562 [9] 51581482 51412647 Smallest eigenvalues: [1] 0.4399150 0.4208253 0.2980640 0.2855796 0.2076432 0.1894704 [7] 0.1833774 0.1710420 -1.2419875 -2.0152343 Largest eigenvalues: [1] 63836011 60169673 57052417 55458551 55344531 53806757 52367084 52214421 [9] 51573106 51281117 Smallest eigenvalues: [1] 0.53875488 0.47593114 0.38327921 0.38137554 0.36900828 0.35832974 [7] 0.31410037 0.28686666 0.01598865 -0.63067804 Largest eigenvalues: [1] 65686353 60443186 57702067 56451625 55058677 53640595 52604128 51954061 [9] 51756421 51141710 Smallest eigenvalues: [1] 0.6032834 0.4546018 0.4216246 0.3932967 0.3325949 0.2875735 [7] 0.2786494 0.2449993 0.2355360 -1.2404562 Largest eigenvalues: [1] 66173796 60524674 57939570 56573687 55321825 53972627 52685442 52488056 [9] 51963098 51526695 Smallest eigenvalues: [1] 0.47471732 0.41001096 0.37543119 0.35652599 0.18515664 0.15704361 [7] 0.06375342 -0.08862345 -1.52155284 -1.85649957 Largest eigenvalues: [1] 65208262 60859311 58154447 56587520 55354355 54065181 52496298 52355682 [9] 52128816 51219621 Smallest eigenvalues: [1] 0.39010591 0.38772164 0.34102365 0.29848154 0.08962970 [6] 0.06336244 -0.79794362 -1.84033589 -2.13556826 -15.01566994 Largest eigenvalues: [1] 64984035 59649025 56652940 56467108 54477533 53017444 52281300 51805761 [9] 51518878 50541685 Smallest eigenvalues: [1] 0.565502102 0.481928124 0.450176821 0.444762778 0.254680255 [6] 0.185377803 0.168778671 0.006248232 -0.791545041 -1.916082975 Largest eigenvalues: [1] 63903269 60301926 57102455 55441762 55389464 53852520 52380464 52100368 [9] 51532276 51361169 Smallest eigenvalues: [1] 0.34335350 0.32955884 0.31210499 0.28523221 0.20733693 0.17953085 [7] 0.15290637 0.09511059 -0.35694884 -8.53844157 Largest eigenvalues: [1] 62109519 60423723 57509442 56030908 55091527 54258754 52722879 52428320 [9] 51586847 51080760 Smallest eigenvalues: [1] 0.54457663 0.50456799 0.42099679 0.39756795 0.25794836 0.21988428 [7] 0.09436892 0.03252724 -1.21052870 -2.42474555 Largest eigenvalues: [1] 64225085 60746350 57121270 55768021 55680021 54068193 52412244 52254165 [9] 51603579 51149800 Smallest eigenvalues: [1] 0.4249970 0.4218964 0.3080185 0.2841112 0.2789110 0.2096348 [7] 0.2081632 0.1909149 -0.8827535 -1.0276920 Largest eigenvalues: [1] 65997044 60156927 57604506 57299503 54940742 53533320 53270265 52143358 [9] 52073714 51213849 Smallest eigenvalues: [1] 0.56352954 0.54750293 0.50053218 0.44036317 0.39531692 0.37396949 [7] 0.28074698 0.20713717 -0.05200555 -0.50019092 Largest eigenvalues: [1] 63554401 60391406 57058316 55398723 55028791 53332468 52090579 51626648 [9] 51437210 51198436 Smallest eigenvalues: [1] 0.5216278 0.4307288 0.4200359 0.4128112 0.3793602 0.3494066 [7] 0.3266821 0.2936509 0.2189408 -0.5980169 Largest eigenvalues: [1] 65356849 60605480 58034169 56449423 55321652 53935545 52534872 52302176 [9] 52238990 51552313 Smallest eigenvalues: [1] 0.5670216 0.4868008 0.4643145 0.3776589 0.3357970 0.1967524 [7] -0.2041937 -0.2798641 -0.3427553 -1.2985528 Largest eigenvalues: [1] 64857935 60050708 57421086 56157476 54776540 53297154 52221990 52155247 [9] 51937533 51432883 Smallest eigenvalues: [1] 0.5204519 0.4595059 0.3175062 0.3045108 0.2837890 0.2703324 [7] 0.2699931 0.2489191 0.1548238 -0.3876310 Largest eigenvalues: [1] 63658788 59593115 57205743 55884840 54326103 52897787 51868289 51569947 [9] 51179189 50504370 Smallest eigenvalues: [1] 0.60215041 0.52312027 0.43963147 0.40742445 0.36040984 0.32678984 [7] 0.23726243 0.15771312 0.08797395 -1.64710534 Largest eigenvalues: [1] 63729224 59870168 57103599 55552808 54842836 53335001 51700393 51589148 [9] 51532808 50732599 Smallest eigenvalues: [1] 0.51699535 0.50554701 0.46953293 0.36119902 0.33526766 0.24925559 [7] 0.20661811 0.01767268 -0.20654133 -2.27933558 Largest eigenvalues: [1] 65474350 59576281 57216172 56437852 54575757 52772914 52502288 51935481 [9] 51389338 51061769 Smallest eigenvalues: [1] 0.5694480 0.5523880 0.5045152 0.5028494 0.4763201 0.4132950 [7] 0.2830584 0.2491897 0.2015181 -1.2580334 Largest eigenvalues: [1] 64449168 60170429 57194726 56224052 54591774 53132886 52092576 51819879 [9] 51444546 50890557 Smallest eigenvalues: [1] 0.56190068 0.46452296 0.44329888 0.34392623 0.29880342 0.29704275 [7] 0.23897772 0.22827357 0.10759848 -0.02860955 Largest eigenvalues: [1] 63464266 60584499 57340173 55646098 55046927 53508497 52082130 52056645 [9] 51779392 51375070 Smallest eigenvalues: [1] 0.26208087 0.24585301 0.21944902 0.16933434 0.04943113 [6] -0.13696131 -0.21953305 -0.49880907 -7.20362046 -30.09318837 Largest eigenvalues: [1] 64549792 59673595 57439029 57057742 54531930 53038942 52667570 52626709 [9] 51898041 51161085 Smallest eigenvalues: [1] 0.4085359 0.3940913 0.3764065 0.2795715 0.2534743 0.2310830 [7] 0.2050530 -0.1491286 -0.6555420 -0.7526958 Largest eigenvalues: [1] 66595143 61672174 58871135 57767475 55776318 54171919 53697429 53028618 [9] 52612064 52299067 Smallest eigenvalues: [1] 0.41985536 0.34744602 0.33963154 0.31382586 0.30230572 0.26991030 [7] 0.07564455 -0.06564710 -0.21107038 -1.26331436 Largest eigenvalues: [1] 64905909 60196206 57572316 56064966 54472796 53404938 52155079 51985153 [9] 51755697 51473477 Smallest eigenvalues: [1] 0.56665657 0.53420415 0.45797345 0.40978592 0.40664044 0.32174511 [7] 0.31384912 0.25903760 0.21983098 -0.03078901 Largest eigenvalues: [1] 62874763 59657330 56979933 55310913 55017296 53414808 51892802 51589644 [9] 51130094 50719204 Smallest eigenvalues: [1] 0.4523856 0.4283625 0.3907697 0.3051477 0.3035231 0.2303833 [7] 0.2218429 -0.2850989 -1.8029084 -3.7914718 Largest eigenvalues: [1] 65377809 60305610 57946480 56234647 55036341 53466446 52154180 52099074 [9] 51646246 51298890 Smallest eigenvalues: [1] 0.5122451 0.4252697 0.3474607 0.2704993 0.2536186 0.2107707 [7] -0.1067480 -0.7252001 -1.4469827 -2.4991351 Largest eigenvalues: [1] 66019221 60793026 58029059 56541345 55605992 54053986 52853602 52756445 [9] 52535871 51894446 Smallest eigenvalues: [1] 0.5480063 0.5343391 0.4154038 0.3745385 0.3115282 0.3097118 [7] 0.2899511 0.2644871 0.2550387 -1.1419339 Largest eigenvalues: [1] 65957063 60428386 57695892 56899556 55281366 53945526 52960656 52205228 [9] 52171616 51310725 Smallest eigenvalues: [1] 0.42313923 0.40991807 0.35546893 0.26965487 0.25743431 0.21984232 [7] 0.17762344 0.03473504 -0.20072486 -0.35606531 Largest eigenvalues: [1] 62806641 59341796 57064658 54891543 54129130 53333256 51664474 51193060 [9] 50610187 50399707 Smallest eigenvalues: [1] 0.40742609 0.38145632 0.33882274 0.29279607 0.24472277 0.24151625 [7] -0.03001365 -0.16345436 -0.65571891 -1.35975963 Largest eigenvalues: [1] 65031702 60393149 57758210 55406343 54893085 53524044 52187803 51585040 [9] 51402406 51309189 Smallest eigenvalues: [1] 0.5486390 0.5156129 0.4195664 0.3918329 0.3564056 0.3364130 [7] 0.3078334 0.2899076 0.1423248 -0.4230701 Largest eigenvalues: [1] 65568706 59932364 57300922 56389533 54783745 53382263 52496445 51913007 [9] 51894024 51087781 Smallest eigenvalues: [1] 0.5202029 0.5140320 0.5114391 0.4569729 0.3193646 0.2008783 [7] 0.1655013 -0.1041523 -0.1415162 -1.9817074 Largest eigenvalues: [1] 62284853 59429629 56001815 54760569 54235189 52787325 51521834 50790275 [9] 50296574 49994857 Smallest eigenvalues: [1] 0.458718532 0.438775672 0.346712783 0.292639995 -0.002781101 [6] -0.488893223 -0.595328606 -0.631138311 -0.997272931 -8.262999017 Largest eigenvalues: [1] 64068459 59915218 57262574 55742748 55510255 53935162 52591694 52047434 [9] 51691952 51551054 Smallest eigenvalues: [1] 0.48634602 0.47936263 0.46160011 0.40297858 0.29135504 0.25391103 [7] 0.15862343 -0.07041424 -0.27646361 -2.43797582 Largest eigenvalues: [1] 64332644 59897209 56470920 55183410 54838770 52954550 51578078 51243264 [9] 51196083 50683648 Smallest eigenvalues: [1] 0.082846267 -0.005581226 -0.030466258 -0.197740171 -0.296137775 [6] -1.473451796 -3.707591644 -15.051128134 -16.126222283 -22.053085868 Largest eigenvalues: [1] 63027655 59188696 56172161 54910120 54447753 52918552 52066746 51512786 [9] 50886452 50576636 Smallest eigenvalues: [1] 0.61443220 0.58391278 0.52931697 0.46519635 0.38714309 0.31769963 [7] 0.31209848 0.28466427 -0.02873817 -0.26177468 Largest eigenvalues: [1] 64458968 60497059 57228017 56402655 55114734 53271518 52691697 52401047 [9] 51809570 51546118 Smallest eigenvalues: [1] 0.47498698 0.43907139 0.38818481 0.36293211 0.33091355 0.29491259 [7] 0.09201517 -0.10576516 -0.35183403 -1.04367754 Largest eigenvalues: [1] 63381666 60251291 57431491 55902782 55061044 53274016 52041578 51976478 [9] 51865078 50966852 Smallest eigenvalues: [1] 0.48231828 0.47064359 0.45700345 0.40907645 0.40052300 [6] 0.22379677 0.20123232 0.12988660 0.04069322 -10.46087346 Largest eigenvalues: [1] 62951268 60869894 57175218 55863040 55280518 53985731 52289225 51903576 [9] 51316391 51023437 Smallest eigenvalues: [1] 0.4530239 0.4006749 0.3989586 0.3836229 0.3066514 0.2944299 [7] 0.2567527 0.2222983 -0.8898274 -1.8020845 Largest eigenvalues: [1] 65057921 60038553 57735901 56732147 54912000 53663192 52542060 52343902 [9] 51908462 51562676 Smallest eigenvalues: [1] 0.36550792 0.35813549 0.35230397 0.34406144 0.26305876 [6] 0.24066573 0.23861919 -0.09986753 -1.20440284 -38.91301801 Largest eigenvalues: [1] 64280823 60552879 57440472 56068947 55365706 53849815 52481967 52422169 [9] 52004825 51428756 Smallest eigenvalues: [1] 0.30389990 0.18237623 0.13047252 0.06924863 0.04933696 -0.46901345 [7] -0.90598384 -2.05739524 -3.17678867 -4.88804782 Largest eigenvalues: [1] 65814289 59346236 56544729 56045852 54180737 52715817 52117799 51668468 [9] 51386058 50818227 Smallest eigenvalues: [1] 0.4704790 0.4511027 0.4456544 0.3703976 0.3397021 0.3101340 [7] 0.2253259 0.1486695 -0.6726460 -7.8476789 Largest eigenvalues: [1] 64782270 60821047 57882959 55958174 55825667 54258539 53097850 52174524 [9] 52009772 51779557 Smallest eigenvalues: [1] 0.45904995 0.42647196 0.37888662 0.34251901 0.29816932 0.25406977 [7] 0.18202582 0.14217355 -0.02940969 -0.37898229 Largest eigenvalues: [1] 65024544 60817490 58143012 56262786 55649739 53885789 52846642 52231988 [9] 52155433 51763212 Smallest eigenvalues: [1] 0.5455218 0.5303258 0.5080793 0.3732920 0.3393157 0.2854801 [7] 0.2603636 0.2111399 0.1835342 -0.2537073 Largest eigenvalues: [1] 61683626 59828641 57000643 55188322 54322432 53347141 52305285 51362369 [9] 50994008 50451246 Smallest eigenvalues: [1] 0.23649434 0.19348165 0.19312155 0.15397270 0.13096985 [6] 0.10018482 -0.03443138 -1.16534576 -3.06160539 -16.53599980 Largest eigenvalues: [1] 66341359 60227728 57649906 57445546 55089442 53828172 53084267 52272703 [9] 52117761 51550276 Smallest eigenvalues: [1] 0.5319380 0.4680688 0.4220319 0.3854596 0.3137564 0.2823258 [7] 0.2642564 0.1643395 0.1085846 -0.7460929 Largest eigenvalues: [1] 64284462 61047810 57952905 56361682 56287940 54565769 52995151 52526545 [9] 52332539 51733625 Smallest eigenvalues: [1] 0.3872983 0.3718288 0.2864391 0.2854666 0.2345735 0.1857269 [7] 0.1423190 0.1057419 -1.5526508 -20.2690897 Largest eigenvalues: [1] 64179396 59689006 56898099 55128441 54901988 53398530 51759432 51524378 [9] 51175761 50990164 Smallest eigenvalues: [1] 0.56961296 0.50211579 0.44720842 0.42223273 0.28130779 0.27534215 [7] 0.25147123 0.21537915 0.13279976 -0.02095331 Largest eigenvalues: [1] 64184582 60436894 57899031 55767740 54944131 54249461 52922033 51960906 [9] 51704696 51225030 Smallest eigenvalues: [1] 0.53460627 0.48513699 0.45841813 0.41870000 0.35149039 0.26360364 [7] 0.18542450 0.18530241 0.06283988 -0.02437856 Largest eigenvalues: [1] 65182962 60004574 57855558 55896936 54950303 53383366 52172631 52169501 [9] 51908222 51320099 Smallest eigenvalues: [1] 0.51792872 0.47212651 0.39845731 0.36518041 0.30676181 0.17766244 [7] 0.16946911 0.02711115 -0.19072387 -1.27581554 Largest eigenvalues: [1] 63289504 60655951 57091378 55756244 55607503 53517099 52384267 51853917 [9] 51375768 50877973 Smallest eigenvalues: [1] 0.35428402 0.31058178 0.24239380 0.22800816 0.14366385 [6] 0.12448140 0.03062687 -0.47869851 -5.06478606 -23.70376459 Largest eigenvalues: [1] 64145724 59963504 57210943 55354251 55349428 53391942 52545954 51901404 [9] 51661341 51559959 Smallest eigenvalues: [1] 0.51276329 0.49977214 0.45915053 0.43379300 0.30729224 0.21820161 [7] 0.21343604 0.07972120 0.07041202 -0.47744528 Largest eigenvalues: [1] 64650803 60190840 56983154 55833077 55120328 53489655 52413247 51909332 [9] 51714069 51121776 Smallest eigenvalues: [1] 0.5025642 0.4721828 0.3668636 0.3230614 0.3146502 0.2637488 [7] 0.2031941 -0.1467369 -1.4206695 -2.1226795 Largest eigenvalues: [1] 63715589 60111156 57618041 56047231 55312315 54392889 52805750 52044473 [9] 51444691 51115785 Smallest eigenvalues: [1] 0.57618936 0.50437109 0.44253556 0.40162290 0.38143383 0.37137165 [7] 0.34330487 0.30554625 0.29375354 -0.01864911 Largest eigenvalues: [1] 64837960 60267482 57162178 56120568 55417987 53476621 52603059 52252707 [9] 51659271 51478283 Smallest eigenvalues: [1] 0.58747222 0.46247493 0.40615564 0.37252154 0.30938274 0.28769590 [7] 0.27621797 0.21745839 -0.09714347 -0.32569202 Largest eigenvalues: [1] 62227312 59514272 57100534 55172135 54543366 53429789 51792465 51402797 [9] 50634725 50505127 Smallest eigenvalues: [1] 0.46147735 0.38056247 0.29618611 0.29002196 0.25084440 0.23936072 [7] 0.16339231 0.08561973 -0.22944040 -0.86014343 Largest eigenvalues: [1] 64639040 60353994 57656192 55508975 55380277 53875566 52403306 52172145 [9] 51728105 51354625 Smallest eigenvalues: [1] 0.57988811 0.51784458 0.51381191 0.45793024 0.37170030 0.25735942 [7] -0.06295068 -0.13836125 -0.52675154 -1.11966227 Largest eigenvalues: [1] 63573915 59632503 56521656 55296162 54347553 52699011 51471821 51310638 [9] 51268506 50448895 Smallest eigenvalues: [1] 0.5214007 0.4768875 0.4298152 0.4212942 0.3716958 0.3493964 [7] 0.3239597 0.2362379 0.0699308 -0.1126082 Largest eigenvalues: [1] 62602423 59104969 56230342 54975342 54357951 52666610 51535995 51278994 [9] 50949311 50449507 Smallest eigenvalues: [1] 0.4619851 0.4373467 0.2804770 0.2619680 0.2446529 0.1830913 [7] 0.1278125 -1.0903324 -10.9656909 -15.0244509 Largest eigenvalues: [1] 62694405 60767248 56922074 55840588 55311746 54200471 52499931 52427577 [9] 51266031 51192816 Smallest eigenvalues: [1] 0.4691136 0.4675890 0.4521460 0.4215578 0.3961748 0.3735821 [7] 0.3233972 0.3086474 0.2560002 -2.5796506 Largest eigenvalues: [1] 64598599 59810243 57125325 56740307 54552084 53168614 52570067 51720052 [9] 51627871 50864959 Smallest eigenvalues: [1] 0.4950739 0.4182841 0.3632045 0.3131121 0.2895653 0.2741059 [7] 0.2276522 0.1932157 -2.8474786 -4.3829595 Largest eigenvalues: [1] 65116606 60196932 57591854 55723036 55332585 53907481 52410544 51780837 [9] 51767593 51596822 Smallest eigenvalues: [1] 0.42881371 0.42843055 0.41330292 0.34826939 0.27471201 0.25118000 [7] 0.22749707 0.05175862 -0.14980698 -0.62629763 Largest eigenvalues: [1] 65562037 60096164 57572794 56167306 55241240 53826638 52312279 52252265 [9] 52149083 51267152 Smallest eigenvalues: [1] 0.4398722 0.3542322 0.3352858 0.3278937 0.2830944 0.2761435 [7] 0.2545866 0.2401905 0.2218608 -2.2757988 Largest eigenvalues: [1] 64910548 60538846 57331118 56481801 55065655 53573763 52537394 52188850 [9] 51958811 51082411 Smallest eigenvalues: [1] 0.5825820 0.5214181 0.4655219 0.3664353 0.2955329 0.2874229 [7] 0.2437339 0.1509109 0.0836512 -0.2135389 Largest eigenvalues: [1] 63600227 60522491 58172235 55890903 55116795 54617482 52792353 52355593 [9] 51564019 51377719 Smallest eigenvalues: [1] 0.5395627 0.4969850 0.4725656 0.4008540 0.3506297 0.3187900 [7] 0.2486233 0.1379814 -0.1586557 -3.6408846 Largest eigenvalues: [1] 65308883 60894089 57845627 55820089 55800405 54306633 52204139 52164038 [9] 52004589 51414024 Smallest eigenvalues: [1] 0.48776266 0.42660923 0.41964758 0.27900997 0.15372980 0.06051094 [7] 0.04615386 0.03363386 -0.44282030 -0.98324188 Largest eigenvalues: [1] 64127109 59514626 56570703 55316417 54641692 53116269 51745080 51484933 [9] 51407195 50627684 Smallest eigenvalues: [1] 0.4480195 0.4290202 0.3620698 0.3434233 0.2289225 0.2185495 [7] 0.2069439 0.1831452 -0.3371043 -0.7102083 Largest eigenvalues: [1] 64740647 60270422 57081019 55734153 55635788 53974028 52272544 52230024 [9] 51709908 51293591 Smallest eigenvalues: [1] 0.42985231 0.41042422 0.34230539 0.23361449 0.22150275 0.14118708 [7] -0.06674456 -0.10785911 -0.23598135 -1.44185056 Largest eigenvalues: [1] 63494786 60188033 57139279 55480965 54894605 53421251 52359781 51744015 [9] 51676020 51441694 Smallest eigenvalues: [1] 0.4120311 0.3530477 0.3252676 0.3194421 0.2684833 0.2350737 [7] 0.2124143 -0.2327599 -1.7259560 -2.9801417 Largest eigenvalues: [1] 65316751 60665054 57846664 56859640 55050516 53122244 52641226 52524708 [9] 51873115 51425983 Smallest eigenvalues: [1] 0.52949050 0.51977566 0.46030365 0.40256656 0.35034502 0.33285267 [7] 0.24269094 0.20226650 0.16547097 -0.01262839 Largest eigenvalues: [1] 65187895 60407227 57679795 56043085 55501186 53840607 52319963 52289786 [9] 52257984 51238223 Smallest eigenvalues: [1] 0.5355013 0.4866217 0.4790100 0.4635764 0.3058997 0.2970957 [7] 0.2919438 0.2288407 0.1453966 -3.0520384 Largest eigenvalues: [1] 65569100 60320504 57311932 57140365 55450412 53761219 53027667 52832023 [9] 52099835 51575430 Smallest eigenvalues: [1] 0.48432657 0.41722013 0.37305041 0.37101165 0.33759755 0.31536109 [7] 0.23168491 0.10351043 0.01477636 -1.72761011 Largest eigenvalues: [1] 63970672 59407406 56841595 55606637 54763370 53214451 51755641 51679362 [9] 51332227 50420492 Smallest eigenvalues: [1] 0.44908713 0.33672758 0.29858326 0.27079519 0.24723851 0.24280154 [7] 0.10900399 0.05530902 -0.18665752 -3.96915671 Largest eigenvalues: [1] 62826251 59780839 56951517 55170505 54967555 53287056 51909405 51533791 [9] 51047624 50584780 Smallest eigenvalues: [1] 0.4030885 0.3232050 0.3224300 0.3159119 0.1967794 0.1060946 [7] -0.2897242 -0.3686685 -1.4298307 -7.2426381 Largest eigenvalues: [1] 65759220 60303184 57770024 56244253 55241131 53816392 52653183 52439571 [9] 52234521 51364901 Smallest eigenvalues: [1] 0.5345002 0.4299528 0.4105145 0.4070320 0.4041669 0.3091196 [7] 0.2758072 0.2374550 0.0174245 -0.6222161 Largest eigenvalues: [1] 63727698 59807558 56994452 55703662 54611526 53082872 51973343 51831475 [9] 51644300 50924872 Smallest eigenvalues: [1] 0.5726498 0.5451262 0.3782607 0.3726637 0.3318796 0.3125551 [7] 0.2861111 0.2766571 0.2449393 -1.8759456 Largest eigenvalues: [1] 65742674 60936223 57944267 56924360 55434213 53981498 52850324 52456395 [9] 52027138 51468123 Smallest eigenvalues: [1] 0.38466282 0.34412500 0.31278743 0.30168756 0.23161936 -0.02942748 [7] -0.25532381 -0.45614524 -4.35004079 -5.87324734 Largest eigenvalues: [1] 65762066 60747064 57700127 56797864 55418049 54033630 52750361 52219799 [9] 51915712 51537272 Smallest eigenvalues: [1] 0.52767391 0.49658116 0.47108715 0.39378270 0.34990204 0.34411725 [7] 0.33183697 0.31351879 0.26861629 -0.05393078 Largest eigenvalues: [1] 63450183 60049111 57222506 55744530 54958459 53491121 51822211 51784969 [9] 51723151 50800995 Smallest eigenvalues: [1] 0.3995092 0.3728310 0.3359519 0.3328351 0.2261396 0.2118650 [7] 0.1919549 0.1627495 -0.6917800 -0.8362633 Largest eigenvalues: [1] 65287175 59755730 57164905 56180634 54982685 53480718 52292760 52168119 [9] 51420429 50551183 Smallest eigenvalues: [1] 0.18401539 0.14786746 0.06978497 0.04196946 -0.84799536 [6] -2.82244893 -2.91878869 -7.83955027 -10.48930386 -10.72465611 Largest eigenvalues: [1] 63015292 59343386 56806285 54941365 54676381 53133107 51948958 51370627 [9] 50939976 50505795 Smallest eigenvalues: [1] 0.4162112 0.3950567 0.3814943 0.3436694 0.3189936 0.2129440 [7] 0.1635790 -0.3169176 -0.3860692 -19.4047729 Largest eigenvalues: [1] 65649748 60371426 56967309 56704262 55039215 53297497 52701752 52199412 [9] 52005626 51578201 Smallest eigenvalues: [1] 0.5782234 0.4555175 0.3931808 0.3645335 0.3009528 0.2992097 [7] 0.2659478 0.2355635 0.1816481 -1.1072331 Largest eigenvalues: [1] 64933711 60068767 57613945 55830360 54769876 53494796 51992486 51883485 [9] 51870576 51180093 Smallest eigenvalues: [1] 0.3864456 0.3462517 0.3379102 0.3135665 0.1996375 0.1664430 [7] 0.1406302 -0.1032846 -0.7843584 -8.0654301 Largest eigenvalues: [1] 64984888 59654481 57039415 55800905 54704032 53336990 51936026 51840380 [9] 51777594 51076770 Smallest eigenvalues: [1] 0.4050711 0.3740097 0.3333073 0.2391651 0.1913153 0.1636822 [7] 0.1235815 -0.2511083 -1.3444760 -2.0810993 Largest eigenvalues: [1] 62823361 60091349 56781597 55657152 55344127 53850259 52184449 52093415 [9] 51217848 50950622 Smallest eigenvalues: [1] 0.4314467 0.4165944 0.4120417 0.4038097 0.4012641 0.3845278 [7] 0.3272880 0.2725798 0.2274015 -1.4135281 Largest eigenvalues: [1] 65653811 60055155 57417268 56343302 55034186 53681498 52401672 52220181 [9] 52020759 51258859 Smallest eigenvalues: [1] 0.4758727 0.4608726 0.4556556 0.4323938 0.3701018 0.2365879 [7] 0.2144270 0.1550570 0.1502910 -0.5561089 Largest eigenvalues: [1] 63738614 60369039 56690112 55442243 55213960 53556840 52328046 51690484 [9] 51385012 51218123 Smallest eigenvalues: [1] 0.56306153 0.52658127 0.47173434 0.45383100 0.42391527 0.42125430 [7] 0.20202586 0.19171824 0.11256320 -0.03131913 Largest eigenvalues: [1] 63656171 60871318 58012191 55488091 55388539 53966137 52083580 51992877 [9] 51481041 51059512 Smallest eigenvalues: [1] 0.5011419 0.4319145 0.4033364 0.4013300 0.3480772 0.2668091 [7] 0.2404480 0.1824264 0.1629935 -1.3841629 Largest eigenvalues: [1] 64912517 60749296 58085408 56624964 55472811 53995104 52562384 52418681 [9] 51998494 51274172 Smallest eigenvalues: [1] 0.020042392 -0.004704113 -0.073676077 -0.306308087 -0.827563103 [6] -1.333066779 -1.896066519 -4.566893032 -31.788612443 -95.315975672 Largest eigenvalues: [1] 64822268 60796234 57662204 57111115 55806840 53922927 53290073 52906370 [9] 52168635 52147320 Smallest eigenvalues: [1] 0.41169973 0.37842981 0.29016466 0.23843720 0.22037619 [6] 0.10446320 0.03065762 -3.20189543 -6.47881696 -20.93161279 Largest eigenvalues: [1] 64472378 60524225 56835352 55875543 55252204 53432428 52377265 51855424 [9] 51297033 51274609 Smallest eigenvalues: [1] 0.44767431 0.43901405 0.41997561 0.37608988 0.35429693 0.29154808 [7] 0.27659556 0.09143168 -0.21071695 -0.41305720 Largest eigenvalues: [1] 64216696 60158780 57132664 55841669 55023064 53131348 51899238 51828994 [9] 51677814 50817483 Smallest eigenvalues: [1] 0.5741196 0.5505421 0.4556008 0.4103342 0.4017258 0.3393958 [7] 0.3138406 0.2927986 0.2920543 -0.9103729 Largest eigenvalues: [1] 64753797 60531812 57880718 55843819 55816233 54306976 52496266 52454427 [9] 51908585 51597589 Smallest eigenvalues: [1] 0.3954106 0.3613995 0.3325060 0.3275516 0.2974220 0.2710702 [7] 0.2502615 0.2367582 -0.6378864 -1.1384685 Largest eigenvalues: [1] 63327263 60199961 57124033 55791567 55489946 53626769 51780834 51686690 [9] 51605775 50720783 Smallest eigenvalues: [1] 0.43212595 0.32741429 0.32567039 0.26011858 0.25440367 [6] 0.24957935 0.15788884 0.05547981 -1.68471039 -19.49401894 Largest eigenvalues: [1] 66625704 60475109 57803166 57116582 54846214 53455785 53159817 52109215 [9] 51885727 51418221 Smallest eigenvalues: [1] 0.5788304 0.4919517 0.4915447 0.4019376 0.3892566 0.3432942 [7] 0.2706531 0.2270635 0.2212239 -2.2417639 Largest eigenvalues: [1] 63714784 60193815 57566657 55528026 54809956 53380310 51738601 51726574 [9] 51665693 50873681 Smallest eigenvalues: [1] 0.4161256 0.3370086 0.2706851 0.2617583 0.2553429 0.2475482 [7] 0.1902336 0.1843731 0.1410241 -2.9327487 Largest eigenvalues: [1] 64423892 60500851 57670418 55968544 55437163 53889326 52529896 52031286 [9] 51790159 51348478 Smallest eigenvalues: [1] 0.48957690 0.47015299 0.46006675 0.37604773 0.30726435 0.29129516 [7] 0.27364006 0.04752531 -0.39124815 -2.31135055 Largest eigenvalues: [1] 62651510 59904429 56950294 55563333 54590043 53724832 51829871 51815446 [9] 50687549 50427098 Smallest eigenvalues: [1] 0.6039265 0.6017610 0.4566132 0.4070116 0.4021365 0.3577973 [7] 0.3567614 0.2973197 0.2168300 -0.2109041 Largest eigenvalues: [1] 62583035 60103371 57022040 55489174 54749865 53764644 52200558 51838826 [9] 50925905 50699356 Smallest eigenvalues: [1] 0.3847111 0.3608571 0.2838315 0.2586309 0.1807085 0.1160849 [7] -0.2037558 -0.9309813 -2.4501460 -7.1487017 Largest eigenvalues: [1] 63856990 59529917 57103437 55498374 54886353 52969433 52444737 51763721 [9] 51519941 51227290 Smallest eigenvalues: [1] 0.4643036 0.4563959 0.3411069 0.3097260 0.3085544 0.2178306 [7] 0.1817973 0.1560109 -0.1715189 -1.5199293 Largest eigenvalues: [1] 64265624 60475686 57731537 55879962 55602103 54342353 52472337 52274148 [9] 51857597 51075721 Smallest eigenvalues: [1] 0.53319784 0.48387200 0.43300546 0.41839598 0.39414981 0.28614480 [7] 0.26960483 0.16740033 0.01359703 -0.01666494 Largest eigenvalues: [1] 64780318 59968615 57461963 56077034 55154664 53411297 52749414 52175812 [9] 51776000 51697869 Smallest eigenvalues: [1] 0.5328656 0.5176262 0.4643269 0.4480038 0.4409601 0.4248786 [7] 0.3531666 0.1299633 -0.3455052 -6.7485879 Largest eigenvalues: [1] 65200333 60587153 57865091 57121154 55281982 53291432 53269892 53163590 [9] 51778087 51717128 Smallest eigenvalues: [1] 0.31608215 0.24069674 0.11354433 0.04292511 0.01785595 [6] -0.09365783 -0.28427092 -0.43040014 -0.58442752 -17.43913944 Largest eigenvalues: [1] 65373349 60285595 57009054 56624893 54527763 53111888 52493104 51968697 [9] 51378361 51278289 Smallest eigenvalues: [1] 0.58440307 0.56496377 0.42533665 0.38660801 0.32656081 0.30282690 [7] 0.26696556 0.26276361 0.22767641 -0.01716992 Largest eigenvalues: [1] 65697616 60555321 58192546 56877296 54969200 53739581 53002544 52134666 [9] 52075852 51494691 Smallest eigenvalues: [1] 0.44304822 0.37265766 0.29829633 0.23858726 0.22991867 0.21105634 [7] 0.19873996 0.11486178 0.03595543 -1.24070248 Largest eigenvalues: [1] 65342020 61300072 58005750 56454558 56428480 54779343 53309136 52659273 [9] 52450986 52106185 Smallest eigenvalues: [1] 0.38217472 0.36485588 0.35094592 0.26728381 0.23247778 0.16547567 [7] 0.09538476 0.02860731 -0.21735869 -7.72457098 Largest eigenvalues: [1] 63334095 59538581 56408176 54624483 54402005 52758295 51463953 50776258 [9] 50634070 50495323 Smallest eigenvalues: [1] 0.30397583 0.25558232 0.14471632 0.07601755 -0.60589255 [6] -0.61994491 -1.51095916 -2.95515444 -3.28992655 -10.47873558 Largest eigenvalues: [1] 65763203 60741780 58185593 55956732 55824054 54485045 52861625 52690921 [9] 52135509 51680100 Smallest eigenvalues: [1] 0.4991781 0.4334595 0.4152560 0.4009806 0.3702056 0.3682359 [7] 0.3159687 0.3019355 0.1282064 -0.4315340 Largest eigenvalues: [1] 62955938 60050256 57713871 55067021 54941557 53317947 52294149 51478923 [9] 51347523 51157836 Smallest eigenvalues: [1] 0.5323462 0.4857399 0.4214185 0.3833629 0.3711478 0.3337403 [7] 0.3203418 0.2487450 0.2050167 -0.7882811 Largest eigenvalues: [1] 62996951 59727261 56551448 55281072 54686373 53071931 51755436 51471138 [9] 51214747 50837088 Smallest eigenvalues: [1] 0.5946170 0.5183249 0.4916747 0.4180030 0.3871741 0.3863442 [7] 0.3564048 0.3301643 0.2541634 -0.3942726 Largest eigenvalues: [1] 63730409 60186546 57120299 55601606 55461010 53529881 52272292 52027080 [9] 51440718 51050315 Smallest eigenvalues: [1] 0.36330113 0.35735802 0.35020490 0.19922920 0.18943896 0.01681169 [7] -0.05716524 -0.47010158 -1.07214941 -6.99305943 Largest eigenvalues: [1] 63722148 60829231 58148699 55463999 55318700 53917759 52690089 52480727 [9] 51897707 51633096 Smallest eigenvalues: [1] 0.55222586 0.45823215 0.45177975 0.42486961 0.37224121 0.31678248 [7] 0.29644523 0.15944283 0.02937954 -3.19650320 Largest eigenvalues: [1] 63376026 59945953 56749059 55369233 55319556 53519502 52251627 51778446 [9] 51407958 51070679 Smallest eigenvalues: [1] 0.58592843 0.52194145 0.47764782 0.44381887 0.44376518 0.40030160 [7] 0.37257114 0.26480777 0.22298196 -0.07080257 Largest eigenvalues: [1] 63485082 60569211 57530077 55770973 55523739 54042364 52642565 52029172 [9] 51497996 51340575 Smallest eigenvalues: [1] 0.43136605 0.38550549 0.32649466 0.26778635 0.25121159 0.21327358 [7] 0.13904030 0.09686388 -0.27884036 -4.44577419 Largest eigenvalues: [1] 64448487 59833774 56855923 55369714 54605800 52882258 51626295 51474303 [9] 51108687 50964307 Smallest eigenvalues: [1] 0.54795927 0.53691621 0.52213423 0.46169288 0.39491044 0.36204463 [7] 0.34326572 0.31803810 0.23958644 -0.05511732 Largest eigenvalues: [1] 65491196 60107113 57099988 55892860 54944890 53350633 52059768 51820849 [9] 51759235 51251340 Smallest eigenvalues: [1] 0.39344414 0.37724984 0.34940665 0.27996271 0.12144554 0.00261382 [7] -0.02613744 -1.41686733 -1.68098458 -3.46434352 Largest eigenvalues: [1] 65277080 60941411 58112631 56686881 55668835 54300135 52824995 52493835 [9] 52304768 51892882 Smallest eigenvalues: [1] 0.6063189 0.5308484 0.3461956 0.3320219 0.2734973 0.2677669 [7] 0.2644860 0.2240272 -0.2719019 -1.2216412 Largest eigenvalues: [1] 64558238 60087415 57245728 56167307 55028116 53528956 52308840 52233006 [9] 51927752 51181048 Smallest eigenvalues: [1] 0.56291728 0.45060296 0.43171305 0.37414273 0.30983884 0.25363964 [7] 0.13281164 -0.03918815 -0.14024569 -1.60148114 Largest eigenvalues: [1] 65287755 60389075 56786491 56654701 54984713 53309914 52584893 51906870 [9] 51833710 50930864 Smallest eigenvalues: [1] 0.51487497 0.48276612 0.43027291 0.36304155 0.30814851 0.27853417 [7] 0.23836498 0.09051503 -0.05880217 -0.28942108 Largest eigenvalues: [1] 65860429 60418873 58047819 57069157 55026846 53186002 53070411 52928777 [9] 52127774 51922596 Smallest eigenvalues: [1] 0.38513789 0.35329402 0.30083898 0.23472265 0.17805962 [6] 0.13328944 0.09622418 0.03881459 -1.38401051 -48.34514255 Largest eigenvalues: [1] 65344881 60958579 57688499 56599388 56063322 54457052 52876054 52660175 [9] 52656877 52090257 Smallest eigenvalues: [1] 0.4312859 0.4173851 0.3891183 0.3484750 0.3449000 0.3259633 [7] 0.2577873 0.2073475 0.1676589 -5.2918387 Largest eigenvalues: [1] 63255498 59533713 56828169 55259564 54862849 53599530 51904267 51385857 [9] 50949594 50448282 Smallest eigenvalues: [1] 0.63734119 0.57445111 0.52384105 0.42092156 0.38533863 0.37679104 [7] 0.33042094 0.29810122 0.23653938 -0.02378385 Largest eigenvalues: [1] 63600365 60051132 57470063 55396019 55391954 53784579 52302689 51889047 [9] 51544347 51095898 Smallest eigenvalues: [1] 0.51994774 0.51639376 0.47663901 0.46760953 0.32900118 0.31842745 [7] 0.30924047 0.26801878 -0.03818643 -1.16756900 Largest eigenvalues: [1] 63662271 60485632 57527631 56326118 55614006 54584158 52731053 52344902 [9] 51634205 51146867 Smallest eigenvalues: [1] 0.48328920 0.42787750 0.36987557 0.30745724 0.30352216 0.27737620 [7] 0.26770761 0.04073542 -1.48947386 -2.50340650 Largest eigenvalues: [1] 64167773 59543924 56578038 56000180 54821535 53184462 52002393 51735733 [9] 51597789 50581031 Smallest eigenvalues: [1] 0.3837986 0.3189130 0.2606605 0.2598902 0.2277843 0.2170432 [7] 0.1256639 -0.1040040 -0.8911664 -1.0151174 Largest eigenvalues: [1] 64005904 61156880 58089652 56573854 55502220 54837168 52846203 52639711 [9] 51865067 51440816 Smallest eigenvalues: [1] 0.35742058 0.34568332 0.33108576 0.29742645 0.21909574 0.17427533 [7] 0.12305939 0.06227753 -0.13489715 -0.76433901 Largest eigenvalues: [1] 63232132 60131839 57142035 55517821 55100759 53803981 52586383 52193985 [9] 51617067 51315934 Smallest eigenvalues: [1] 0.5466208 0.4967246 0.3807028 0.3712237 0.2574054 0.2535420 [7] 0.2340367 0.2301929 0.1325831 -0.1254779 Largest eigenvalues: [1] 64052832 60691122 57469384 56026900 55660761 53956005 52736235 52131179 [9] 52114103 51282560 Smallest eigenvalues: [1] 0.4037012 0.3521072 0.3280791 0.2550376 0.2417018 0.2400799 [7] 0.2278215 0.1771234 -0.7800077 -6.1343407 Largest eigenvalues: [1] 62133088 59409572 56274144 54916464 54198771 53182483 51833913 50767242 [9] 50291487 50061494 Smallest eigenvalues: [1] 0.53718516 0.48817502 0.40652090 0.40084619 0.37524395 0.34283589 [7] 0.32066116 0.25596458 0.16594763 -0.03977973 Largest eigenvalues: [1] 64666573 59813277 56967995 55927469 54979719 53237422 52018191 51599059 [9] 51411081 50654344 Smallest eigenvalues: [1] 0.5863206 0.5540619 0.3660004 0.3357883 0.3308424 0.3035866 [7] 0.2564905 0.1926957 0.1348714 -0.6011687 Largest eigenvalues: [1] 64549217 60455773 57580895 55754282 55281208 53622331 52292144 51778729 [9] 51761486 51282293 Smallest eigenvalues: [1] 0.4233936 0.3923690 0.3565185 0.3522399 0.2706483 0.1992710 [7] 0.1937219 0.1574523 -0.4014794 -0.7171172 Largest eigenvalues: [1] 64772814 60561956 57355931 56220468 55725827 53578165 53198393 52350586 [9] 52340102 51879462 Smallest eigenvalues: [1] 0.06490486 -1.80228086 -2.69572036 -3.52033941 -3.55069947 [6] -3.84548309 -5.71278350 -31.46560668 -35.47167959 -63.46264795 Largest eigenvalues: [1] 64997748 59963960 57058946 56641242 54610984 53009910 52891822 52115119 [9] 51965522 51151556 Smallest eigenvalues: [1] 0.4831236 0.4593811 0.4016475 0.3778138 0.3434826 0.3240533 [7] 0.2739518 -0.2593484 -0.3011723 -1.0297635 Largest eigenvalues: [1] 65545649 60161552 57590318 56614626 55251940 53558575 52815210 52746128 [9] 51984869 51710529 Smallest eigenvalues: [1] 0.5499005 0.4761912 0.4751196 0.3409258 0.2214093 0.1936841 [7] 0.1374441 -0.2217093 -0.2720919 -0.4819296 Largest eigenvalues: [1] 64653491 59996375 57353618 56287928 54929199 53304119 52242095 52139553 [9] 51892960 51162272 Smallest eigenvalues: [1] 0.482074080 0.460566062 0.385325015 0.228719676 0.204170119 [6] 0.203174929 0.196435913 0.055128857 -0.005558804 -0.326605294 Largest eigenvalues: [1] 62768595 60424613 57366627 56084040 54315705 54177786 52396494 51857246 [9] 50831455 50780357 Smallest eigenvalues: [1] 0.33616348 0.30931887 0.24539654 0.21218479 0.19538602 0.16675887 [7] -0.04329842 -0.69152847 -3.69108248 -3.70084264 Largest eigenvalues: [1] 66730562 60734822 58651687 56911715 55320015 53843097 52873511 52833433 [9] 52210005 52131775 Smallest eigenvalues: [1] 0.3611995 0.3274914 0.3050859 0.3032461 0.2313873 0.1929277 [7] -0.6057555 -1.7203846 -6.0100409 -6.2851009 Largest eigenvalues: [1] 65276626 60435392 57738273 56471316 55756719 54336068 52382170 52308816 [9] 52272510 51459525 Smallest eigenvalues: [1] 0.4335927 0.3927939 0.3713157 0.3186559 0.2776129 0.2157777 [7] 0.1130594 -0.1613570 -0.4355709 -0.7732010 Largest eigenvalues: [1] 63031142 60317934 57502074 55434523 54969485 53726933 52281038 52160996 [9] 51554053 51441035 Smallest eigenvalues: [1] 0.5193983 0.4570162 0.3336109 0.2595471 0.2309372 0.1836258 [7] 0.1728076 0.1150490 -0.1525138 -0.9321288 Largest eigenvalues: [1] 65418361 61047491 58192914 56319833 56028300 54807647 53364910 52520563 [9] 52260960 52038206 Smallest eigenvalues: [1] 0.4268365 0.3927026 0.3802362 0.2556951 0.2540186 0.1327133 [7] -0.1691681 -0.1740369 -0.7788713 -7.8781130 Largest eigenvalues: [1] 62830070 60802078 56983708 55954913 55551738 53578210 52451131 51827853 [9] 51608119 50635326 Smallest eigenvalues: [1] 0.53814031 0.43750791 0.42313005 0.34093855 0.32466209 0.23680186 [7] 0.17705006 0.11334663 0.01340931 -0.08469750 Largest eigenvalues: [1] 63555464 60490871 57430637 55738280 54921299 53881775 52456179 52068906 [9] 51293499 51061757 Smallest eigenvalues: [1] 0.4333640 0.4317225 0.3928476 0.3572899 0.2367908 0.1986234 [7] 0.1922412 0.1784152 0.1477908 -1.9821548 Largest eigenvalues: [1] 65152205 59676858 57135198 56774622 54493271 53259100 52539180 51869170 [9] 51610097 51147730 Smallest eigenvalues: [1] 0.48435633 0.40264210 0.36446977 0.36301620 0.32316294 0.24950164 [7] 0.19704065 0.09462268 -0.96091428 -1.29952398 Largest eigenvalues: [1] 64065666 59934080 56998028 55770122 55225703 53370099 52637581 51871130 [9] 51796019 51531562 Smallest eigenvalues: [1] 0.4106107 0.3917283 0.3747283 0.2766745 0.2655919 0.2452429 [7] 0.1711048 -0.1104001 -0.5303969 -0.6167583 Largest eigenvalues: [1] 66347962 59627369 57501559 56844415 54610971 53257406 52851364 51812852 [9] 51751618 51205624 Smallest eigenvalues: [1] 0.3818560 0.3622534 0.3585395 0.3434945 0.3060358 0.2726398 [7] 0.1727128 0.1078282 -1.1614511 -6.9716373 Largest eigenvalues: [1] 65220544 60027510 57054620 55816913 55283493 53766530 51961272 51960431 [9] 51725012 50968240 Smallest eigenvalues: [1] 0.4059022 0.3530834 0.3361140 0.3195295 0.2869012 0.2324727 [7] 0.1811697 0.1787874 0.1682798 -1.3636802 Largest eigenvalues: [1] 62953397 60254564 57754141 55633894 55078550 53966077 51886474 51805769 [9] 51118635 50921819 Smallest eigenvalues: [1] 0.619214797 0.616442213 0.584535630 0.460510220 0.435279445 [6] 0.345675152 0.303333379 0.246263739 0.167528658 -0.002613377 Largest eigenvalues: [1] 63338416 60494701 57078485 55733066 54895248 53254074 52016268 51831658 [9] 51710907 51100720 Smallest eigenvalues: [1] 0.4716803 0.3844930 0.3749503 0.3587162 0.3251543 0.3150077 [7] 0.2847899 0.2483912 0.1770407 -2.3884923 Largest eigenvalues: [1] 65042623 60892258 57715940 56646422 56036754 54388616 52892757 52558994 [9] 52485842 51851005 Smallest eigenvalues: [1] 0.4895471 0.4573535 0.4067461 0.4025775 0.3292774 0.3281108 [7] 0.3122810 0.1748698 0.1436429 -2.3075010 Largest eigenvalues: [1] 64436462 60550646 57432767 56493112 55535528 53834227 52602911 52405994 [9] 52347225 51596706 Smallest eigenvalues: [1] 0.4855649 0.4806738 0.4493792 0.4257337 0.4082319 0.3735515 [7] 0.3304049 0.2607255 0.1915591 -0.9385318 Largest eigenvalues: [1] 64387570 59921530 57110558 55931866 55157099 53491320 51791941 51746275 [9] 51692209 50844819 Smallest eigenvalues: [1] 0.40843473 0.32427276 0.31404083 0.28269195 0.25819740 0.20088638 [7] 0.15872948 -0.05990638 -0.40760688 -1.56795718 Largest eigenvalues: [1] 61387319 59136736 56580228 54256121 54200180 52605164 51293670 51223159 [9] 50441478 50253623 Smallest eigenvalues: [1] 0.28950387 0.21357170 0.19234762 0.17185247 0.03154836 [6] -2.17331564 -4.86923620 -13.51039474 -20.12396804 -21.59833755 Largest eigenvalues: [1] 65245542 60127559 57761262 56001396 55146296 53612514 52432609 52082065 [9] 51579811 51486569 Smallest eigenvalues: [1] 0.39205837 0.31352983 0.30824127 0.18453919 0.13212866 0.12475500 [7] -0.03321208 -0.43045756 -1.82916584 -6.20041403 Largest eigenvalues: [1] 63583849 59890614 56364157 55975814 54306776 52795132 51825314 51663233 [9] 51222232 50367169 Smallest eigenvalues: [1] 0.4417341 0.4038176 0.2764126 0.2090916 0.1918436 0.1719696 [7] 0.1196186 -1.2944904 -3.1554940 -10.6048038 Largest eigenvalues: [1] 64910314 59780734 56499646 55538812 54685551 53039032 51768858 51550473 [9] 51236687 51055376 Smallest eigenvalues: [1] 0.49598739 0.47153020 0.38643072 0.32012031 0.29891131 0.28403887 [7] 0.19823060 0.10982614 -0.07062857 -1.37500070 Largest eigenvalues: [1] 64122822 60164936 57021753 56138603 54995170 53078490 52399287 52108555 [9] 51936459 51337943 Smallest eigenvalues: [1] 0.43790307 0.42965487 0.42093261 0.39689484 0.32490137 0.29326572 [7] 0.18560769 0.14404229 0.08376391 -5.96082852 Largest eigenvalues: [1] 62395166 59918541 56974262 55364335 54878954 53654648 52038522 52011692 [9] 51105441 50938925 Smallest eigenvalues: [1] 0.58033472 0.55348785 0.55319654 0.46123111 0.39062386 0.33984309 [7] 0.33279145 0.26923419 0.26738863 -0.02851748 Largest eigenvalues: [1] 63921647 60853449 57697019 56174340 55496605 53631706 52174747 52131082 [9] 52016515 50972321 Smallest eigenvalues: [1] 0.44672618 0.42344827 0.28009525 0.21728263 0.04270283 -0.24956196 [7] -0.38973148 -0.65082647 -1.04833091 -1.20644654 Largest eigenvalues: [1] 64033331 60440040 57434177 55940394 55471909 53570874 52698263 52079971 [9] 51945936 51654200 Smallest eigenvalues: [1] 5.229017e-01 4.872134e-01 4.091669e-01 3.871437e-01 3.374349e-01 [6] 2.724708e-01 2.646559e-02 4.953285e-05 -2.159932e-01 -1.022007e+01 Largest eigenvalues: [1] 64585766 60772815 57768232 55733029 55649730 54203728 52804990 52194973 [9] 51786908 51641055 Smallest eigenvalues: [1] 0.39485902 0.35743264 0.29258255 0.26565283 0.21072465 [6] 0.05240952 -0.52427941 -1.78479060 -3.69658365 -13.50641203 Largest eigenvalues: [1] 65252481 60701004 58545524 56854701 55362679 54052209 52863939 52717160 [9] 52422373 51850961 Smallest eigenvalues: [1] 0.4260388 0.3843881 0.3199751 0.2957491 0.2919985 0.2727853 [7] 0.2296530 0.1868074 -0.2691620 -33.6905296 Largest eigenvalues: [1] 64659464 60283454 57135113 56598090 54910010 53312651 52638118 51763427 [9] 51735213 50828911 Smallest eigenvalues: [1] 0.45245959 0.43137403 0.42789055 0.41377461 0.27000240 0.15589950 [7] 0.06469077 0.02853310 -0.55176870 -4.58658188 Largest eigenvalues: [1] 65043370 60333388 57283807 56284134 55269108 53172234 52410858 52087600 [9] 51866501 51260698 Smallest eigenvalues: [1] 0.39484097 0.32028836 0.28356366 0.26924378 0.16560932 0.02345127 [7] -0.29873418 -0.54655779 -1.30287880 -3.55914105 Largest eigenvalues: [1] 63300354 59384292 56769794 55386602 54802349 53057496 51936379 51613263 [9] 51292005 50570245 Smallest eigenvalues: [1] 0.5090463 0.4855877 0.4854849 0.4402381 0.3986666 0.3634851 [7] 0.3071932 0.2615275 0.1640894 -0.4264008 Largest eigenvalues: [1] 63605236 59899879 56995324 55933483 54689395 53049682 51927081 51768912 [9] 51065334 50474857 Smallest eigenvalues: [1] 0.4426110 0.3924150 0.3596015 0.3576191 0.2842544 0.2478722 [7] 0.2419023 0.2189636 -0.6422768 -1.0990688 Largest eigenvalues: [1] 65854651 60392332 58206567 57219409 54917368 53739538 53203900 51959474 [9] 51769853 51272527 Smallest eigenvalues: [1] 0.4949781 0.4140768 0.3787345 0.3448595 0.3333660 0.3259888 [7] 0.2844763 0.2524878 0.1310555 -1.6280998 Largest eigenvalues: [1] 64238811 60040281 57171062 56542604 54825437 53367394 52436649 52229641 [9] 51998420 51034604 Smallest eigenvalues: [1] 0.35386660 0.31129898 0.27713572 0.26879827 0.25843558 0.23912535 [7] 0.17438173 0.06320406 -0.12203291 -1.33315029 Largest eigenvalues: [1] 66317305 60312688 58051522 56936628 55235273 53884129 52940023 52699727 [9] 51739837 51548984 Smallest eigenvalues: [1] 0.5510319 0.5161116 0.5037409 0.4154655 0.4120026 0.3990238 [7] 0.3271287 0.2679941 0.2270957 -0.1703969 Largest eigenvalues: [1] 64154331 60503779 57492130 55541542 55345073 53710495 51905311 51791781 [9] 51718372 51017918 Smallest eigenvalues: [1] 0.4462222 0.4413162 0.3764029 0.3592977 0.2907381 0.2880201 [7] 0.2393497 0.1297328 -4.4514676 -15.6981149 Largest eigenvalues: [1] 63816159 60564082 57121921 55900641 55222074 54073102 51895720 51650771 [9] 51268021 50550616 Smallest eigenvalues: [1] 0.581633838 0.494953119 0.465368073 0.406638838 0.325886603 [6] 0.313158887 0.306838249 0.268819250 0.207593516 -0.009696508 Largest eigenvalues: [1] 65146062 60099226 56879229 56228445 54718501 52981955 52338662 51812001 [9] 51147366 51014058 Smallest eigenvalues: [1] 0.398131529 0.381355802 0.364193841 0.321923968 0.318962823 [6] 0.287641207 0.199177536 0.175516353 0.008682012 -13.697321706 Largest eigenvalues: [1] 62586258 59671900 56939990 55172669 54620691 53391229 51834535 51496248 [9] 50957699 50791267 Smallest eigenvalues: [1] 0.5373549 0.3872080 0.3834492 0.3232014 0.3185726 0.3099545 [7] 0.2930033 -0.3948456 -0.6872954 -0.7143613 Largest eigenvalues: [1] 65016429 60373698 57780454 56620777 55399207 53834880 52838026 52743138 [9] 52149093 51270082 Smallest eigenvalues: [1] 0.4628780 0.3568853 0.3260001 0.2822877 0.2800484 0.2474752 [7] 0.2427732 0.2266537 0.2103802 -46.3683064 Largest eigenvalues: [1] 63598151 59883891 57031902 55800920 54973653 53321992 51884066 51850233 [9] 51779028 51005041 Smallest eigenvalues: [1] 0.5545398 0.5217730 0.5112008 0.4545997 0.4518587 0.3429025 [7] 0.2798084 0.2561103 0.1991687 -0.1232933 Largest eigenvalues: [1] 64484433 60315178 57468264 55982883 54868379 53522754 52060384 52016813 [9] 51755214 51244827 Smallest eigenvalues: [1] 0.58673801 0.56720582 0.50854628 0.40485383 0.39769796 0.35089211 [7] 0.25830660 0.22392965 0.01674273 -0.93324220 Largest eigenvalues: [1] 63886977 60729946 57621728 55869068 55771665 54311748 52564797 52165203 [9] 51889929 51282359 Smallest eigenvalues: [1] 0.34698327 0.24479120 0.21234660 0.19986008 0.17859472 [6] 0.09196713 0.06446403 -0.22413795 -14.59909836 -21.32771476 Largest eigenvalues: [1] 64865361 60133172 56897101 56342744 55436304 53807472 52311100 52247735 [9] 51796752 51360835 Smallest eigenvalues: [1] 0.37312771 0.37184272 0.36667553 0.32592863 0.02734883 0.02222577 [7] -0.06980914 -0.16022570 -0.81788154 -1.96318679 Largest eigenvalues: [1] 64687280 59339129 56755609 55437233 53972644 52396293 51836459 51311588 [9] 50960750 50905212 Smallest eigenvalues: [1] 0.5897315 0.5828536 0.5721948 0.5049707 0.4852852 0.3320432 [7] 0.3168799 0.2096651 0.1794736 -0.9524993 Largest eigenvalues: [1] 64715781 60298513 56894736 56242623 55206968 53365362 52215443 52039307 [9] 51799506 50854229 Smallest eigenvalues: [1] 0.4642808 0.4515403 0.4476178 0.3966770 0.3521420 0.2985550 [7] 0.2366061 0.1849280 0.1127254 -0.6650059 Largest eigenvalues: [1] 65738517 60204478 57370096 56469144 55383243 53559289 52556160 52479965 [9] 51578968 51266802 Smallest eigenvalues: [1] 0.5572239 0.4581508 0.4485191 0.3912046 0.3837334 0.2791748 [7] 0.2131950 0.1473619 0.1430001 -0.2701492 Largest eigenvalues: [1] 65247883 60923462 57981055 56172890 56056063 54551032 52922420 52639435 [9] 52234702 51988180 Smallest eigenvalues: [1] 0.4278794 0.3476179 0.3183024 0.2369793 0.2132186 0.1871104 [7] -0.1011245 -0.2236885 -5.7885355 -5.9580871 Largest eigenvalues: [1] 64286370 60488102 57529748 55757762 55600341 54161487 52751630 52529613 [9] 51838513 51656311 Smallest eigenvalues: [1] 0.46965636 0.38818181 0.23838787 0.21927810 0.12616960 0.02622104 [7] -0.49254969 -0.58047406 -0.61184724 -0.66725288 Largest eigenvalues: [1] 62967702 59133922 56397725 55423130 54243728 52665853 51389320 51213887 [9] 51164835 50103864 Smallest eigenvalues: [1] 0.42825641 0.39942765 0.36942551 0.33032954 0.26166593 [6] 0.23420744 0.23011344 0.11908614 -0.09278426 -26.28260262 Largest eigenvalues: [1] 62750030 59768004 56684393 55236055 55054427 53387009 52023520 51215090 [9] 51066586 50587866 Smallest eigenvalues: [1] 0.4816451 0.4668635 0.2941645 0.2504987 0.2145759 0.1991994 [7] 0.1981649 0.1351890 0.1006855 -0.8509431 Largest eigenvalues: [1] 63257582 60351017 57108991 55608188 55059808 53621656 51913832 51618678 [9] 50875572 50648289 Smallest eigenvalues: [1] 0.54546501 0.51450324 0.48724536 0.45671083 0.39243157 0.36990241 [7] 0.34163215 0.05913585 -0.11125103 -0.11468128 Largest eigenvalues: [1] 64991354 59947584 57046232 56478948 54597889 53066801 52412655 51765989 [9] 51355717 50773118 Smallest eigenvalues: [1] 0.44728753 0.35795645 0.33933782 0.32804442 0.21225882 0.21049584 [7] 0.15980083 0.14846945 -0.06079634 -0.18078756 Largest eigenvalues: [1] 67266219 60669648 57623456 56922178 55185723 53488630 53024284 52573740 [9] 52055097 51973084 Smallest eigenvalues: [1] 0.4866668 0.4786676 0.4489369 0.3615731 0.3022249 0.2778196 [7] 0.2182407 -0.1331183 -0.2604480 -0.8549073 Largest eigenvalues: [1] 64523437 59928819 57432788 55326168 55255790 53452493 52103472 51758429 [9] 51592691 50858343 Smallest eigenvalues: [1] 0.43850409 0.38427917 0.25357374 0.24798042 -0.05440934 [6] -0.24140800 -0.71673711 -4.93092252 -8.02792029 -20.90923070 Largest eigenvalues: [1] 65249773 60106396 57294159 56064667 54739048 53252048 52352397 51677287 [9] 51463083 50458460 Smallest eigenvalues: [1] 0.5991883 0.5281029 0.5178836 0.4622291 0.4454491 0.4059809 [7] 0.2962903 0.1331650 -0.1296811 -1.1521993 Largest eigenvalues: [1] 64526084 60285005 57265766 56190777 55278706 53471709 52690261 52267597 [9] 51623127 51275306 Smallest eigenvalues: [1] 0.4188800 0.3487356 0.3279679 0.3269908 0.3075070 0.2495696 [7] 0.2208671 0.2091194 -1.3076344 -4.1788323 Largest eigenvalues: [1] 64366927 60693923 57820655 55579550 55544610 54149107 52438327 51997257 [9] 51667113 51598606 Smallest eigenvalues: [1] 0.4661149 0.4407696 0.3560121 0.3428487 0.3228056 0.2507656 [7] 0.1896730 0.1462090 -2.6825332 -28.2155618 Largest eigenvalues: [1] 61986590 59683254 56485676 55499970 54402611 53489888 51767450 51112500 [9] 50399418 50229598 Smallest eigenvalues: [1] 0.5329010 0.4513208 0.4414890 0.3713458 0.3555911 0.3053348 [7] 0.2269964 -0.2588324 -0.3180586 -0.4310804 Largest eigenvalues: [1] 65358608 60603954 58086456 56869578 55079701 53290685 52894107 52768550 [9] 51954210 51784438 Smallest eigenvalues: [1] 0.5617092 0.5354533 0.4306728 0.4148428 0.3158316 0.3071711 [7] 0.2266957 0.2207708 0.2206010 -0.5619875 Largest eigenvalues: [1] 64734970 60953231 57507971 56017674 55625522 54040222 52357535 52323881 [9] 52120162 51547714 Smallest eigenvalues: [1] 0.4700373 0.4265857 0.4048073 0.3963303 0.3359164 0.3233833 [7] 0.2706780 0.2436359 -0.2125806 -10.2950976 Largest eigenvalues: [1] 64422931 60170357 57548662 56342241 55244688 53709279 52339785 51944408 [9] 51928136 50815782 Smallest eigenvalues: [1] 0.596600063 0.580191868 0.541670645 0.530609083 0.497916460 [6] 0.436080669 0.306870086 0.241490864 0.169635234 -0.001726538 Largest eigenvalues: [1] 64294945 60516733 57663696 55909461 55163800 53264149 52199414 52112162 [9] 51571047 51089777 Smallest eigenvalues: [1] 0.4961910 0.4902026 0.4806140 0.4553746 0.4390719 0.2595080 [7] 0.1791196 -0.2440164 -0.6227254 -3.0845770 Largest eigenvalues: [1] 64387207 60315566 57771970 55909323 55112907 53611629 52287926 52091550 [9] 51807467 51117083 Smallest eigenvalues: [1] 0.3165348 0.2868056 0.2435300 0.2355389 0.1478802 0.1392101 [7] 0.1313882 -1.8590454 -7.4206405 -12.6158730 Largest eigenvalues: [1] 64169161 60745713 57632644 55876968 55282915 54205999 52662057 52153117 [9] 51798160 51468295 Smallest eigenvalues: [1] 0.4425852 0.4177886 0.3940021 0.2782246 0.1765252 -0.2251043 [7] -1.3219801 -2.1602911 -7.2638773 -16.2835269 Largest eigenvalues: [1] 65463398 59849089 57004151 56818991 54575699 52753964 52405633 51836765 [9] 51404133 50852713 Smallest eigenvalues: [1] 0.595002753 0.499714627 0.496328368 0.429235879 0.405218161 [6] 0.382180088 0.262937485 0.200909666 0.002652293 -0.499905603 Largest eigenvalues: [1] 64468475 60624678 57449008 55784301 55496268 53769662 52911557 51938199 [9] 51561082 51431505 Smallest eigenvalues: [1] 0.402866174 0.391950759 0.326876034 0.280944028 0.274173956 [6] 0.182973124 -0.005183514 -0.534444484 -1.481506686 -21.430849617 Largest eigenvalues: [1] 64859279 60681333 57672223 55802533 55648619 54313291 52602615 52348499 [9] 51829606 51524747 Smallest eigenvalues: [1] 0.4119543 0.4046272 0.3730116 0.3507124 0.3311649 0.2710863 [7] 0.1903433 0.1051565 -0.1564091 -0.1932710 Largest eigenvalues: [1] 65973088 60914917 57724318 56058834 55645614 53826329 52704344 52195036 [9] 51983071 51843962 Smallest eigenvalues: [1] 0.47219064 0.38574298 0.37339287 0.34166300 0.33395930 0.27276534 [7] 0.24513438 0.22089711 0.03058645 -1.93180410 Largest eigenvalues: [1] 65625374 60427104 57648340 56737618 55186455 53755204 52605260 52450966 [9] 51990118 51601657 Smallest eigenvalues: [1] 0.5020374 0.4191968 0.3869501 0.2561177 0.2272818 0.2118193 [7] -0.2205335 -0.3867581 -1.6421047 -2.6228899 Largest eigenvalues: [1] 66398218 61009272 58434454 56750705 55942717 54161086 53024288 52873617 [9] 52418817 52080028 Smallest eigenvalues: [1] 0.38320997 0.36041026 0.32108723 0.31321878 0.24711360 0.23687529 [7] 0.18993739 0.09900609 -0.11287443 -7.11540963 Largest eigenvalues: [1] 65209274 59383444 56863153 56030463 54684419 53108447 51999627 51305003 [9] 51194510 50584511 Smallest eigenvalues: [1] 0.44748223 0.41966422 0.40973741 0.29212575 0.24848101 0.24345831 [7] 0.20466526 0.09570455 -0.10115300 -0.28204296 Largest eigenvalues: [1] 66835808 61391501 58492227 56927542 55580044 53831180 53109222 52908205 [9] 52086839 52022214 Smallest eigenvalues: [1] 0.55870135 0.52577165 0.47899852 0.46535595 0.46441455 0.44421676 [7] 0.23913658 0.23565963 0.04982777 -0.05214577 Largest eigenvalues: [1] 62705148 60130743 56777315 55465905 55262063 53405581 52249528 51664529 [9] 51217419 50464234 Smallest eigenvalues: [1] 0.6335170 0.6058209 0.5532983 0.5524656 0.4573758 0.4543889 [7] 0.3424434 0.2313038 0.2235777 -0.8873691 Largest eigenvalues: [1] 64776839 60419149 57624121 56267497 55176198 53743129 52237618 52009423 [9] 51825588 50989582 Smallest eigenvalues: [1] 0.4809460 0.4000531 0.3643749 0.3633007 0.3445975 0.3377922 [7] 0.2070527 0.1865913 -0.5667321 -2.3734881 Largest eigenvalues: [1] 64019446 59980557 57263975 56189248 54889406 53251221 52132000 52064996 [9] 51700317 50635496 Smallest eigenvalues: [1] 0.6369606 0.5302138 0.5200224 0.4815634 0.4375574 0.3863850 [7] 0.3701213 0.3085190 0.2146247 -0.1748042 Largest eigenvalues: [1] 65155071 61211659 58338330 56544796 56325039 54708452 53472067 52642735 [9] 52528081 51940575 Smallest eigenvalues: [1] 0.4785571 0.4746846 0.4410983 0.4118512 0.3841887 0.3668965 [7] 0.3277161 0.1811739 0.1408216 -0.6609918 Largest eigenvalues: [1] 64909126 61115423 58179149 56212328 56057032 54498844 52544017 52510847 [9] 52190004 51690883 Smallest eigenvalues: [1] 0.47117178 0.46469081 0.41250110 0.34659523 0.34399625 0.32194163 [7] 0.31081005 0.12085568 0.06078797 -2.71815573 Largest eigenvalues: [1] 64350075 59518803 56663317 55984812 54508994 52817657 51998067 51519314 [9] 51497351 50560359 Smallest eigenvalues: [1] 0.4346896 0.3733635 0.3646124 0.3505277 0.2973378 0.2606022 [7] 0.2281173 0.1832396 -1.3018144 -6.9913078 Largest eigenvalues: [1] 64948744 60146340 57352168 56005045 55060614 53669277 52084438 51805155 [9] 51760344 50830627 Smallest eigenvalues: [1] 0.40427683 0.34842963 0.30804670 0.24481902 0.15717935 [6] 0.05892585 -0.00211258 -0.78667016 -1.56359745 -12.26724365 Largest eigenvalues: [1] 65621086 60871049 58196565 56339127 55622847 54115936 52829808 52349538 [9] 52103273 51605139 Smallest eigenvalues: [1] 0.51651388 0.48494782 0.46418786 0.46389734 0.44118384 0.41089926 [7] 0.40272391 0.30869897 0.09280225 -0.11407244 Largest eigenvalues: [1] 63662340 59634720 57365275 55432102 54967724 53265366 51598050 51544271 [9] 51452041 50482966 Smallest eigenvalues: [1] 0.32354642 0.32169932 0.26056856 0.25879940 0.21499204 0.11053373 [7] -0.08515092 -0.54543152 -1.41498525 -2.72793053 Largest eigenvalues: [1] 65450136 59518139 57091560 56065267 54313443 52782946 52178448 51804085 [9] 51517405 51122820 Smallest eigenvalues: [1] 0.4367802 0.3624695 0.3374817 0.3349788 0.2379174 0.2035338 [7] -1.1352942 -1.7838715 -3.0375818 -8.8461238 Largest eigenvalues: [1] 65747952 60107712 57451055 57318072 54778518 53192069 53168751 52449707 [9] 52265871 51682659 Smallest eigenvalues: [1] 0.37074622 0.32964236 0.25232790 0.23409043 0.14494076 [6] 0.13759617 0.11152770 0.07757987 -0.57253582 -13.93100786 Largest eigenvalues: [1] 65781897 59924479 57497598 56680141 54718461 53090438 52722620 51923643 [9] 51659170 51122536 Smallest eigenvalues: [1] 0.5831168 0.5639826 0.3837977 0.3826191 0.3035591 0.2863617 [7] 0.2745112 0.2731092 0.2431454 -1.4086800 Largest eigenvalues: [1] 65137463 60643966 57849733 56184126 55552678 54203133 52339115 52319215 [9] 52256902 51332130 Smallest eigenvalues: [1] 0.3683887 0.3512420 0.3408925 0.3232900 0.2787079 0.2724606 [7] 0.2245215 0.1846142 -0.2622792 -1.5402836 Largest eigenvalues: [1] 64623202 60783323 57881613 56446604 55995575 54235915 52386160 52236666 [9] 52109384 51197995 Smallest eigenvalues: [1] 0.46198582 0.45573780 0.43610679 0.36581319 0.35699677 0.34375384 [7] 0.25456610 0.14674583 0.08096377 -0.26255144 Largest eigenvalues: [1] 64448147 61161415 57735874 56329391 55854340 54270310 52482906 52143619 [9] 52012443 51288637 Smallest eigenvalues: [1] 0.4454687 0.4390658 0.4226786 0.3351076 0.3039356 0.2955374 [7] 0.2863432 0.2531215 0.1173429 -0.3254932 Largest eigenvalues: [1] 63319878 59730634 56756909 55304533 54739660 53105694 51500323 51455907 [9] 51228466 50587355 Smallest eigenvalues: [1] 0.50226669 0.45125814 0.41137682 0.33723767 0.33328902 0.21965764 [7] 0.12710130 0.04384981 -0.12613060 -1.86189819 Largest eigenvalues: [1] 61730491 59517124 56837496 54670470 54418834 52959528 51681618 51557314 [9] 50819779 50630242 Smallest eigenvalues: [1] 0.4082084 0.3809722 0.3175078 0.3117375 0.3034126 0.2684511 [7] 0.2369499 0.2207037 -0.3627658 -0.9675033 Largest eigenvalues: [1] 64127099 60297681 57598985 55669821 55220419 53732401 51926088 51745300 [9] 51737051 51057534 Smallest eigenvalues: [1] 0.472090059 0.457929953 0.372775765 0.320080079 0.255523639 [6] 0.234289583 0.228135878 0.005882272 -0.007653789 -0.180203494 Largest eigenvalues: [1] 65302765 60951090 58156776 55806616 55607269 54387828 52698923 52422608 [9] 51864350 51707824 Smallest eigenvalues: [1] 0.5217158 0.4826237 0.3938609 0.3764443 0.3246314 0.2812599 [7] 0.2804431 0.2751018 -0.8850331 -1.4925676 Largest eigenvalues: [1] 64889062 59795307 57211664 55956867 54999276 53616969 52016384 51972910 [9] 51716295 51143142 Smallest eigenvalues: [1] 0.42296270 0.41268900 0.40888269 0.37646961 0.31108342 0.27795950 [7] 0.19224440 0.16648144 0.15671339 -0.09273714 Largest eigenvalues: [1] 64267331 60084489 57393624 55524141 55430005 53850331 52270825 52006573 [9] 51570610 51225934 Smallest eigenvalues: [1] 3.193495e-01 2.013858e-01 9.200554e-02 8.926988e-02 9.936771e-04 [6] -2.215423e-02 -1.101043e-01 -8.727731e-01 -1.565285e+01 -1.840693e+01 Largest eigenvalues: [1] 62460189 60161864 56292925 55248765 55189474 53442812 51989511 51885954 [9] 50976871 50455187 Smallest eigenvalues: [1] 0.5385928 0.4965616 0.4868131 0.4751368 0.4265040 0.4066629 [7] 0.3680893 0.3539590 0.2986524 -0.9663422 Largest eigenvalues: [1] 65287550 60627157 57758124 56718238 55491871 53974496 52592540 52320014 [9] 51865157 51279229 Smallest eigenvalues: [1] 0.56935255 0.56354283 0.54377823 0.53103914 0.47037046 0.37939205 [7] 0.36660544 0.33274338 0.31475206 -0.05407509 Largest eigenvalues: [1] 65572468 61072960 58293329 57137740 55616490 53992113 53098514 52812922 [9] 52335700 51810663 Smallest eigenvalues: [1] 0.39771853 0.36605174 0.35853521 0.28550846 0.22965467 -0.06847966 [7] -0.30470030 -1.54637995 -2.25399036 -9.44133852 Largest eigenvalues: [1] 63105488 60083343 57030489 55284656 55239587 53482165 52226953 51869946 [9] 51269099 51061421 Smallest eigenvalues: [1] 0.5171361 0.4865891 0.4518466 0.4104234 0.3556949 0.2574824 [7] 0.2164616 0.1135890 -0.4051819 -0.4166858 Largest eigenvalues: [1] 64173327 60655314 58378402 55888399 55454987 54630121 52780321 52214480 [9] 51606673 51422334 Smallest eigenvalues: [1] 0.4029243 0.4018202 0.3899124 0.3105355 0.2693868 0.2628813 [7] 0.2519655 0.2371773 0.2353172 -0.7939161 Largest eigenvalues: [1] 64607546 60727005 57790348 55740800 55681926 54315022 52456711 52037329 [9] 51845447 51196923 Smallest eigenvalues: [1] 0.366884917 0.275665985 0.218540002 0.007691799 -0.006153075 [6] -0.191619157 -0.672055184 -0.864089060 -0.901121715 -1.334254853 Largest eigenvalues: [1] 62099733 60216656 56901223 55598598 55188973 53763432 52376058 51891639 [9] 50930336 50819007 Smallest eigenvalues: [1] 0.42610577 0.33129939 0.32683798 0.26952448 0.25144868 0.24254517 [7] 0.11172515 0.07045316 -2.62996106 -6.92126661 Largest eigenvalues: [1] 63799434 60628491 57881872 55808186 55791607 54155629 52676672 52200287 [9] 51794047 51657184 Smallest eigenvalues: [1] 0.5487412 0.4565224 0.4462112 0.4244772 0.4183680 0.3785733 [7] 0.3549216 0.3367931 0.3349219 -0.4078569 Largest eigenvalues: [1] 63489102 59887664 56903379 55705661 54786918 53210919 51700762 51474477 [9] 51185618 50363963 Smallest eigenvalues: [1] 0.5405838 0.4536518 0.4077796 0.3958012 0.3701455 0.3227531 [7] 0.2808164 0.2673987 0.1986518 -1.3182308 Largest eigenvalues: [1] 64164268 60062226 56977050 56058612 55020514 53400863 52003669 51861822 [9] 51733894 51039032 Smallest eigenvalues: [1] 0.4270398 0.2864364 0.2571402 0.2373492 0.2039900 0.1876548 [7] 0.1817205 -2.1896355 -3.1294113 -6.5270451 Largest eigenvalues: [1] 64892434 59937071 56962640 56583702 54665060 53176919 52351480 52247487 [9] 51744908 51006328 Smallest eigenvalues: [1] 0.5341144 0.4107927 0.4005878 0.3090971 0.2481083 0.2461680 [7] -0.1281613 -0.2992312 -0.6081750 -19.7901473 Largest eigenvalues: [1] 65382267 60099102 57087956 55870202 54976591 53418825 52080401 52032896 [9] 51658714 51250411 Smallest eigenvalues: [1] 0.51259405 0.50985427 0.46812844 0.38045732 0.36816855 0.36809214 [7] 0.27374988 0.23827465 -0.02485813 -0.38040892 Largest eigenvalues: [1] 62650980 59780044 56743963 55194066 54722693 53315350 51948454 51735596 [9] 50874021 50628503 Smallest eigenvalues: [1] 0.50521696 0.46510991 0.43458252 0.39244545 0.38267005 0.35211441 [7] 0.34020312 0.09802594 0.04738960 -0.02482130 Largest eigenvalues: [1] 63739581 60305508 57361615 55468862 54863352 53439318 51993580 51522328 [9] 51517327 51152138 Smallest eigenvalues: [1] 0.46761774 0.42545473 0.42043402 0.38920906 0.30095922 0.27767208 [7] 0.25500262 0.17357523 0.17339234 -0.07817236 Largest eigenvalues: [1] 64608709 61206609 58213748 56061023 55700191 54158954 52831963 52208762 [9] 52180561 51948289 Smallest eigenvalues: [1] 0.4989402 0.4619286 0.3987685 0.3691881 0.3585004 0.2764301 [7] 0.2401817 -0.1596020 -0.2613991 -0.5504757 Largest eigenvalues: [1] 63736179 59813801 57434454 55337619 54933574 53661507 51936093 51500664 [9] 51226749 50693658 Smallest eigenvalues: [1] 0.48503699 0.43655895 0.40992494 0.38106473 0.34250827 0.32877577 [7] 0.28788444 0.21054488 0.16162259 -0.03885352 Largest eigenvalues: [1] 64206663 59447133 57262210 55571173 54493701 53059324 51848335 51729715 [9] 51275121 50839147 Smallest eigenvalues: [1] 0.4441993 0.4173982 0.4049454 0.3850415 0.3815862 0.3424496 [7] 0.3171507 0.2675028 -0.3561928 -33.5318669 Largest eigenvalues: [1] 66225916 60488782 57869109 57080502 55102329 53714415 53090096 51956956 [9] 51913401 51097694 Smallest eigenvalues: [1] 0.4457368 0.3469112 0.3111173 0.2777945 0.2741597 0.2596741 [7] -0.1852783 -0.4284197 -3.5392829 -4.9668615 Largest eigenvalues: [1] 65313613 59957328 57855888 56466579 55224343 54015896 52719527 52402783 [9] 52395980 51834450 Smallest eigenvalues: [1] 0.3377719 0.3016237 0.2998872 0.2683010 0.2435994 0.2341296 [7] -0.6551704 -0.7253914 -1.4010014 -9.6362314 Largest eigenvalues: [1] 62368185 59927158 57522380 55937590 54214348 54102724 52385871 52107340 [9] 51047245 50735455 Smallest eigenvalues: [1] 0.260392160 0.246198173 0.186251639 0.137679517 0.081803619 [6] 0.044102629 0.018894230 0.005853617 -0.990973008 -17.603513577 Largest eigenvalues: [1] 62908863 60733371 57767519 55569707 55207542 53982085 52193411 51845545 [9] 51372746 51224998 Smallest eigenvalues: [1] 0.6131991 0.5135985 0.5011057 0.4633477 0.3946598 0.3463550 [7] 0.3091917 0.2928958 0.2560634 -1.0221547 Largest eigenvalues: [1] 65238470 61076332 57875594 56809465 55393005 53901856 52814122 52722993 [9] 52182180 51926616 Smallest eigenvalues: [1] 0.5355943 0.4957699 0.4848498 0.4499409 0.4378068 0.3363424 [7] 0.2886285 0.2509242 0.2167049 -0.1989357 Largest eigenvalues: [1] 65458743 60026275 57834345 56593570 54697921 53062377 52831881 51795006 [9] 51477791 50890314 Smallest eigenvalues: [1] 0.4387782 0.4277284 0.4100086 0.3495594 0.3489280 0.2971214 [7] 0.1925726 0.1919807 -0.5387739 -21.0813380 Largest eigenvalues: [1] 65004417 60376581 57702056 56532773 55130848 53414412 52714241 52001861 [9] 51906824 50990053 Smallest eigenvalues: [1] 0.5256431 0.4572065 0.4491234 0.4113677 0.3850087 0.3790004 [7] 0.3171255 0.1960669 0.1807790 -1.9247137 Largest eigenvalues: [1] 62940405 60269618 57575250 55412373 54921097 53843621 51914001 51808395 [9] 51081605 50929350 Smallest eigenvalues: [1] 0.6205814 0.5906973 0.5541414 0.5475933 0.4521749 0.3755399 [7] 0.2649637 0.2049598 0.1841806 -0.8680196 Largest eigenvalues: [1] 64353659 60059015 56872269 55844029 55007882 53352383 51725673 51651644 [9] 51422861 50519991 Smallest eigenvalues: [1] 0.12920234 0.07653261 0.06371167 -0.04779952 -0.34083850 [6] -1.92409911 -9.72468340 -27.61676598 -33.29934368 -44.89290360 Largest eigenvalues: [1] 65180621 60207937 56484016 56340252 55208204 53330429 52327657 52303894 [9] 52194607 51147638 Smallest eigenvalues: [1] 0.37429053 0.34924468 0.34516069 0.34213494 0.28880090 0.09359304 [7] 0.07296078 0.05012915 -1.28637025 -3.38288881 Largest eigenvalues: [1] 62689806 59049125 56601700 55003811 54732128 53093561 51879078 51489399 [9] 50876470 50486287 Smallest eigenvalues: [1] 0.47232773 0.45977329 0.43119076 0.36240963 0.32969283 0.25910272 [7] 0.23378894 0.02993916 -0.18171418 -0.24359475 Largest eigenvalues: [1] 62234920 59332481 56892529 54813651 54477956 52900682 51874847 51266706 [9] 50945506 50799773 Smallest eigenvalues: [1] 0.4153222 0.3721074 0.3648583 0.3597596 0.3279138 0.2510410 [7] 0.2327371 0.1508180 0.1263878 -0.7126174 Largest eigenvalues: [1] 63577332 60097602 57111281 55502187 55245232 53909106 52332234 51916698 [9] 51393220 51173762 Smallest eigenvalues: [1] 0.5033041 0.5028158 0.3602542 0.3423207 0.3097934 0.2378690 [7] 0.2302833 0.1502926 -1.0370043 -5.8579513 Largest eigenvalues: [1] 64680500 60901910 57293572 56249877 55814252 54005386 52474461 52274526 [9] 51954039 51479185 Smallest eigenvalues: [1] 0.4363476 0.4250772 0.3885742 0.3249050 0.2703968 0.2699337 [7] 0.2582783 -0.1438690 -0.3453970 -0.7135927 Largest eigenvalues: [1] 64614830 60386060 57820301 56550732 55390296 53923850 52997069 52582632 [9] 52169874 51713304 Smallest eigenvalues: [1] 0.4570453 0.4069215 0.3449191 0.3265189 0.3156249 0.2754068 [7] 0.2434499 0.1960337 -0.2192655 -2.0999734 Largest eigenvalues: [1] 64012457 60461494 57354408 56073168 55690807 54014159 52241063 52112263 [9] 52017083 50998877 Smallest eigenvalues: [1] 0.4798902 0.4523935 0.3724019 0.3239674 0.2783808 0.2624360 [7] 0.2622589 0.1560630 0.1261194 -0.1911510 Largest eigenvalues: [1] 63582006 60115770 57810428 55284706 55250052 53883565 52254894 52162502 [9] 51444836 51278298 Smallest eigenvalues: [1] 0.473308256 0.401127285 0.334910641 0.322614510 0.286410878 [6] 0.283300887 0.194000008 0.047672795 -0.004845634 -0.292629510 Largest eigenvalues: [1] 64558938 61130217 57782812 56540130 55437595 53800198 52441661 52407814 [9] 51749690 51345857 Smallest eigenvalues: [1] 0.4848754 0.4563133 0.4359468 0.3283973 0.3072911 0.2526044 [7] 0.1913358 -0.1546851 -0.2407034 -4.5787521 Largest eigenvalues: [1] 61991750 60031365 56568428 55263409 54337442 53486483 52057173 51534840 [9] 50573657 50333762 Smallest eigenvalues: [1] 0.4570738 0.3474239 0.3350057 0.2766244 0.2600711 0.2315790 [7] 0.2209667 0.1974956 -1.7134918 -5.2846710 Largest eigenvalues: [1] 64274292 60140438 57252366 56165528 54930888 53579782 52358009 52237435 [9] 52197215 51365213 Smallest eigenvalues: [1] 0.49670168 0.49394717 0.44829228 0.36448408 0.32831097 0.31792781 [7] 0.10269757 0.07532116 -0.15397033 -0.20599405 Largest eigenvalues: [1] 64363426 59878684 57104908 56088550 54249504 52786876 52087835 51823916 [9] 51434253 50963480 Smallest eigenvalues: [1] 0.5167286 0.4824251 0.3597968 0.3111099 0.2555201 0.2021249 [7] 0.1219693 -0.1239433 -0.8158369 -6.6270137 Largest eigenvalues: [1] 63320238 60817045 57641719 56159222 55196536 54326377 52965386 52316766 [9] 51996043 51352786 Smallest eigenvalues: [1] 0.50290442 0.47585084 0.47098028 0.40679262 0.33466914 0.31840766 [7] 0.30616957 0.25841052 0.02244975 -1.47613820 Largest eigenvalues: [1] 65447523 60485006 57435826 56876586 55352013 53730149 52920697 52447010 [9] 51860555 51438062 Smallest eigenvalues: [1] 0.3383644 0.2979536 0.2618785 0.2103490 0.2046308 0.1647281 [7] -0.2224727 -4.2857895 -6.4515612 -8.6066024 Largest eigenvalues: [1] 66507608 61108059 58847356 57035193 55712819 54346549 53014014 52925881 [9] 52581974 52269794 Smallest eigenvalues: [1] 0.4252840 0.3423662 0.3336869 0.3323679 0.2306571 0.2033730 [7] 0.1020442 -0.2578452 -1.5659658 -5.8674456 Largest eigenvalues: [1] 66077594 59809813 56904559 56805066 54488160 52998364 52539768 51375897 [9] 51336507 50597457 Smallest eigenvalues: [1] 0.63793933 0.52631474 0.43413163 0.41457364 0.32760467 0.32722992 [7] 0.29616832 0.17152286 0.05353258 -0.46194262 Largest eigenvalues: [1] 63828026 60126248 57351873 55447429 54739545 53282513 51977171 51636795 [9] 51497797 50927279 Smallest eigenvalues: [1] 0.5222351 0.4562282 0.4485056 0.4196149 0.4015466 0.3842206 [7] 0.3312612 0.2452085 0.2279085 -0.7680761 Largest eigenvalues: [1] 64024180 61105254 57827067 56250724 55873003 54252140 52567359 52415834 [9] 52111082 51355014 Smallest eigenvalues: [1] 0.5519751 0.4872064 0.4747355 0.4578739 0.4470574 0.4217565 [7] 0.2450505 0.1807670 0.0219168 -4.1126368 Largest eigenvalues: [1] 63577667 59716110 57128273 55359317 55340230 53770377 52120032 52087750 [9] 51340085 51059569 Smallest eigenvalues: [1] 0.1186554 0.0825284 0.0529728 -0.0372975 -0.1339336 -0.5006408 [7] -0.6340608 -5.3942508 -9.0506397 -10.7815102 Largest eigenvalues: [1] 60197593 59660633 57177402 55554625 53771355 53535568 51798011 51774512 [9] 50876604 50181561 Smallest eigenvalues: [1] 0.6035463 0.5954294 0.5759948 0.5109591 0.4127615 0.2858684 [7] 0.2626945 0.2203413 -0.7094681 -0.9064164 Largest eigenvalues: [1] 65283980 60389947 57340141 56593202 55224555 53487125 52489125 52288459 [9] 52051476 51226028 Smallest eigenvalues: [1] 0.33051335 0.32947440 0.32208165 0.28144278 0.20115887 [6] 0.10026024 0.02786063 -1.57545617 -5.72180767 -13.01099703 Largest eigenvalues: [1] 66766159 60644655 58073269 57145833 55261515 53464085 53400369 52299392 [9] 52034857 51386274 Smallest eigenvalues: [1] 0.1787263 0.1694780 -0.1508300 -0.1618422 -0.2092064 -2.6735940 [7] -10.8811268 -13.9918489 -16.1152760 -45.2920170 Largest eigenvalues: [1] 64181573 60385359 57681995 55624559 55139120 53978694 52483650 52397406 [9] 51458610 51359352 Smallest eigenvalues: [1] 0.55709940 0.44304761 0.43967077 0.24651467 0.21007720 [6] 0.07587060 0.03942532 -0.06699987 -1.22521144 -13.42529864 Largest eigenvalues: [1] 63738121 60120180 57069934 55617674 55327418 53629248 52393111 52082738 [9] 51650625 51243038 Smallest eigenvalues: [1] 0.31741735 0.29445243 0.26649249 0.15290198 0.14590069 0.01748872 [7] -0.02409168 -0.97643113 -2.48616229 -2.69990715 Largest eigenvalues: [1] 64645061 60039385 56551220 56093698 54579275 52924085 52139720 51588420 [9] 51466508 50635687 Smallest eigenvalues: [1] 0.1898011 0.1779258 -0.2048827 -0.3105301 -0.3244568 -0.6612220 [7] -0.7574761 -9.0586112 -12.3224468 -45.5009116 Largest eigenvalues: [1] 63169532 61208265 57581156 56074674 55009955 54392361 52306164 52170824 [9] 51041471 50923017 Smallest eigenvalues: [1] 0.4469115 0.4369492 0.3852842 0.3410604 0.2868728 0.2702469 [7] 0.1745803 -0.0855023 -0.3849818 -0.9510035 Largest eigenvalues: [1] 65252960 60425611 58126205 56877061 54898749 53225959 52740829 52410286 [9] 51893976 51624976 Smallest eigenvalues: [1] 0.5096993 0.4690237 0.3976463 0.3880216 0.3637760 0.3054254 [7] 0.2829234 0.2599532 0.1933149 -0.7891419 Largest eigenvalues: [1] 65924624 59684389 56611975 56340959 54443394 52705533 52350657 51798634 [9] 51530241 51042740 Smallest eigenvalues: [1] -0.1306257 -0.2182491 -0.4359008 -0.5852863 -1.1135423 -1.6209949 [7] -1.8196521 -2.2606164 -2.4056539 -11.1826519 Largest eigenvalues: [1] 63929336 60765465 57684461 56001098 55794429 54214258 52600603 52521789 [9] 51943063 51675518 Smallest eigenvalues: [1] 0.3996114 0.3851469 0.3834856 0.3747796 0.3739012 0.2204755 [7] -0.6547359 -0.7969780 -3.7007032 -4.6063026 Largest eigenvalues: [1] 65111569 59930882 57508501 56327488 54775501 53097587 52410190 52366181 [9] 51636071 51499959 Smallest eigenvalues: [1] 0.49717037 0.44398068 0.33357902 0.32290876 0.16551153 0.11560995 [7] 0.01621756 -0.31879867 -0.43762964 -6.27493168 Largest eigenvalues: [1] 64756233 59566271 57041714 55570610 54146153 52653235 52048032 51750849 [9] 51214058 51075972 Smallest eigenvalues: [1] 0.5280886 0.5229860 0.5163932 0.4758649 0.4746665 0.4543488 [7] 0.3745868 0.2968540 0.2602990 -0.5961865 Largest eigenvalues: [1] 64009321 60606589 57143668 56323018 55377409 53661104 52287254 52082333 [9] 52009968 51226181 Smallest eigenvalues: [1] 0.42972082 0.37327617 0.32616719 0.25645898 0.25346892 0.20537717 [7] 0.07521011 -0.02827733 -0.11018006 -0.51743350 Largest eigenvalues: [1] 61290100 60031369 57133066 55819832 53867922 53851609 52174240 51635254 [9] 50746817 50707498 Smallest eigenvalues: [1] 0.4838751 0.4833004 0.4393723 0.3841969 0.2933796 0.2815018 [7] 0.2175510 0.1997441 -1.7149451 -28.3217400 Largest eigenvalues: [1] 63829585 59968574 57081574 55657127 55174927 53322796 52153221 51690406 [9] 51555364 51042939 Smallest eigenvalues: [1] 0.46707631 0.46191817 0.36168906 0.29191823 0.28113160 0.27180736 [7] 0.19479707 0.04415995 -0.18954797 -1.97918844 Largest eigenvalues: [1] 64718511 59452673 56622443 55988099 54291841 52823758 52016166 51700274 [9] 51213750 50847463 Smallest eigenvalues: [1] 0.4660506 0.4599969 0.4131064 0.3923726 0.3892344 0.3143654 [7] 0.2647937 0.2221240 -0.1185449 -3.4275015 Largest eigenvalues: [1] 63537445 60421480 57546608 55664746 55451003 54147554 52344905 52314703 [9] 51575202 51251961 Smallest eigenvalues: [1] 0.4056294 0.3800859 0.3677871 0.3472109 0.2619507 0.2334085 [7] 0.1778901 0.1465146 -0.3718325 -0.6810458 Largest eigenvalues: [1] 65145399 61156549 58473966 56551354 55873371 54296463 53116771 52557560 [9] 52053291 51930585 Smallest eigenvalues: [1] 0.4047533 0.3961447 0.3761853 0.3121273 0.3105423 0.2957181 [7] 0.2280731 0.2215193 -0.7267893 -1.1710817 Largest eigenvalues: [1] 64978227 59900672 57844393 56155312 55024515 53940857 52191911 52158163 [9] 51779626 51200255 Smallest eigenvalues: [1] 0.5094213 0.4887179 0.4350756 0.3718631 0.3454801 0.3173984 [7] 0.2981974 0.2455020 0.1727210 -1.0740660 Largest eigenvalues: [1] 64660658 59901449 57277046 55567244 54947603 53478410 52105215 51708121 [9] 51680084 51284710 Smallest eigenvalues: [1] 0.23666775 0.19696834 0.16535025 0.13610663 0.07894434 [6] -0.06924628 -0.15111873 -2.95676465 -12.11895385 -12.66048797 Largest eigenvalues: [1] 63078323 58732346 56016653 55248847 53883715 52688534 51431821 51127713 [9] 50889641 50050161 Smallest eigenvalues: [1] 0.4052114 0.3977633 0.3518903 0.3464258 0.3031983 0.2768000 [7] 0.2580313 0.2407707 0.1873606 -2.9965878 Largest eigenvalues: [1] 65124315 60438801 57102924 57043930 54950138 53450674 52805348 52546452 [9] 52017693 51660801 Smallest eigenvalues: [1] 0.5477875 0.4588957 0.4520199 0.3379817 0.2525528 0.2217774 [7] 0.1773967 0.1738130 0.1545247 -0.2604269 Largest eigenvalues: [1] 63736110 60366337 57321776 55295173 55274215 53485717 52936781 51827820 [9] 51765377 51497498 Smallest eigenvalues: [1] 0.4816732 0.4739031 0.4259841 0.4072189 0.3362325 0.2803447 [7] 0.1677723 0.1128676 -0.6205316 -1.3516641 Largest eigenvalues: [1] 65095020 59765952 57366970 56114894 54864578 53368385 52159709 52067841 [9] 51932334 51221450 Smallest eigenvalues: [1] 0.29010428 0.24140761 0.20818745 0.11323732 0.02074865 [6] -0.33961604 -13.07879631 -16.28979150 -56.76642877 -70.64630226 Largest eigenvalues: [1] 63027284 59421479 56231444 54706048 54562277 53028310 51814327 51507339 [9] 50830466 50597701 Smallest eigenvalues: [1] 0.5647435 0.3920006 0.3366998 0.2980104 0.2973342 0.2718065 [7] 0.2709506 -0.1080825 -1.0100542 -1.1747386 Largest eigenvalues: [1] 62408256 59614678 57393694 55353284 54565459 53588408 52406147 51886748 [9] 50863848 50740281 Smallest eigenvalues: [1] 0.57144900 0.52921040 0.52911305 0.50753726 0.48910617 0.45276255 [7] 0.37900531 0.07620250 0.05655370 -0.01034054 Largest eigenvalues: [1] 65419041 59907847 57169638 56226242 54652356 52926350 52404559 51574323 [9] 51552065 50761521 Smallest eigenvalues: [1] 0.371271890 0.330851213 0.307232654 0.281531137 0.256668163 [6] 0.232274056 0.193993701 0.182034178 -0.005417974 -0.302951598 Largest eigenvalues: [1] 63789800 59241096 57039615 55103653 54506807 53149607 51400099 51336439 [9] 51092612 50372391 Smallest eigenvalues: [1] 0.4909831 0.4549253 0.4099944 0.3741369 0.3719137 0.2222549 [7] 0.1747840 -0.3199870 -4.0824018 -4.3992507 Largest eigenvalues: [1] 63554601 60075734 56807171 55074291 54931844 53146499 51787747 51057811 [9] 51009623 50725826 Smallest eigenvalues: [1] 0.57592619 0.54454884 0.50724665 0.36937398 0.36003625 0.31825666 [7] 0.25611902 0.23308721 0.22615272 -0.04615426 Largest eigenvalues: [1] 63053855 60229365 56868888 55576619 55183520 53737069 52080177 51891840 [9] 51300620 50879257 Smallest eigenvalues: [1] 0.5589331 0.4863285 0.4112946 0.3783604 0.3362585 0.2128650 [7] 0.1215538 -0.2453996 -0.4138166 -1.0953834 Largest eigenvalues: [1] 64953052 60249766 57455140 56518763 55019934 53460661 52457286 52097709 [9] 51611383 50985717 Smallest eigenvalues: [1] 0.5972178 0.5456131 0.4455389 0.4226966 0.3205695 0.3148668 [7] 0.2679887 0.2527282 0.1654921 -0.5227497 Largest eigenvalues: [1] 65243761 60006447 56832069 56368450 54727375 53024001 52441960 51826070 [9] 51778153 51063630 Smallest eigenvalues: [1] 0.38359621 0.36222014 0.35961793 0.26874270 0.20798768 [6] 0.08574142 -0.41520101 -5.17263069 -11.23711291 -38.95989049 Largest eigenvalues: [1] 62789801 59712578 56427323 54950722 54868390 52852027 51819028 51118818 [9] 50854511 50411281 Smallest eigenvalues: [1] 0.4909796 0.4570228 0.4066567 0.3032244 0.2554636 0.2424323 [7] 0.2384851 -0.4434140 -0.8030490 -2.3378398 Largest eigenvalues: [1] 67150421 60669272 58591803 57408161 55274280 53620116 53564825 52896289 [9] 52227571 52064083 Smallest eigenvalues: [1] 0.5579982 0.5051204 0.3622174 0.3388242 0.2910276 0.2906055 [7] 0.2526001 0.1288093 0.1058786 -0.9665361 Largest eigenvalues: [1] 65983704 60976055 58410422 57315994 55543214 54136413 53258475 52768257 [9] 52473207 51747584 Smallest eigenvalues: [1] 0.4335797 0.4310832 0.3973678 0.3264764 0.2949178 0.2167845 [7] 0.1722916 0.1245493 0.1232390 -0.3697616 Largest eigenvalues: [1] 63363120 60481686 57178352 55545719 55256142 53928166 52441585 52338007 [9] 51405894 51281093 Smallest eigenvalues: [1] 0.5092447 0.4580002 0.4432456 0.3791556 0.2967002 0.2387923 [7] 0.2172654 0.1813795 -0.1203716 -0.3629448 Largest eigenvalues: [1] 63005277 59507447 56539402 54936544 54658541 52937044 51505806 51095008 [9] 50982621 50339473 Smallest eigenvalues: [1] 0.46291563 0.38719190 0.31786026 0.29318455 0.19211782 0.16450483 [7] -0.04082186 -0.12421561 -0.83118975 -2.12806154 Largest eigenvalues: [1] 65394117 60275985 57693786 56521421 55051914 53605746 52458415 52410567 [9] 52337765 51609474 Smallest eigenvalues: [1] 0.44524083 0.33245889 0.32462086 0.25437299 0.24604660 0.23578911 [7] 0.17555370 0.09603666 -0.01507374 -0.19263204 Largest eigenvalues: [1] 64906064 59519019 57160557 55722279 54727460 53363251 51797701 51737353 [9] 51250806 50731940 Smallest eigenvalues: [1] 0.41492594 0.29416226 0.28393718 0.28006142 0.18150681 0.14976376 [7] 0.14608236 0.07471617 -0.77893733 -1.07189272 Largest eigenvalues: [1] 64983449 60648684 57972259 55649599 55561426 54057784 53003278 52137233 [9] 52052877 51781663 Smallest eigenvalues: [1] 0.4577545 0.4522391 0.4027851 0.3863218 0.3476765 0.3327155 [7] 0.2706671 0.2129754 -1.0122043 -20.5550455 Largest eigenvalues: [1] 63515113 60002132 57141020 55851145 55311790 53615514 51988878 51967686 [9] 51778499 50941847 Smallest eigenvalues: [1] 0.54853294 0.50670621 0.43630769 0.42127703 0.39077436 0.28047300 [7] 0.27437091 0.27193397 0.25827140 -0.09679595 Largest eigenvalues: [1] 65329281 60762509 57832429 56852817 55367283 53742499 52927568 52432303 [9] 52172398 51360320 Smallest eigenvalues: [1] 0.5483294 0.5379973 0.5170185 0.3726293 0.3230770 0.3121718 [7] 0.2450974 0.2203398 0.0599361 -5.3187898 Largest eigenvalues: [1] 62669562 60249016 56921224 55580776 54825988 53797765 52224272 51661710 [9] 51005158 50788887 Smallest eigenvalues: [1] 0.30186246 0.25588873 0.22552097 0.17886503 0.04501903 [6] -0.17855591 -0.48106412 -10.43718676 -13.43292393 -24.39000393 Largest eigenvalues: [1] 62345266 59068683 56452822 54424568 54355514 52693592 51603877 51499862 [9] 50607549 50361774 Smallest eigenvalues: [1] 0.5029969 0.4924368 0.4343908 0.4127689 0.3936988 0.3684727 [7] 0.3423737 0.2358618 -0.1057755 -0.2538911 Largest eigenvalues: [1] 64414116 60106720 57646132 56283123 54645963 53203514 52327673 51834114 [9] 51693769 51057981 Smallest eigenvalues: [1] 0.5258422 0.4687241 0.4557539 0.4278174 0.3596955 0.3399936 [7] 0.3066862 0.1886756 -0.2935807 -0.4541939 Largest eigenvalues: [1] 65254733 60385691 57041037 56303551 55570412 53723274 52300271 52221783 [9] 51738451 51113930 Smallest eigenvalues: [1] 0.238454453 0.095073277 -0.007738026 -0.161267824 -0.368006568 [6] -1.702313950 -6.342835540 -18.344036839 -23.197898678 -95.354781700 Largest eigenvalues: [1] 65296510 60911543 57177145 57000834 55917603 53967696 53321942 52893030 [9] 51963347 51883159 Smallest eigenvalues: [1] 0.4991829 0.4818742 0.3902265 0.3703390 0.3133894 0.2937669 [7] 0.1900952 0.1659271 0.1239934 -0.5915255 Largest eigenvalues: [1] 64302211 60716873 57685295 56023991 55870578 54208739 52796191 52538021 [9] 52020759 51807013 Smallest eigenvalues: [1] 0.429156932 0.368938493 0.325209364 0.241678838 0.226363620 [6] 0.153614750 -0.003838937 -0.130597834 -1.006863253 -2.150462474 Largest eigenvalues: [1] 62477984 59853835 57105826 55674597 54204036 53824487 52107679 51568295 [9] 50698970 50496817 Smallest eigenvalues: [1] 0.2789917 0.2225079 0.1954517 0.1855275 -0.2659694 [6] -0.6825136 -0.7343493 -1.7496139 -6.4743192 -100.3148702 Largest eigenvalues: [1] 66884428 60727530 57939227 56612360 55508821 53538982 52925127 52178014 [9] 52109953 51010463 Smallest eigenvalues: [1] 0.5461506 0.4823923 0.4672295 0.3512405 0.3175798 0.2802527 [7] 0.2663688 0.2644027 0.2258517 -0.4020982 Largest eigenvalues: [1] 62906218 60603242 57310859 55776414 55097754 54178427 52751712 51888506 [9] 51265792 50969062 Smallest eigenvalues: [1] 0.4625740 0.4010580 0.3619648 0.3291956 0.3288281 0.2895016 [7] 0.2553185 0.2263961 0.2109011 -3.3883164 Largest eigenvalues: [1] 64932886 60317744 57475822 56630719 55104380 53516737 52474525 52437673 [9] 52419629 51452034 Smallest eigenvalues: [1] 0.52715344 0.43580318 0.38113151 0.32608084 0.31390926 0.19302616 [7] -0.05792133 -0.93230301 -1.91622521 -6.09469851 Largest eigenvalues: [1] 64517255 60109472 57331116 56545376 54876978 53172348 52340385 52301442 [9] 51780712 51186017 Smallest eigenvalues: [1] 0.44887669 0.42603683 0.41961486 0.41196201 0.37011495 0.17941008 [7] 0.14942029 0.14904827 0.05206293 -1.94679354 Largest eigenvalues: [1] 64203103 60492865 57359657 56044722 55344547 53440895 52741323 52071351 [9] 51698724 51591883 Smallest eigenvalues: [1] 0.3892820 0.3487393 0.3113848 0.2719389 0.2204615 0.0496663 [7] -0.2384710 -0.5021606 -0.5821858 -3.1487417 Largest eigenvalues: [1] 65609042 60671337 58168512 56122139 55410158 53825258 52993446 52289341 [9] 52052802 51959624 Smallest eigenvalues: [1] 0.3921902 0.3769315 0.3519380 0.3496981 0.2686873 0.2389682 [7] 0.1381529 0.1366931 -0.9824289 -1.0151289 Largest eigenvalues: [1] 65782954 60798656 58210469 56374832 55633437 54264241 52434761 52415451 [9] 52353673 51677285 Smallest eigenvalues: [1] 0.59710702 0.54076646 0.52405931 0.49091527 0.42684775 0.39801605 [7] 0.27760095 0.14651228 0.11536004 -0.02958352 Largest eigenvalues: [1] 64891688 60407884 57291069 55306151 55149069 53551103 52079719 51520547 [9] 51514934 51198273 Smallest eigenvalues: [1] 0.53794929 0.42607518 0.30905173 0.26351827 0.21458911 0.02477885 [7] -0.02717911 -0.16207734 -1.02056580 -2.80488081 Largest eigenvalues: [1] 63291348 59431319 56748974 55163999 54910435 53023954 51818178 51532302 [9] 51263653 50697319 Smallest eigenvalues: [1] 0.5318254 0.4674420 0.3899673 0.3229714 0.2784848 0.2699827 [7] 0.1655744 -0.1108428 -0.1673049 -1.1428309 Largest eigenvalues: [1] 64448618 60730551 57304818 56627205 55459424 53505813 52740090 52501294 [9] 51901187 51070646 Smallest eigenvalues: [1] 0.25243659 0.21358580 0.19323473 0.18336026 0.09014207 -0.71495101 [7] -1.16325950 -2.01383008 -4.18354226 -5.26476507 Largest eigenvalues: [1] 65518080 59796194 57316053 56510531 55031019 53501384 52611474 52060676 [9] 51870141 50819031 Smallest eigenvalues: [1] 0.4910755 0.4891466 0.4774769 0.4365560 0.4104876 0.3207398 [7] 0.3188411 0.3007056 0.2665099 -0.2975243 Largest eigenvalues: [1] 64208698 59919816 57112887 55732158 55158474 53411081 52265271 51740662 [9] 51638936 50902639 Smallest eigenvalues: [1] 0.5101966 0.4951504 0.4665691 0.3619481 0.3521903 0.3331943 [7] 0.2803387 -0.3407573 -1.5429698 -2.1064550 Largest eigenvalues: [1] 67419690 60898653 58684381 57775396 55279604 53791756 53763943 52741421 [9] 52232406 51983087 Smallest eigenvalues: [1] 0.5696144 0.5590046 0.4389156 0.3974480 0.3645191 0.3583544 [7] 0.3416514 0.2737678 0.1813640 -1.8833488 Largest eigenvalues: [1] 64871755 60282387 57177814 56218951 55325217 53843399 52221401 52102718 [9] 52018948 50934637 Smallest eigenvalues: [1] 0.4693469 0.4518112 0.3918816 0.3859981 0.3344764 0.3247012 [7] 0.2740529 0.2253304 0.1303382 -0.0675637 Largest eigenvalues: [1] 65381241 59405266 56627087 56373903 54257151 52803392 52403884 51544328 [9] 51286517 50622072 Smallest eigenvalues: [1] 0.5149883 0.4299325 0.4092290 0.3678656 0.3144539 0.2852062 [7] 0.2502052 -0.2123847 -0.5578747 -1.5390840 Largest eigenvalues: [1] 64785318 60554602 57631317 56480150 55190970 53384658 52500148 52281630 [9] 52105357 51159596 Smallest eigenvalues: [1] 0.4722795 0.4650883 0.4566886 0.4523340 0.4111263 0.4048655 [7] 0.3561046 0.3181576 0.3020069 -0.2281016 Largest eigenvalues: [1] 64963433 60252594 57667626 56279449 55156992 53719120 52367111 52129632 [9] 51905101 51220596 Smallest eigenvalues: [1] 0.4813249 0.4633643 0.4425030 0.3960609 0.3827651 0.3703349 [7] 0.3567444 0.3300237 -0.2133325 -3.0614927 Largest eigenvalues: [1] 63039208 59986948 57170072 55602980 55163735 53530057 51909456 51679701 [9] 51416241 50544673 Smallest eigenvalues: [1] 0.33992788 0.33117354 0.24444898 0.16244912 0.16041558 0.02198482 [7] -0.03019142 -0.04202999 -0.69409640 -4.92509489 Largest eigenvalues: [1] 64303371 60012434 57103694 55855808 55827790 53966460 52150433 51788493 [9] 51760883 50690858 Smallest eigenvalues: [1] 0.3739392 0.3400950 0.3374348 0.2752155 0.2492474 0.2432026 [7] 0.2187203 0.2043097 -3.0246086 -9.9196261 Largest eigenvalues: [1] 64510963 60626035 57711355 55719739 55574296 54148691 52370501 52177869 [9] 51655977 51564711 Smallest eigenvalues: [1] 0.5550998 0.4613133 0.3985648 0.3393245 0.3329940 0.3010023 [7] 0.2456954 0.1834303 -0.5305284 -2.3738032 Largest eigenvalues: [1] 66580830 59676158 57142087 56878847 54361913 53231395 52558753 51759258 [9] 51380248 51058168 Smallest eigenvalues: [1] 0.4774911 0.4439654 0.4332345 0.3126872 0.3014802 0.2551789 [7] 0.1868672 0.1186505 -2.1765488 -4.3838795 Largest eigenvalues: [1] 63389818 59813482 57254308 55899256 54896559 53372822 52739198 52192275 [9] 51700891 51484188 Smallest eigenvalues: [1] 0.43328845 0.38719455 0.37674980 0.27752984 0.12302446 [6] -0.07760758 -0.11254720 -0.41678797 -3.89305747 -14.39757724 Largest eigenvalues: [1] 63721875 59221417 56626464 55014390 54261307 52626148 51366186 51048924 [9] 51001995 50472366 Smallest eigenvalues: [1] 0.5049877 0.4139814 0.3794518 0.3507782 0.3320662 0.2714831 [7] 0.2431447 0.2112054 0.1881777 -0.2357201 Largest eigenvalues: [1] 63363523 59721126 57030640 55540033 54812756 53299844 51787395 51676671 [9] 51585476 50791837 Smallest eigenvalues: [1] 0.4198794 0.3204345 0.3035517 0.2641293 0.2438497 0.2095091 [7] 0.1592699 0.1364110 -1.1454457 -4.0666950 Largest eigenvalues: [1] 65093158 59097482 56547614 56075054 53901870 52596559 52102653 51245021 [9] 51099102 50486599 Smallest eigenvalues: [1] 0.5227194 0.5059859 0.4981923 0.4457535 0.3767528 0.3616820 [7] 0.2974851 0.2890158 -0.4473132 -2.1675098 Largest eigenvalues: [1] 66617715 61003702 58140449 57788429 55209434 53823945 53382298 52434736 [9] 52113933 51524019 Smallest eigenvalues: [1] 0.445328417 0.385286421 0.364609395 0.315363511 0.273160561 [6] 0.261115992 0.254419890 0.203082302 -0.004028773 -1.052138807 Largest eigenvalues: [1] 65084793 60246996 57372672 56263051 55367276 53722296 52323883 52022610 [9] 51834624 51014821 Smallest eigenvalues: [1] 0.4341606 0.3577792 0.3255446 0.3157514 0.2818044 0.2334308 [7] 0.2146404 -0.4799234 -1.6754531 -4.5124258 Largest eigenvalues: [1] 63383427 60232910 57210838 55661666 55578067 53675023 51953631 51771568 [9] 51471919 51237151 Smallest eigenvalues: [1] 0.42093704 0.37580775 0.31111732 0.29431373 0.27486582 0.24140553 [7] 0.19546482 0.03669958 -0.14103699 -5.23249640 Largest eigenvalues: [1] 65359462 60576357 57823392 56572610 56182118 54262181 52595117 52410399 [9] 51955369 51251053 Smallest eigenvalues: [1] 0.2729783 0.2706867 0.2384592 0.2278426 0.1235578 -0.4504019 [7] -0.5971150 -1.4395688 -16.3249884 -34.0914851 Largest eigenvalues: [1] 64901160 59759172 56958042 56667693 54905439 53217128 52489484 51370122 [9] 51198887 50426340 Smallest eigenvalues: [1] 0.4554501 0.3550554 0.3425412 0.3238883 0.2681186 0.2454067 [7] -0.1319494 -0.3589444 -1.5479449 -8.7067886 Largest eigenvalues: [1] 63402451 59613515 56936391 54913542 54746845 52954454 51685464 51163980 [9] 51013426 50560135 Smallest eigenvalues: [1] 0.50499464 0.50237240 0.46944764 0.45110610 0.28366685 0.26981990 [7] 0.12573600 -0.01493711 -0.43155697 -9.48172877 Largest eigenvalues: [1] 64984141 60068182 57095392 55869088 54885385 53134114 52120017 51964467 [9] 51894852 51237814 Smallest eigenvalues: [1] 0.43274085 0.40635116 0.39121924 0.38072803 0.33036984 0.28694404 [7] 0.21678863 0.20260673 0.06202214 -1.07354130 Largest eigenvalues: [1] 64923661 61194443 58218019 56469070 56263877 54855320 53132086 52796651 [9] 52185622 51983742 Smallest eigenvalues: [1] 0.48516217 0.36710366 0.29781240 0.20398797 -0.07905503 [6] -0.36319719 -0.37410108 -1.24833610 -2.03155426 -24.59923755 Largest eigenvalues: [1] 65748158 60418040 57699642 56553541 55557636 53669555 52679027 52323301 [9] 52193404 51390377 Smallest eigenvalues: [1] 0.5499865 0.4208013 0.4102624 0.3910351 0.3840838 0.2929361 [7] 0.2620767 0.1673236 0.1459602 -1.1357819 Largest eigenvalues: [1] 65232715 60516047 57818024 56383629 55534259 54121014 52830329 52455888 [9] 52364252 51829765 Smallest eigenvalues: [1] 0.24334952 0.22008136 0.20946134 0.20289071 0.19768708 -0.01684957 [7] -0.05938816 -0.07341618 -1.40394549 -3.74934048 Largest eigenvalues: [1] 68040001 60681448 58564870 57737275 54968708 53959572 53753965 52351765 [9] 51793378 51688121 Smallest eigenvalues: [1] 0.4822019 0.4618066 0.3679673 0.3482136 0.3172875 0.3096675 [7] 0.2920842 0.2557456 0.2378626 -0.1069289 Largest eigenvalues: [1] 64715112 60386260 57290028 56280337 54909910 53360729 52496448 51746698 [9] 51714526 50854797 Smallest eigenvalues: [1] 0.40366129 0.35584743 0.34893782 0.26607788 0.25617216 0.24545336 [7] 0.23088991 0.07835972 -0.06808716 -0.71303065 Largest eigenvalues: [1] 64418227 60272024 57538448 55416779 55135472 53764506 52055857 51945465 [9] 51643290 51106653 Smallest eigenvalues: [1] 0.6458670 0.5290819 0.4215005 0.3536802 0.3200041 0.2503895 [7] 0.2296752 0.1531097 -0.1155864 -0.5435428 Largest eigenvalues: [1] 63183821 59985908 57502172 55322395 55038142 53752840 52348876 51810737 [9] 51198202 50840139 Smallest eigenvalues: [1] 0.4640593 0.4377243 0.3644144 0.3194029 0.3104610 0.2795312 [7] 0.2055138 0.1923308 -1.2375955 -12.4058702 Largest eigenvalues: [1] 64573106 59936877 56722379 55809260 55104462 53406175 52353098 51918984 [9] 51852662 51219078 Smallest eigenvalues: [1] 0.45384324 0.37035798 0.35794837 0.32435794 0.25690769 0.25328091 [7] 0.24230546 0.05948428 -0.75149526 -1.32151493 Largest eigenvalues: [1] 64449102 60377059 57220185 55480173 55462660 53830333 52192780 51873629 [9] 51413374 51156962 Smallest eigenvalues: [1] 0.49027024 0.44953124 0.42905935 0.42731675 0.36738142 0.30615057 [7] 0.24320575 0.21787247 0.16608311 -0.08800963 Largest eigenvalues: [1] 63324737 59538915 56864243 55083026 55073825 53210917 51888727 51500722 [9] 51158414 50660139 Smallest eigenvalues: [1] 0.5442891 0.5004407 0.4789799 0.4641114 0.3300991 0.3097456 [7] 0.3088163 0.2767147 0.2209505 -0.8225658 Largest eigenvalues: [1] 64463616 59933708 57098043 55853022 54863078 53391108 52313894 51896564 [9] 51627284 51003963 Smallest eigenvalues: [1] 0.4654656 0.4138306 0.3295331 0.2914700 0.2825199 0.2504557 [7] 0.2406395 0.2264968 0.1826636 -4.7170459 Largest eigenvalues: [1] 66806578 60182174 57652106 57160939 54902998 53537384 53148556 52223214 [9] 52068645 51477767 Smallest eigenvalues: [1] 0.49404084 0.43808708 0.37417089 0.35002741 0.34270305 0.30349633 [7] 0.28832401 0.18733932 -0.04115719 -0.38155206 Largest eigenvalues: [1] 65596407 60748616 57948171 56464715 55692419 54062004 53442958 52657923 [9] 52140380 51994919 Smallest eigenvalues: [1] 0.43767714 0.41360798 0.29450200 0.26490822 0.24130288 0.20592951 [7] 0.16103586 0.07000476 -0.41737411 -0.50971827 Largest eigenvalues: [1] 67168498 60566866 57849403 57404401 54764190 53469202 53123933 52272941 [9] 51948122 51711059 Smallest eigenvalues: [1] 0.4287099 0.4282514 0.3973804 0.3892213 0.3123146 0.2358853 [7] 0.1612999 0.1605497 -0.2688335 -5.8299995 Largest eigenvalues: [1] 65084274 59743409 56896469 56346631 54535488 52725316 52411718 51643999 [9] 51561855 50930849 Smallest eigenvalues: [1] 0.3082562 0.3047844 0.2716003 0.2579050 0.1788843 -0.2576115 [7] -0.3452661 -0.9506603 -2.0562081 -2.6868315 Largest eigenvalues: [1] 65264885 60778802 57708336 56415326 55899069 54367923 52810124 52405618 [9] 52093863 51653800 Smallest eigenvalues: [1] 0.59600416 0.53213548 0.51288707 0.47686931 0.46248450 0.38031461 [7] 0.30797385 0.30478171 0.20292123 -0.01065626 Largest eigenvalues: [1] 65765198 60987537 58210608 56764277 55471310 53732148 52709991 52519562 [9] 52020629 51685092 Smallest eigenvalues: [1] 0.6034738 0.5556320 0.5199809 0.4999030 0.4861337 0.4641957 [7] 0.4211815 0.3063336 0.2672209 -0.2760835 Largest eigenvalues: [1] 64124588 59773195 56768950 55984895 54821312 53177997 51973039 51811308 [9] 51628959 50833276 Smallest eigenvalues: [1] 0.4404908 0.4034500 0.3996555 0.3893506 0.3052125 0.2917697 [7] 0.1438516 -0.3118468 -9.3989921 -18.2183983 Largest eigenvalues: [1] 65500943 60219216 57519340 56635008 54742896 53386022 52744574 51496580 [9] 51475777 50514245 Smallest eigenvalues: [1] 0.46474102 0.37507310 0.36475399 0.28321383 0.23768977 0.23375274 [7] 0.19428444 0.05959832 0.04432313 -6.34832757 Largest eigenvalues: [1] 61708688 59864826 57140470 56000404 54333436 53803108 52122637 51134929 [9] 50551509 50525734 Smallest eigenvalues: [1] 0.4706150 0.4617676 0.4283637 0.4041858 0.3622399 0.3478138 [7] 0.2470418 0.2353118 -0.6615252 -1.0302431 Largest eigenvalues: [1] 65180634 60288309 58247009 56440038 55256285 54039406 52539085 52509700 [9] 52187060 51768085 Smallest eigenvalues: [1] 0.47066771 0.38953935 0.35319067 0.29865405 0.04963312 0.01243067 [7] -0.12960261 -0.13251663 -1.29890621 -2.15787959 Largest eigenvalues: [1] 65055322 59994988 56704071 56240372 54695048 53018451 52309600 52188075 [9] 51422350 51171086 Smallest eigenvalues: [1] 0.42271475 0.37708931 0.36209363 0.33430741 0.28253021 0.24862574 [7] 0.20156792 0.15752430 0.08164249 -3.32906415 Largest eigenvalues: [1] 61367940 59582945 56825009 55424000 53504078 53409756 51673331 50917345 [9] 50245675 50109295 Smallest eigenvalues: [1] 0.28327777 0.27753930 0.10578123 0.07314426 -0.16387648 [6] -0.88582894 -1.55372743 -2.32373572 -2.52625439 -27.40042386 Largest eigenvalues: [1] 63004957 60612180 57156802 55952653 55483519 54309703 52438970 52367865 [9] 51399196 51253812 Smallest eigenvalues: [1] 0.47750982 0.46956939 0.44915818 0.42281053 0.35592319 0.19446157 [7] 0.18962537 0.16803872 0.08330244 -0.32227640 Largest eigenvalues: [1] 65523492 60063624 56901120 56376583 55001407 53157168 52437940 52200364 [9] 51999228 51485916 Smallest eigenvalues: [1] 0.4571964 0.3238459 0.2648202 0.2493922 0.2049719 0.2019953 [7] 0.1837542 -0.5546926 -2.1066588 -21.2173276 Largest eigenvalues: [1] 65229683 60393280 57768877 56105495 54799568 53196929 52388765 52113475 [9] 51972804 51710292 Smallest eigenvalues: [1] 0.41078896 0.35949319 0.34406070 0.32722415 0.31474933 [6] 0.29921865 0.27754639 0.09137449 -0.02184615 -29.39202358 Largest eigenvalues: [1] 63022377 59484776 57100237 55226959 55194210 53428889 51724593 51475606 [9] 51288230 50596320 Smallest eigenvalues: [1] 0.36847322 0.34207286 0.33981044 0.27570306 0.25959508 0.22660283 [7] 0.17982102 0.03736938 -0.33792894 -2.94218894 Largest eigenvalues: [1] 64995722 60254030 57290980 55896512 55322786 53625187 51823965 51548462 [9] 51526877 50883196 Smallest eigenvalues: [1] 0.4955103 0.4726134 0.4609949 0.3370033 0.3052478 0.3018187 [7] 0.2919358 0.2790933 0.2225502 -0.4303885 Largest eigenvalues: [1] 61920249 59872713 56871954 55567620 54250349 53663278 52162575 51672359 [9] 50790756 50459394 Smallest eigenvalues: [1] 0.48895418 0.46394416 0.45855480 0.42888069 0.41184146 0.31492873 [7] 0.28350104 0.27625885 0.09075314 -3.54530943 Largest eigenvalues: [1] 64043044 60509385 57318820 55474611 55434749 53804844 52156129 51656538 [9] 51607360 50997015 Smallest eigenvalues: [1] 0.452059327 0.450230083 0.399109587 0.240694255 0.173602166 [6] 0.154327437 0.066358713 -0.008891906 -1.682021539 -3.384752104 Largest eigenvalues: [1] 63903868 60786594 57278680 56008697 55397039 53990673 52489251 52194596 [9] 51931905 51254613 Smallest eigenvalues: [1] 0.3655935 0.3329792 0.2606046 0.2589456 0.2511102 0.2165988 [7] 0.2043469 -0.6491771 -8.5410615 -16.9960753 Largest eigenvalues: [1] 64497420 61351850 57931601 56981107 56359736 55256138 53113711 52663058 [9] 52255885 51664821 Smallest eigenvalues: [1] 0.46277828 0.45676796 0.44092611 0.43662052 0.35244114 0.28151719 [7] 0.23070772 0.19887279 0.04933185 -1.02341151 Largest eigenvalues: [1] 65890518 59920846 57251140 57034471 54819032 53363671 52921575 52189240 [9] 52064594 51554353 Smallest eigenvalues: [1] 0.11801268 0.09489184 0.08466386 0.07295297 -0.22823110 [6] -0.63592599 -1.93349065 -6.46042397 -17.86811655 -67.45496709 Largest eigenvalues: [1] 63867038 59435600 56543078 54968586 54542654 52832065 51947736 51299224 [9] 51285669 51006173 Smallest eigenvalues: [1] 0.5278092 0.4939030 0.4748969 0.4338467 0.4239038 0.4017272 [7] 0.3793102 0.3614124 0.3346325 -0.5934390 Largest eigenvalues: [1] 63959375 60847791 57545913 56281084 55855382 54118737 52261688 52190027 [9] 52085476 51105563 Smallest eigenvalues: [1] 0.6247623 0.5476715 0.4598102 0.4455974 0.4411331 0.4318708 [7] 0.3728331 0.2579648 -0.1275022 -0.1724734 Largest eigenvalues: [1] 64797134 60195553 57625071 56073197 55273474 53481629 52518988 52242795 [9] 51812093 51410050 Smallest eigenvalues: [1] 0.5584616 0.5545359 0.4930952 0.4839450 0.3540002 0.3452527 [7] 0.3301492 0.3117685 0.2383850 -0.1593142 Largest eigenvalues: [1] 63363949 59670131 57190772 55369679 55204815 53698423 52031428 51669022 [9] 51246827 50811008 Smallest eigenvalues: [1] 0.47844117 0.41895707 0.40023332 0.39309687 0.35261705 0.33232005 [7] 0.05061357 0.01728149 -0.14966521 -4.74192526 Largest eigenvalues: [1] 64413604 59608540 56700461 56022953 54331782 52694243 52069234 51614090 [9] 51250684 50674572 Smallest eigenvalues: [1] 0.5676876 0.5214993 0.4597463 0.3925009 0.3615232 0.3507187 [7] 0.2664203 0.1855388 0.1679822 -0.6563396 Largest eigenvalues: [1] 65042474 60765130 57521496 56683838 55783312 53960441 52919359 52613443 [9] 52462212 51773650
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 4.344984 | 0.7528672 | 126.3173 | 0.04 | 2.611653 | 2.863883 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + acc + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
acceleration = acceleration_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_acc_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e4),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e4),
acceleration = list(nbetabasis = 80, norder = 4, lambda = 1e4),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e4))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 606 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.3603906 0.3206480 0.2860769 0.2596945 0.2094575 0.1474205 [7] 0.1147731 -0.1408713 -0.1589878 -3.8942672 Largest eigenvalues: [1] 64042812 60125820 57559805 55670773 55051760 53392896 52138209 51717479 [9] 51678901 51142828 Smallest eigenvalues: [1] 0.19308764 0.17015664 0.10711512 0.02288223 -0.01647957 -0.01698404 [7] -0.02461813 -0.18648999 -0.18929676 -2.45392676 Largest eigenvalues: [1] 63355450 61056600 57701327 55871095 55332918 53938763 52739427 52427972 [9] 51869486 51615887 Smallest eigenvalues: [1] 0.313184927 0.299904415 0.297226800 0.272611956 0.223798356 [6] 0.129874123 0.067220822 -0.005984975 -0.153001156 -0.633852607 Largest eigenvalues: [1] 64140129 61112687 58366275 55856481 55741450 54327511 53206043 52322060 [9] 52089966 51897926 Smallest eigenvalues: [1] 0.486435822 0.484210632 0.414051726 0.353098383 0.346720503 [6] 0.259123560 0.251768800 -0.006308419 -0.043910305 -0.102562167 Largest eigenvalues: [1] 61984148 60501986 57601754 55831981 54968196 54066883 52461370 52415988 [9] 51222636 51000972 Smallest eigenvalues: [1] 0.3567004 0.3285938 0.2976389 0.2334785 0.2046435 0.1983599 [7] 0.1705519 0.1184595 -0.1281541 -3.2064522 Largest eigenvalues: [1] 65163173 59818161 57293665 56025018 54719041 53144375 52121514 51967281 [9] 51426274 51120415 Smallest eigenvalues: [1] 0.41800093 0.41103957 0.37141810 0.28186811 0.27306749 0.14039522 [7] 0.05665045 -0.02675393 -0.10474338 -0.33093004 Largest eigenvalues: [1] 64358283 60638162 57254916 56045643 55652612 53846201 52740030 52017768 [9] 51714901 51420528 Smallest eigenvalues: [1] 0.2635689 0.1968254 0.1840918 0.1463388 0.1367938 0.0774332 [7] -0.1700209 -0.1777492 -0.3643735 -0.4571581 Largest eigenvalues: [1] 65013751 60998681 57648795 56151025 55480723 53867210 52962816 52135892 [9] 52042929 51761050 Smallest eigenvalues: [1] 0.34805612 0.31317840 0.23050060 0.22377275 0.18881466 -0.05365539 [7] -0.12786940 -0.30029511 -0.38798873 -0.65147113 Largest eigenvalues: [1] 64870413 59853259 56521056 56464943 54495022 52690414 52475124 52167009 [9] 51688408 51233785 Smallest eigenvalues: [1] 0.4924669167 0.4224823921 0.4110749524 0.3006899051 0.2739084512 [6] 0.2118511766 0.2073970513 0.0566545630 0.0004435585 -1.9697097632 Largest eigenvalues: [1] 63897554 59811350 57221227 55815994 54681379 53175611 52229504 51781375 [9] 51653218 51043701 Smallest eigenvalues: [1] 0.37594417 0.35853443 0.33685754 0.32689900 0.23091090 0.22691332 [7] 0.22173925 0.10436881 0.06168631 -0.03016414 Largest eigenvalues: [1] 64507451 60409949 58002489 55634486 55321207 54073815 52718494 52110591 [9] 51872357 51712245 Smallest eigenvalues: [1] 0.44564453 0.40144457 0.35814751 0.33064016 0.20256703 0.06430269 [7] -0.43919089 -0.45225889 -1.04595515 -3.72937176 Largest eigenvalues: [1] 64699010 60039590 57230094 55798586 55200344 52971868 52186125 51956598 [9] 51697452 51235547 Smallest eigenvalues: [1] 0.3637690 0.3179382 0.2953825 0.2815649 0.2708426 0.1716318 [7] 0.1256518 0.0709207 -0.2944240 -1.8981729 Largest eigenvalues: [1] 63315355 59864465 57107461 55193265 54822933 53603761 52141302 52028246 [9] 51338200 51002270 Smallest eigenvalues: [1] 0.38703956 0.38204369 0.35914554 0.27981298 0.27351546 0.21683480 [7] 0.20852930 -0.05007726 -0.21218630 -1.18122172 Largest eigenvalues: [1] 64864962 59719156 57151947 56535418 54774457 53303421 52543399 52172525 [9] 51483342 50767655 Smallest eigenvalues: [1] 0.5666210 0.5128652 0.5047648 0.4344818 0.3820561 0.3682778 [7] 0.2593738 0.2163635 0.1474606 -0.0161257 Largest eigenvalues: [1] 65018802 59485575 56759327 55961013 54888526 53236899 52142138 51950984 [9] 51851831 51205014 Smallest eigenvalues: [1] 0.49674605 0.38986244 0.36977487 0.32981922 0.22408674 0.21679872 [7] 0.14659607 0.09302246 -0.08805735 -0.11807157 Largest eigenvalues: [1] 66291866 59307802 57238030 56639429 54034094 53259521 52543575 51326778 [9] 51117772 50519245 Smallest eigenvalues: [1] 0.5048780 0.5018486 0.4783975 0.4409971 0.4168265 0.3654423 [7] 0.2558727 0.1582258 -0.1423267 -0.2183561 Largest eigenvalues: [1] 63345416 60087174 56783771 55243839 54976033 53456167 51999856 51371631 [9] 50839683 50520652 Smallest eigenvalues: [1] 0.3680907 0.2673715 0.2556593 0.2264717 0.2032561 0.1806324 [7] 0.1578470 0.1348485 -0.1274604 -0.5267096 Largest eigenvalues: [1] 66512102 60534115 57855623 57260735 55043218 53384080 53184007 52933113 [9] 51654632 51496812 Smallest eigenvalues: [1] 0.46250142 0.40812451 0.38320941 0.23381370 0.21528419 0.12381999 [7] 0.10875845 0.07737656 0.06233337 -0.79995766 Largest eigenvalues: [1] 65753544 60501423 56960768 56753694 55112839 53464936 52724815 52234591 [9] 52020426 51263068 Smallest eigenvalues: [1] 0.48720891 0.47571582 0.45112471 0.39529391 0.33727289 0.27785494 [7] 0.15250768 0.02060553 -0.07968460 -0.71683640 Largest eigenvalues: [1] 63421109 59880816 57059970 55351813 54886550 53781939 52421157 51800205 [9] 50989232 50887761 Smallest eigenvalues: [1] 0.39905433 0.36072808 0.34246557 0.30407559 0.29587872 0.27107999 [7] 0.24143192 0.11505289 0.11430622 -0.06455022 Largest eigenvalues: [1] 64281762 61489955 58090710 56617451 55655382 54025692 52788376 52530737 [9] 52474244 51781334 Smallest eigenvalues: [1] 0.4524249 0.4297710 0.3758639 0.3483349 0.3256069 0.2992669 [7] 0.2661505 0.2370527 0.1072519 -0.1315416 Largest eigenvalues: [1] 64822507 61097914 58013734 56414784 56408389 54708214 53058937 52587644 [9] 52315629 51706456 Smallest eigenvalues: [1] 0.30172964 0.25823254 0.15310404 0.09629276 0.09252563 0.01557363 [7] -0.06069795 -0.11263539 -0.43452943 -1.44370508 Largest eigenvalues: [1] 64743454 60218965 56999694 55926177 54883767 53329324 51982796 51929633 [9] 51562484 50890426 Smallest eigenvalues: [1] 0.49313171 0.43804805 0.40373882 0.32104682 0.27865145 0.26023728 [7] 0.18798723 0.16612590 0.07420535 -0.06207839 Largest eigenvalues: [1] 63228762 60339728 57141445 55692928 54834423 53103843 51918880 51757665 [9] 51683771 50766304 Smallest eigenvalues: [1] 0.3815686 0.2937906 0.2934616 0.2672913 0.2637593 0.2198001 [7] 0.2107763 0.1004381 -0.4090973 -0.5188172 Largest eigenvalues: [1] 63894586 59758694 57239506 55185835 54421974 52959164 51919518 51354950 [9] 51113528 51070084 Smallest eigenvalues: [1] 0.34347383 0.27432736 0.26188890 0.23710049 0.22722438 0.21810667 [7] 0.19475320 0.01777969 -0.18448097 -0.26251265 Largest eigenvalues: [1] 65754532 60415101 57841584 56729040 55100359 53409275 52978023 52750692 [9] 51987324 51898316 Smallest eigenvalues: [1] 0.4341985 0.3725930 0.3666928 0.3291824 0.2923235 0.2614658 [7] 0.1960324 0.1268017 0.1227838 -1.4700311 Largest eigenvalues: [1] 64976715 59836961 57158468 56027573 55025189 53202778 52093152 52054413 [9] 51493984 51140531 Smallest eigenvalues: [1] 0.49515698 0.44302564 0.35624174 0.34921851 0.33763801 0.29688016 [7] 0.26949354 0.14490958 -0.08477671 -1.05720891 Largest eigenvalues: [1] 63539838 59124913 56986340 55537837 54439466 52891167 51600459 51493504 [9] 51429997 50568226 Smallest eigenvalues: [1] 0.43287209 0.39230530 0.33789149 0.31164282 0.26393407 0.19947962 [7] -0.03676008 -0.07383353 -0.08369749 -0.22410323 Largest eigenvalues: [1] 61127531 59035791 56117928 54820812 54126598 52912263 51797545 50841255 [9] 50128339 49932966 Smallest eigenvalues: [1] -0.2460616 -0.3330930 -0.3729782 -0.3737812 -0.4331279 -0.5176597 [7] -0.5487857 -0.9669094 -1.1436436 -1.2282288 Largest eigenvalues: [1] 64858128 61061489 58209202 55631681 55550754 54216186 52454133 51974642 [9] 51671098 51419047 Smallest eigenvalues: [1] 0.27058774 0.23880427 0.23389710 0.20867380 0.17934001 0.02470653 [7] -0.01126291 -0.21387908 -0.34756716 -0.76965295 Largest eigenvalues: [1] 64842719 61059995 57733046 56630744 55598746 54004868 52775192 52599737 [9] 52376831 51802623 Smallest eigenvalues: [1] 0.39886268 0.30092224 0.25846460 0.24828442 0.21635403 0.11846062 [7] 0.09696379 -0.05399715 -1.18493062 -1.22707519 Largest eigenvalues: [1] 64505280 60140247 56638533 56268165 55292871 53292063 52537867 52240039 [9] 52193336 51205387 Smallest eigenvalues: [1] 0.468809909 0.374803091 0.341744479 0.286649767 0.249555276 [6] 0.189182536 0.142985110 -0.009777275 -0.622729528 -1.012807441 Largest eigenvalues: [1] 64029117 58805802 56461250 55821379 53978132 52250512 51751027 51256342 [9] 51020191 49960559 Smallest eigenvalues: [1] 0.424019349 0.324891136 0.238578223 0.228276122 0.226693893 [6] 0.206355120 0.186955433 0.149452847 0.003521582 -7.045044203 Largest eigenvalues: [1] 61832975 59825418 56886563 55066069 54669400 53472166 52120498 51468919 [9] 50728614 50525906 Smallest eigenvalues: [1] 0.26833906 0.22044811 0.21640131 0.21348019 0.07544258 0.04953039 [7] -0.12830040 -0.17947132 -1.00590867 -2.90901045 Largest eigenvalues: [1] 66492448 60572966 57389874 56426197 55331903 53686182 52545385 52417101 [9] 51793282 51658011 Smallest eigenvalues: [1] 0.43086981 0.35695808 0.34527069 0.34409043 0.25809766 0.24956918 [7] 0.22633378 0.18869623 0.04441534 -0.06619720 Largest eigenvalues: [1] 64569776 60746734 58209546 55780995 55604053 54234904 52757165 52437905 [9] 51782170 51522448 Smallest eigenvalues: [1] 0.3199920 0.3085092 0.2815040 0.2192651 0.2166413 0.1703417 [7] 0.1068566 -0.1781967 -0.2262937 -2.1929220 Largest eigenvalues: [1] 65075273 60567053 57749733 55895980 55826053 54154201 52434478 52240629 [9] 52204402 51355481 Smallest eigenvalues: [1] 0.36679593 0.36204198 0.30321159 0.27852106 0.20601523 0.09675696 [7] 0.02474611 -0.08693992 -0.22011251 -1.60236497 Largest eigenvalues: [1] 63877916 59888506 57013986 55192226 55033924 53438740 52166670 51471107 [9] 51344018 51183333 Smallest eigenvalues: [1] 0.474959591 0.388621819 0.357229674 0.342993411 0.324167216 [6] 0.310567632 0.241170437 0.013774104 -0.006679943 -0.073915400 Largest eigenvalues: [1] 65237018 60365372 57467544 56411339 54843198 53060364 52541326 52121609 [9] 51296529 50886352 Smallest eigenvalues: [1] 0.34471929 0.32909510 0.30661962 0.25509392 0.24737358 0.20364714 [7] 0.06887637 0.05206281 -0.10369626 -2.43385066 Largest eigenvalues: [1] 63171106 59821566 56965008 55146968 54994103 53372462 51709603 51671283 [9] 51149930 50895599 Smallest eigenvalues: [1] 0.48916970 0.39957389 0.38312140 0.35914591 0.25344685 0.21311593 [7] 0.18543280 0.12980339 0.03028597 -0.77720909 Largest eigenvalues: [1] 65238373 59942593 57167130 57130370 54517661 53085943 52858254 52016865 [9] 51906367 51073233 Smallest eigenvalues: [1] 0.37306304 0.32342526 0.32011327 0.17822441 0.14853715 0.14105478 [7] -0.06471892 -0.22865453 -0.57631561 -0.71568892 Largest eigenvalues: [1] 65070191 60984772 58054948 56780020 55345357 53402084 53005991 52656621 [9] 51832038 51704852 Smallest eigenvalues: [1] 0.28908031 0.24141226 0.22387002 0.15346420 0.10963183 0.07682236 [7] -0.03741547 -0.04481323 -0.79968007 -0.82843491 Largest eigenvalues: [1] 64853322 60580673 58070284 56409408 55069526 53499647 52708025 52469870 [9] 52087559 51785470 Smallest eigenvalues: [1] 0.33057720 0.28530559 0.27569552 0.22232186 0.13690152 0.02835007 [7] -0.10745943 -0.36032917 -0.40872622 -1.11880970 Largest eigenvalues: [1] 64155923 59585147 56853874 54875791 54761907 53058820 51286058 51238972 [9] 51113988 50490770 Smallest eigenvalues: [1] 0.39960852 0.23095879 0.21918600 0.16759046 0.08511106 0.06018156 [7] -0.03117794 -0.05202401 -0.09417116 -1.33545675 Largest eigenvalues: [1] 63335509 59835216 56962529 55206734 54747277 53152608 51682359 51488730 [9] 51309686 50888761 Smallest eigenvalues: [1] 0.5364285 0.5353717 0.4451344 0.4384927 0.4352319 0.3925692 [7] 0.3231796 0.2993528 0.2874640 -0.2740327 Largest eigenvalues: [1] 64168402 60433535 57581693 55838796 55364991 53658423 51735558 51697195 [9] 51564242 50652737 Smallest eigenvalues: [1] 0.54477934 0.53961058 0.46571162 0.40663906 0.37828691 0.34767162 [7] 0.20242885 0.10694160 0.01386924 -0.32716346 Largest eigenvalues: [1] 62134351 59525841 56632421 55230589 54338034 53394068 51681453 51589397 [9] 50455817 50289707 Smallest eigenvalues: [1] 0.44576428 0.32286257 0.31535376 0.25187381 0.14262545 0.12887404 [7] 0.06061520 0.04429567 -0.05580773 -2.15177198 Largest eigenvalues: [1] 63505411 59554332 56760102 55289636 55039486 53369357 52378995 51839392 [9] 51441216 51216217 Smallest eigenvalues: [1] 0.5205121 0.5028372 0.4369018 0.3663844 0.3630000 0.3339224 [7] 0.3291279 0.2937270 0.2668510 -0.4076816 Largest eigenvalues: [1] 63812606 59626039 57210590 55512293 54681728 52916285 51692881 51525854 [9] 51044999 50389901 Smallest eigenvalues: [1] 0.37353636 0.31628203 0.24671127 0.23271970 0.21987027 0.12945540 [7] -0.01279438 -0.20582004 -0.29160393 -0.86838223 Largest eigenvalues: [1] 64246167 60069298 57089796 56026719 55078598 53558221 52425139 51965156 [9] 51934191 51448378 Smallest eigenvalues: [1] 0.387618700 0.350842220 0.313729781 0.274074025 0.230364909 [6] 0.201045632 0.191965046 0.005931078 -0.145759565 -0.261922357 Largest eigenvalues: [1] 64812748 61049897 58348316 56108538 55789309 54391289 52461537 52307812 [9] 52019069 51537906 Smallest eigenvalues: [1] 0.35843234 0.35473116 0.33890849 0.32846012 0.31521429 0.28887962 [7] 0.22239760 0.01641749 -0.23299799 -0.32896698 Largest eigenvalues: [1] 65476519 60479513 57689154 56575188 55216963 53689845 52491133 52169096 [9] 51982746 51247026 Smallest eigenvalues: [1] 0.46052563 0.43961626 0.41741332 0.40072946 0.30383083 0.25091436 [7] 0.19061881 0.16642050 0.07783223 -0.13221950 Largest eigenvalues: [1] 65440331 60869551 57965413 56422599 55596541 54095370 52633987 52530999 [9] 52022117 51526187 Smallest eigenvalues: [1] 0.48360484 0.47577667 0.42888151 0.42256623 0.34681360 0.34478007 [7] 0.27721432 0.25140540 0.22366972 -0.03321141 Largest eigenvalues: [1] 65390979 60730666 57959144 56619766 56027558 54435551 52608311 52367810 [9] 52286101 51354269 Smallest eigenvalues: [1] 0.3373224 0.3266732 0.2598420 0.2295445 0.2081416 0.1724380 [7] 0.1444689 -0.5320565 -0.6962719 -0.7924707 Largest eigenvalues: [1] 66333537 60712971 57981165 57139470 55098263 53523924 53274765 52331288 [9] 51896990 51522859 Smallest eigenvalues: [1] 0.358128201 0.321289787 0.306916866 0.273582428 0.264583667 [6] 0.191468149 0.163286958 -0.005859051 -0.391608586 -0.424768896 Largest eigenvalues: [1] 63886544 60503146 57149465 55781985 55736539 54049574 52905981 52206455 [9] 51954925 51687018 Smallest eigenvalues: [1] 0.48178954 0.40723983 0.39895801 0.38145384 0.31096653 0.25125948 [7] 0.23717507 0.19727587 0.06835951 -0.09234222 Largest eigenvalues: [1] 64917614 59570925 57013438 56450765 54200155 52678059 52445773 51409487 [9] 51177865 50346307 Smallest eigenvalues: [1] 0.49139837 0.47513540 0.44025141 0.42538513 0.36614629 0.30053951 [7] 0.28887771 0.07024903 -0.02697186 -0.46653374 Largest eigenvalues: [1] 65266549 60192459 57627485 56337903 55479689 53456239 52604307 52102947 [9] 51738313 51063413 Smallest eigenvalues: [1] 0.28076112 0.22395012 0.22355702 0.21288323 0.15382624 0.03527388 [7] -0.13569635 -0.42121597 -0.59959270 -5.43688229 Largest eigenvalues: [1] 66269055 60853321 57240954 57222216 55622334 53782052 53247162 52414815 [9] 52221674 51469603 Smallest eigenvalues: [1] 0.27821730 0.19862006 0.19819928 0.13485490 0.07339599 -0.13500070 [7] -0.28586167 -0.40306937 -0.99114765 -1.90357430 Largest eigenvalues: [1] 64427041 60545555 57908962 56640833 55541517 53868869 52600700 52428444 [9] 52259322 51271379 Smallest eigenvalues: [1] 0.14068416 0.09121334 -0.02220390 -0.06431161 -0.21434716 -0.26956082 [7] -0.60929578 -1.21714060 -1.34764833 -1.48726618 Largest eigenvalues: [1] 66219887 60093450 57918014 55880813 54851939 53048982 52343802 51705149 [9] 51278967 50943662 Smallest eigenvalues: [1] 0.46875744 0.43413460 0.37802219 0.37219335 0.27783285 0.23231523 [7] 0.17196609 0.15705356 0.05810619 -0.18960095 Largest eigenvalues: [1] 65498045 61244736 58057107 56841727 55886177 54275404 53471337 52840763 [9] 52377361 52076991 Smallest eigenvalues: [1] 0.30065156 0.28012827 0.24835356 0.24701815 0.13455353 0.12902444 [7] 0.12729337 0.03730063 -0.78035003 -2.06242905 Largest eigenvalues: [1] 63508021 59788113 56961370 55547485 54800061 53196096 51960334 51743953 [9] 51524377 50954353 Smallest eigenvalues: [1] 0.29180419 0.27555984 0.24628449 0.22956510 0.20239016 0.18006428 [7] 0.11235817 0.09156804 -0.04272696 -5.83561262 Largest eigenvalues: [1] 63345500 60597202 57177419 55826058 54903460 53904659 51950536 51776875 [9] 51023165 50725203 Smallest eigenvalues: [1] 0.51898108 0.51190742 0.49346421 0.45000858 0.44590826 0.40245592 [7] 0.26890601 0.17226099 0.01089595 -0.01735811 Largest eigenvalues: [1] 65450490 60164291 57661918 56539077 54888937 53282850 52370456 52311259 [9] 51956350 51530022 Smallest eigenvalues: [1] 0.3058265 0.2989377 0.2661292 0.1974696 0.1739128 0.1180772 [7] 0.1179815 0.1047524 -0.0267872 -1.6321315 Largest eigenvalues: [1] 65868486 60961942 58268142 56642964 55654836 53985039 53045952 52600567 [9] 52474029 52195419 Smallest eigenvalues: [1] 0.29353112 0.26421254 0.24069880 0.21331116 0.14220334 0.13595383 [7] 0.08201721 -0.02624704 -1.37526050 -1.59779590 Largest eigenvalues: [1] 66324597 60409218 57749827 56802431 55062561 53910980 52636040 52490835 [9] 52366116 51812154 Smallest eigenvalues: [1] 0.3238356 0.2496848 0.2159286 0.1849888 0.1712111 0.1618124 [7] -0.1586719 -0.2831307 -0.3315398 -0.9900699 Largest eigenvalues: [1] 66198155 59954691 57371542 56871274 54652198 53037627 52860533 52456301 [9] 51650825 51589338 Smallest eigenvalues: [1] 0.28030410 0.23164345 0.16569131 0.14974950 0.07352849 -0.04166859 [7] -0.04956359 -0.38941178 -0.44200870 -0.53847499 Largest eigenvalues: [1] 63973941 60192981 57661301 55427909 54774789 53571659 51624257 51540728 [9] 51529087 50945402 Smallest eigenvalues: [1] 0.42430077 0.37351528 0.36916465 0.33133912 0.22922266 0.22083748 [7] 0.14874419 0.08477195 0.06912904 -0.16018647 Largest eigenvalues: [1] 64611572 60355340 57490467 56329037 55303275 53826454 52384693 52383575 [9] 52180474 51306512 Smallest eigenvalues: [1] 0.50171588 0.46687751 0.45267226 0.39188347 0.34826348 0.32061463 [7] 0.31232823 0.12021224 0.09798791 -0.13610437 Largest eigenvalues: [1] 64772381 59660125 57134377 55753136 54904515 53502594 51926088 51854032 [9] 51320852 50429195 Smallest eigenvalues: [1] 0.38531642 0.34042368 0.23556259 0.20364124 0.17823409 -0.04027302 [7] -0.04702928 -0.05179629 -0.07915303 -1.30598756 Largest eigenvalues: [1] 64284780 60462140 57269798 55685606 55474462 53795416 52884626 51973386 [9] 51892705 51644598 Smallest eigenvalues: [1] 0.4215706 0.4121962 0.3736347 0.3310153 0.2855394 0.2404173 [7] 0.2231569 0.2040454 0.1198840 -0.1835219 Largest eigenvalues: [1] 62627336 60759937 57180116 55433331 55365360 53677334 52273855 52176674 [9] 51348637 51157193 Smallest eigenvalues: [1] 0.4916969 0.4845972 0.4465242 0.4170723 0.3137256 0.3047418 [7] 0.2508813 0.2288577 0.2121150 -0.0672257 Largest eigenvalues: [1] 64235432 59578502 57258443 55447346 54628133 53072705 51695272 51402215 [9] 51306666 50653162 Smallest eigenvalues: [1] 0.3842260 0.3788244 0.3093946 0.2491844 0.2410652 0.1990001 [7] 0.1674324 -0.4061881 -0.6413068 -1.5163069 Largest eigenvalues: [1] 62641300 59213911 56765481 55065029 54852673 53142059 51877363 51746645 [9] 50950153 50613542 Smallest eigenvalues: [1] 0.60627072 0.59890510 0.54791023 0.44315392 0.38616628 0.35894897 [7] 0.26408105 0.22032031 0.12442103 -0.01300647 Largest eigenvalues: [1] 62810815 60171645 57072618 55771058 54808337 54115070 52447664 52203238 [9] 51068261 50844478 Smallest eigenvalues: [1] 0.28762597 0.27535851 0.27197888 0.24981564 0.22488444 0.15031248 [7] 0.02205735 -0.64347616 -0.90645808 -1.62884934 Largest eigenvalues: [1] 64811016 60261258 57815952 56154256 55134026 53305000 52437683 52147419 [9] 52080975 51590695 Smallest eigenvalues: [1] 0.43939866 0.38067198 0.30842538 0.29381131 0.25166320 0.14475968 [7] 0.10947469 0.08465491 -0.13708031 -1.16591922 Largest eigenvalues: [1] 65503611 60526228 57455322 56213183 55119027 53370079 52370235 52310403 [9] 51914938 51329582 Smallest eigenvalues: [1] 0.114355585 -0.004635647 -0.008848434 -0.159913929 -0.164976422 [6] -0.246746159 -0.336428536 -0.475751998 -0.693432413 -1.421451540 Largest eigenvalues: [1] 63031583 59916935 57118657 55164654 54726760 53107658 52182645 51350157 [9] 51156730 50926974 Smallest eigenvalues: [1] 0.45998872 0.41580810 0.39184842 0.33953891 0.33800481 0.33182469 [7] 0.27681551 0.25551057 0.21870749 -0.02127224 Largest eigenvalues: [1] 61723181 59132596 56775358 54843397 54310412 53083041 51443760 51092701 [9] 50398566 50087078 Smallest eigenvalues: [1] 0.4124039 0.3006569 0.2514511 0.2511782 0.2249729 0.2143911 [7] 0.1778251 0.1097218 -0.1895180 -0.2528983 Largest eigenvalues: [1] 64547811 60215328 57630273 56368777 54897717 53369060 52518681 51626623 [9] 51478585 50467374 Smallest eigenvalues: [1] 0.3579867 0.3538659 0.3065763 0.2799404 0.2398964 0.2322097 [7] 0.1360400 0.1043339 -0.4957799 -1.1937904 Largest eigenvalues: [1] 65307097 60270620 58356998 55588030 55510642 54424149 52858980 52693364 [9] 51851792 51550041 Smallest eigenvalues: [1] 0.4043210 0.3438279 0.3292763 0.3054532 0.2274421 0.1681585 [7] 0.1507635 0.1159263 -0.2828722 -0.4291482 Largest eigenvalues: [1] 63682380 59316459 57318296 55877214 54162732 52832241 51785944 51713349 [9] 51387607 50693001 Smallest eigenvalues: [1] 0.431394797 0.420844315 0.360916333 0.359955744 0.346086671 [6] 0.339005585 0.285401444 0.257995076 -0.002866243 -5.545150798 Largest eigenvalues: [1] 64216750 60061595 57117564 55598064 55108613 53333083 52120494 51716823 [9] 51626127 50854276 Smallest eigenvalues: [1] 0.4608246 0.3841535 0.3712152 0.3627737 0.2946871 0.2719265 [7] 0.2047346 0.1746251 0.1477002 -0.1509604 Largest eigenvalues: [1] 64045586 59697654 57065280 55967590 54704728 53200363 52078906 51823622 [9] 51804903 50923302 Smallest eigenvalues: [1] 0.522567142 0.508919326 0.412642972 0.352535295 0.307459818 [6] 0.302199698 0.158631452 0.134830209 0.024603845 -0.002993484 Largest eigenvalues: [1] 63177302 59624004 57131831 54773680 54626686 53134592 51864442 51348919 [9] 50898124 50539322 Smallest eigenvalues: [1] 0.51385050 0.45614854 0.42400424 0.35775865 0.33238024 0.28848757 [7] 0.24921755 0.16494337 0.02533496 -0.02961978 Largest eigenvalues: [1] 61446744 59820695 56948255 56035796 54095329 53944818 52733495 51624963 [9] 50741235 50665946 Smallest eigenvalues: [1] 0.46139118 0.44187490 0.39909965 0.33792925 0.31125959 0.29159161 [7] 0.27961396 0.17456575 0.14171066 -0.03839334 Largest eigenvalues: [1] 63714964 60702691 57312911 55907357 55824463 54108635 52535897 52011540 [9] 51875612 51479550 Smallest eigenvalues: [1] 0.42639968 0.39559155 0.36525013 0.34761243 0.34320671 0.28718473 [7] 0.26210578 0.21108925 0.05909535 -0.14595074 Largest eigenvalues: [1] 61834668 60856656 57519513 55647639 55020232 53877479 52142949 52131096 [9] 51248404 50990330 Smallest eigenvalues: [1] 0.30001491 0.29098047 0.26735308 0.20674120 0.16650157 0.12895381 [7] 0.08717612 -0.13805674 -0.42287786 -0.51276924 Largest eigenvalues: [1] 64617957 61378016 58295062 56594013 55839873 54005981 53775110 52832017 [9] 52238143 52083503 Smallest eigenvalues: [1] 0.4068207 0.4065248 0.3910243 0.3167281 0.2799650 0.2734857 [7] 0.2637625 0.2035177 -0.1255357 -4.0310711 Largest eigenvalues: [1] 64923755 60501512 57783306 56311142 55204456 53720725 52398973 52116895 [9] 52065385 51204325 Smallest eigenvalues: [1] 0.284458278 0.239570607 0.161864226 0.078653164 0.001354026 [6] -0.049783775 -0.107340000 -0.436127485 -0.590370738 -1.137575036 Largest eigenvalues: [1] 64891547 59770522 56935810 55457870 54649439 52996751 51960321 51644092 [9] 51297891 51122953 Smallest eigenvalues: [1] 0.3988811 0.3785343 0.3597117 0.3264402 0.3187563 0.3079406 [7] 0.2994325 0.1886132 0.1358960 -0.1118437 Largest eigenvalues: [1] 65289964 60791535 57433230 57124862 55243598 53653674 52871165 52665504 [9] 52329115 51409997 Smallest eigenvalues: [1] 0.42503823 0.39471310 0.26896249 0.23419675 0.23267573 0.19209878 [7] 0.18739692 -0.06811077 -0.54508634 -0.63416543 Largest eigenvalues: [1] 65320022 61025858 57394836 56222003 56006665 54116520 53056581 52540694 [9] 52208895 51664922 Smallest eigenvalues: [1] 0.5547804 0.4796298 0.4590903 0.4184093 0.3740510 0.3720161 [7] 0.3422207 0.3344018 0.2337584 -0.2264861 Largest eigenvalues: [1] 64118028 60212374 57337982 56028139 55373081 53506169 52063641 51965326 [9] 51773277 50799994 Smallest eigenvalues: [1] 0.29195785 0.26514031 0.22143992 0.21376256 0.16918389 0.15121911 [7] 0.12781814 0.05062987 -0.04063535 -0.26847746 Largest eigenvalues: [1] 62134203 58916993 56411820 54813421 54712013 53001419 51976627 51491648 [9] 50715303 50466484 Smallest eigenvalues: [1] 0.57420020 0.53871151 0.48216025 0.44775400 0.39620996 0.39488092 [7] 0.36739665 0.22070880 0.13224398 -0.06623388 Largest eigenvalues: [1] 63968624 60037365 56660136 55413056 55287549 53582239 52220309 51450455 [9] 51410823 50580619 Smallest eigenvalues: [1] 0.352742067 0.337433782 0.334528432 0.270141273 0.265758769 [6] 0.173941368 0.162504619 0.062101215 0.006925509 -0.129423609 Largest eigenvalues: [1] 64924472 59172526 56684532 56374077 54581068 53022179 52416933 51606833 [9] 50762362 50190823 Smallest eigenvalues: [1] 0.397795416 0.375662603 0.335943325 0.311856821 0.294155796 [6] 0.204684635 0.003725602 -0.216922536 -0.242593855 -2.926670356 Largest eigenvalues: [1] 65461585 60376823 57493288 56042344 55495960 53954256 52660679 52163290 [9] 51972204 51782551 Smallest eigenvalues: [1] 0.18194292 0.08483852 -0.06535354 -0.23098375 -0.23570552 -0.29365374 [7] -0.43288915 -0.71670623 -0.83823223 -4.91196316 Largest eigenvalues: [1] 62451671 59615497 56787975 55366325 54455170 53447420 52074444 51802714 [9] 51036027 50681459 Smallest eigenvalues: [1] 0.637143917 0.538830483 0.513684301 0.504624488 0.431139853 [6] 0.386743562 0.303686175 0.217925661 0.156696251 -0.001484799 Largest eigenvalues: [1] 65111852 60550941 57706261 56389305 55355203 53864406 52454220 52406028 [9] 52019443 51352038 Smallest eigenvalues: [1] 0.4381370 0.4163145 0.3968833 0.3435968 0.2781574 0.2569211 [7] 0.1466814 0.1412468 0.1271378 -1.8012059 Largest eigenvalues: [1] 63956777 60373091 57520828 55380189 55318216 53820383 52203252 52113608 [9] 51522971 51319108 Smallest eigenvalues: [1] 0.4074957 0.3736822 0.3610401 0.3152661 0.2545363 0.2487171 [7] 0.1374125 0.1346574 -0.3316199 -0.4561040 Largest eigenvalues: [1] 63134456 60483048 56862999 55826770 54949694 53260382 52170498 51709374 [9] 51536848 50733833 Smallest eigenvalues: [1] 0.3730152 0.3535112 0.3378832 0.3305521 0.2481641 0.2221549 [7] 0.1935049 0.1100101 -0.1051907 -1.9676151 Largest eigenvalues: [1] 61936147 59599615 56855775 54932905 54400927 53029978 51361980 51207151 [9] 50618151 50410146 Smallest eigenvalues: [1] 0.46423913 0.40073847 0.36553243 0.34260564 0.32537861 0.29811718 [7] 0.28135759 0.18887851 0.12339765 -0.04777045 Largest eigenvalues: [1] 64927043 59830651 57435423 56049643 54706435 53080973 52191417 51846698 [9] 51758212 51008885 Smallest eigenvalues: [1] 0.53378569 0.52429601 0.48888533 0.48028643 0.44036744 0.33179848 [7] 0.18613807 0.11911690 0.06998202 -0.11580793 Largest eigenvalues: [1] 63563802 60240938 57434281 55583602 55165952 53637103 52165471 51917817 [9] 51678109 51046726 Smallest eigenvalues: [1] 0.4625514 0.4098466 0.3950050 0.3897157 0.3592403 0.1428243 [7] 0.1260283 0.1138990 -0.1988930 -1.3626917 Largest eigenvalues: [1] 64519744 59214123 56732450 54844362 54837469 53120083 52147075 51286113 [9] 51212950 50596867 Smallest eigenvalues: [1] 0.44985555 0.43340665 0.39665318 0.37379911 0.29793721 0.17104380 [7] 0.16079471 0.10643018 0.06518246 -1.59781987 Largest eigenvalues: [1] 64446842 60147472 56881250 55975115 55313850 53315808 52367494 52052142 [9] 51597967 51215915 Smallest eigenvalues: [1] 0.269956889 0.168703941 0.128518350 0.045044792 0.039120644 [6] 0.003191129 -0.116530282 -0.330270907 -0.590093810 -0.851078350 Largest eigenvalues: [1] 64240755 60878508 57548537 55651574 55272276 53572096 52107573 51850581 [9] 51539419 51213731 Smallest eigenvalues: [1] 0.41871591 0.38195318 0.35698294 0.32602633 0.29134595 0.24158548 [7] 0.22386232 0.19775791 -0.05521472 -2.23561446 Largest eigenvalues: [1] 63191346 60076232 57326240 55869687 54709059 53356190 52177186 51715577 [9] 51652003 51200595 Smallest eigenvalues: [1] 0.39243812 0.37778438 0.29793035 0.25610061 0.22433754 0.22185230 [7] 0.01741347 -0.03202508 -0.08575769 -5.24342707 Largest eigenvalues: [1] 63363168 59695982 56724347 55117036 54980511 52899753 51465013 51446686 [9] 51224826 50449030 Smallest eigenvalues: [1] 0.49175672 0.40112003 0.36323426 0.29570560 0.27596625 0.23047658 [7] 0.19690478 0.17238320 0.04136418 -0.98022697 Largest eigenvalues: [1] 64944767 59798967 57647056 55922501 54627372 53456253 52215664 51699038 [9] 51483015 50796357 Smallest eigenvalues: [1] 0.35680785 0.33378388 0.25902892 0.23487622 0.23211194 0.21514133 [7] 0.16171935 0.09826078 -0.22083617 -0.80487036 Largest eigenvalues: [1] 62464811 60246060 57279819 55640718 55052970 53486891 52297287 52177961 [9] 51454446 50813074 Smallest eigenvalues: [1] 0.21809328 0.17766232 0.17054201 0.16118970 0.07402816 0.07078496 [7] -0.10071888 -0.28095705 -1.46274409 -1.55358804 Largest eigenvalues: [1] 63606322 59473104 56973373 54813005 54695710 53216161 51599122 51123121 [9] 50987209 50443197 Smallest eigenvalues: [1] 0.36202829 0.35079600 0.24234965 0.20275350 0.16940017 0.10203958 [7] 0.02006566 -0.04535303 -0.23270112 -3.57495525 Largest eigenvalues: [1] 64980942 59705304 56925347 56302661 54872859 53152064 52460402 52262021 [9] 51759935 51262943 Smallest eigenvalues: [1] 0.31840516 0.20177103 0.15939058 0.13932871 -0.02069221 -0.03142577 [7] -0.11038247 -0.22070981 -1.09169964 -2.05762710 Largest eigenvalues: [1] 65888465 59784264 57060916 56618711 54568943 53057364 52664335 52188248 [9] 51414871 51391962 Smallest eigenvalues: [1] 0.46273726 0.36205484 0.22338922 0.19390587 0.18597176 0.15130079 [7] 0.11961507 -0.06721433 -0.36030320 -1.67870313 Largest eigenvalues: [1] 63818053 59417184 56343085 55084596 54632459 52934193 51713555 51286134 [9] 51128063 50371408 Smallest eigenvalues: [1] 0.416692834 0.364815114 0.240203085 0.191391103 0.118741762 [6] 0.063732697 0.004530815 -0.015170372 -0.077513604 -0.632270320 Largest eigenvalues: [1] 63359283 59430167 56752892 54791207 54516702 53005746 51683104 51252831 [9] 51073236 50643275 Smallest eigenvalues: [1] 0.48314931 0.39699723 0.38656114 0.36852205 0.31081783 0.29669520 [7] 0.28052225 -0.03951312 -0.04482099 -2.32612212 Largest eigenvalues: [1] 64308431 60612838 56984282 55689644 55565238 53620448 52189609 51984478 [9] 51817341 51126469 Smallest eigenvalues: [1] 0.255893637 0.255496711 0.222270377 0.034376715 -0.009442275 [6] -0.140263386 -0.433526406 -0.723518822 -1.077376241 -1.454730069 Largest eigenvalues: [1] 65895119 59530534 56850827 56252136 54400012 52998113 52314320 51750849 [9] 51363202 50943201 Smallest eigenvalues: [1] 0.31448537 0.31089953 0.24469739 0.18495554 0.12219551 0.02676088 [7] -0.30076956 -0.85848804 -1.58658861 -1.85757015 Largest eigenvalues: [1] 66457410 60426487 58459040 56947635 55141540 53193619 52890811 52219571 [9] 51797093 51481297 Smallest eigenvalues: [1] 0.39882907 0.36988662 0.34962567 0.34640457 0.32618712 0.30297334 [7] 0.25496569 0.19267631 0.18536449 -0.01011802 Largest eigenvalues: [1] 64526635 60723027 58150356 55814539 55688479 54371589 52435290 52057851 [9] 51923014 51186804 Smallest eigenvalues: [1] 0.10331314 0.09411901 -0.05479243 -0.10662159 -0.12199998 -0.31617443 [7] -0.32968892 -0.38409834 -0.74752024 -1.24051087 Largest eigenvalues: [1] 66153630 60398999 57972392 57252778 54850598 53367460 53112243 52797847 [9] 51888651 51518140 Smallest eigenvalues: [1] 0.38241794 0.35423516 0.33731761 0.30472545 0.30069783 0.20922189 [7] 0.10869108 -0.08314438 -0.15020855 -1.32186369 Largest eigenvalues: [1] 63638549 60277715 57401201 56276972 55013923 53339215 52519683 52066540 [9] 51829671 51332714 Smallest eigenvalues: [1] 0.49799915 0.44928913 0.44581410 0.41499356 0.33121849 0.27941617 [7] 0.23813911 0.20386552 0.05577655 -0.06201129 Largest eigenvalues: [1] 66259222 60049795 57766631 57093564 54859826 53569324 53193417 51933343 [9] 51746823 50986621 Smallest eigenvalues: [1] 0.38344711 0.33708112 0.33666557 0.27678748 0.26551530 0.21773843 [7] 0.20135358 0.05200353 -0.02940766 -0.41362848 Largest eigenvalues: [1] 64948306 60119483 57028828 56571925 54897534 53300319 52546207 52486640 [9] 51982007 51535200 Smallest eigenvalues: [1] 0.20179198 0.19685450 0.18101021 0.13777247 -0.03113217 -0.23597599 [7] -0.51116234 -1.00738849 -1.38620527 -1.51914677 Largest eigenvalues: [1] 65295663 60301423 57699408 56512384 54765000 53432575 52643772 52164124 [9] 51620770 51354129 Smallest eigenvalues: [1] 0.5354128 0.5036787 0.4995127 0.4318419 0.3589464 0.3519149 [7] 0.1788749 0.1578994 0.1156847 -0.2320354 Largest eigenvalues: [1] 64203162 59266658 56591366 55558831 54351875 52286714 51617249 51118063 [9] 51098441 50270800 Smallest eigenvalues: [1] 0.5313828 0.4991924 0.4406278 0.4039710 0.3529575 0.2939176 [7] 0.2645401 0.0338451 -0.3570618 -4.0684087 Largest eigenvalues: [1] 65487650 59825436 56828623 56436953 54550995 52546916 52259940 51470609 [9] 51418905 50639626 Smallest eigenvalues: [1] 0.21519902 0.15399032 0.10489712 -0.02301297 -0.05059752 -0.12224821 [7] -0.13170798 -0.77349678 -1.06153459 -1.88610184 Largest eigenvalues: [1] 66332553 60411304 57380203 57188388 54998345 53277662 53126460 52821210 [9] 51854920 51802795 Smallest eigenvalues: [1] 0.3746854 0.3275190 0.3178091 0.2250618 0.1771928 0.1572432 [7] 0.1093535 -0.1651058 -0.3501318 -0.9610655 Largest eigenvalues: [1] 64128097 59864698 56886956 55135106 54682539 53092378 51768006 51661962 [9] 51289161 51044492 Smallest eigenvalues: [1] 0.39885408 0.37649569 0.36196943 0.28037889 0.26043615 0.20837866 [7] 0.18578268 0.05003467 0.04163188 -1.45146658 Largest eigenvalues: [1] 64616076 60324247 56857436 56039624 55398832 53639036 51908081 51784943 [9] 51716899 50874203 Smallest eigenvalues: [1] 0.376280719 0.307968800 0.270685000 0.171366752 0.160953665 [6] 0.108070901 0.072151884 0.020834484 0.002786508 -1.987170405 Largest eigenvalues: [1] 63983121 60170079 57266457 55482300 55072229 53896826 52008947 51582188 [9] 51111977 50789597 Smallest eigenvalues: [1] 0.24094082 0.16113435 0.07831721 0.04222213 -0.03530437 -0.04026649 [7] -0.07239794 -0.12900239 -0.35897698 -0.82937782 Largest eigenvalues: [1] 66149144 60763201 58175050 56352719 55258555 53761435 52584161 52274386 [9] 51911871 51441598 Smallest eigenvalues: [1] 0.45072375 0.44930617 0.42707307 0.33227141 0.27608788 0.25176901 [7] 0.05342844 0.04366002 -0.05559960 -2.35706928 Largest eigenvalues: [1] 65316235 60092150 57101572 56471027 55207253 53717852 52384138 52138233 [9] 51965542 51267309 Smallest eigenvalues: [1] 0.46426041 0.43155913 0.39258429 0.37299448 0.36460008 0.30936865 [7] 0.28669020 0.17339815 0.13165021 -0.07712913 Largest eigenvalues: [1] 64447110 59828114 56546209 55860706 54700493 53110423 51915110 51875719 [9] 51444778 50799338 Smallest eigenvalues: [1] 0.32180708 0.30948438 0.28262209 0.22483686 0.19245215 -0.05613209 [7] -0.09511850 -0.17865712 -0.56782904 -2.91985104 Largest eigenvalues: [1] 65494462 60770984 57409712 55881813 55367889 53448261 51999398 51898515 [9] 51631644 51150789 Smallest eigenvalues: [1] 0.4215955 0.3830922 0.3608919 0.3411174 0.3170894 0.3020075 [7] 0.2732070 0.2585327 0.2136132 -0.0904391 Largest eigenvalues: [1] 64170768 60128314 57281690 55445678 55411005 53774799 51903407 51567664 [9] 51325856 50429510 Smallest eigenvalues: [1] 0.41027462 0.34991550 0.33201372 0.28719242 0.23969036 0.17322448 [7] 0.08775426 -0.03237588 -0.07105975 -0.25147471 Largest eigenvalues: [1] 65732569 60345982 57423459 56437619 55366065 53937114 52478352 51988905 [9] 51832965 50614801 Smallest eigenvalues: [1] 0.30067100 0.25692767 0.17869120 0.14802603 0.13641694 0.11662896 [7] 0.02789947 -0.76134603 -0.96719689 -1.04722745 Largest eigenvalues: [1] 65316550 59817144 57643068 55937888 55004182 53727770 52529449 52012799 [9] 52006955 51646610 Smallest eigenvalues: [1] 0.4718204 0.3725984 0.3688057 0.3619263 0.3417680 0.2895856 [7] 0.2668145 0.2288515 0.1696846 -0.0419761 Largest eigenvalues: [1] 65430252 60186549 57902544 56708130 54799905 53182629 52727318 51983730 [9] 51787673 51207025 Smallest eigenvalues: [1] 0.16163110 0.10226022 0.07016115 0.01021784 -0.01938875 -0.15511759 [7] -0.20201882 -0.28235975 -0.83649657 -1.41196324 Largest eigenvalues: [1] 63589651 60474192 57779315 55120910 54979755 53748396 51942201 51879761 [9] 51166026 50946444 Smallest eigenvalues: [1] 0.43652355 0.42026365 0.39998526 0.39097169 0.31227609 0.27948034 [7] 0.26460260 0.19855633 0.06991435 -0.03640425 Largest eigenvalues: [1] 65120762 60300018 58019377 55737396 55382700 53653209 52427660 52078487 [9] 51952404 51482757 Smallest eigenvalues: [1] 0.365817485 0.253268375 0.245423941 0.174328665 0.139668327 [6] 0.035727625 0.009370155 -0.049486401 -0.160140997 -0.538150752 Largest eigenvalues: [1] 66174484 60557071 57955294 56600992 54988746 53595055 52667171 52608848 [9] 51925991 51758373 Smallest eigenvalues: [1] 0.37421177 0.37286524 0.36146869 0.27574148 0.24273759 0.16643424 [7] 0.16437171 0.10164275 0.03150259 -0.41895148 Largest eigenvalues: [1] 66555193 61015849 57875134 57278162 56051532 54362047 53313086 53219235 [9] 52404952 52003054 Smallest eigenvalues: [1] 0.42999126 0.39400374 0.32997726 0.30741752 0.29716140 0.24433894 [7] 0.17649854 0.13992982 0.09912456 -0.68463267 Largest eigenvalues: [1] 65480565 59535569 57271541 56789497 54602543 53325300 52731957 51867612 [9] 51482190 50987039 Smallest eigenvalues: [1] 0.56084345 0.49043668 0.48142433 0.41932512 0.36428754 0.26911925 [7] 0.25576346 0.21769094 -0.04888047 -3.80561657 Largest eigenvalues: [1] 64832032 60105255 57402449 56089024 55128969 53440947 52201383 51955887 [9] 51932038 50968290 Smallest eigenvalues: [1] 0.43845323 0.42975066 0.39989268 0.38468818 0.34356178 0.22839252 [7] 0.20607929 0.08697602 0.07640505 -5.50472005 Largest eigenvalues: [1] 63794133 60633576 57902608 56019595 55698928 54404253 52707114 52662581 [9] 51882010 51585602 Smallest eigenvalues: [1] 0.4624995 0.3755231 0.3703261 0.3592630 0.3440499 0.3248258 [7] 0.2752419 0.2409431 0.1158476 -0.7668570 Largest eigenvalues: [1] 64221205 60318583 57709171 55619533 55531237 54156202 52544302 52282630 [9] 51618503 51105844 Smallest eigenvalues: [1] 0.45448890 0.42029267 0.39848239 0.29456969 0.20575790 0.15607533 [7] 0.13126174 0.08395056 0.01181098 -1.42544809 Largest eigenvalues: [1] 63006324 60062214 56941706 55361428 54650641 53614751 51778485 51688758 [9] 50917214 50820470 Smallest eigenvalues: [1] 0.51249200 0.45822914 0.40281296 0.39870987 0.36076613 0.35794471 [7] 0.34564490 0.14319905 0.10718640 -0.07663943 Largest eigenvalues: [1] 65176484 61281441 57663689 56588514 56289128 54564393 53434200 52573449 [9] 52280838 51819554 Smallest eigenvalues: [1] 0.42829448 0.41753283 0.38087157 0.36199592 0.33765541 0.29052853 [7] 0.26068976 0.01377166 -0.20060367 -0.87768029 Largest eigenvalues: [1] 64144509 60444007 57639448 56127475 55400155 53856133 52361648 52171013 [9] 51806209 51182076 Smallest eigenvalues: [1] 0.308025995 0.206761619 0.203216503 0.186286851 0.113052555 [6] 0.076307466 0.006604131 -0.181839664 -0.291542576 -21.811795757 Largest eigenvalues: [1] 65871585 59810854 57759104 56107180 54956920 53792945 52488773 52300045 [9] 51995030 51435775 Smallest eigenvalues: [1] 0.4434678 0.3933192 0.3548960 0.2414716 0.2047585 0.1569187 [7] 0.1048188 -0.1947996 -0.3046727 -0.7510127 Largest eigenvalues: [1] 65753249 60422185 57651871 56907886 54849631 52897648 52848862 52433092 [9] 51726218 51532197 Smallest eigenvalues: [1] 0.5779033 0.5601017 0.4521349 0.4358426 0.3057825 0.2802577 [7] 0.2698895 0.2403582 -0.2231736 -0.2502104 Largest eigenvalues: [1] 65495792 60740763 57667770 56644212 55475239 53738347 52781202 52599364 [9] 51953171 51400325 Smallest eigenvalues: [1] 0.39276884 0.35729847 0.34816612 0.30998125 0.27557320 0.22853905 [7] 0.14775489 0.11577115 0.08818914 -3.10563628 Largest eigenvalues: [1] 63716726 59893907 57517720 55575251 54941132 53477474 51870779 51750287 [9] 51570194 50904700 Smallest eigenvalues: [1] 0.34195849 0.24133060 0.21694165 0.19503112 0.10672832 0.02787603 [7] -0.10118311 -0.21591306 -0.67050739 -1.28075896 Largest eigenvalues: [1] 65171880 60592546 57871300 56212817 55299538 53882689 52342246 52080007 [9] 51797614 51116417 Smallest eigenvalues: [1] 0.40662046 0.38647370 0.33170701 0.33162997 0.30318397 0.22392881 [7] 0.20000899 0.08068127 0.05883845 -0.39544448 Largest eigenvalues: [1] 65145845 60237238 57688219 56369463 55097132 53466215 53217061 52567880 [9] 51852069 51605759 Smallest eigenvalues: [1] 0.4959148 0.4117465 0.3925934 0.3892781 0.2854885 0.2722464 [7] 0.1915873 0.1864380 -0.1529678 -0.1771534 Largest eigenvalues: [1] 64485225 60417703 57274239 55921359 55124532 53399009 51904648 51825347 [9] 51797969 50898568 Smallest eigenvalues: [1] 0.6139020 0.5804288 0.5208425 0.5147206 0.4563544 0.3409322 [7] 0.2962343 0.2506831 0.2447080 -0.6830423 Largest eigenvalues: [1] 64533801 59843461 57051366 55700044 55026546 53588815 52152621 51836739 [9] 51632093 50798520 Smallest eigenvalues: [1] 0.38089860 0.36074590 0.30022144 0.28137132 0.27443576 0.18334242 [7] 0.17583582 0.16014067 0.13095374 -0.07063696 Largest eigenvalues: [1] 65799156 60657443 58331932 56359963 55470306 53900753 52569202 52415561 [9] 52330166 51790033 Smallest eigenvalues: [1] 0.3616097 0.3286228 0.3181877 0.3007739 0.2525987 0.2037673 [7] 0.1977944 0.1026287 -0.5029078 -3.1767412 Largest eigenvalues: [1] 65431182 59830413 57109716 56758413 54850195 52841188 52646603 52424251 [9] 51838168 51478743 Smallest eigenvalues: [1] 0.4471657 0.4327267 0.3227875 0.2972009 0.2606796 0.2331267 [7] 0.2251395 0.1442445 0.1034761 -0.6873129 Largest eigenvalues: [1] 61983548 59479073 56151308 54809728 54805144 53062109 51964424 51953472 [9] 50874982 50679640 Smallest eigenvalues: [1] 0.38179778 0.29670344 0.26829412 0.21802983 0.15912084 0.07662484 [7] -0.02784264 -0.12456120 -0.57823318 -0.78838126 Largest eigenvalues: [1] 65278982 61455893 58255280 57242291 55362965 53669651 53381839 52675368 [9] 52285646 51440846 Smallest eigenvalues: [1] 0.4701700 0.4498259 0.4130603 0.3694225 0.3263399 0.2567731 [7] 0.2288796 0.1915548 0.1630194 -0.6071124 Largest eigenvalues: [1] 62909426 59399446 56885421 54818310 54707668 53234116 51921570 51200939 [9] 50850083 50466636 Smallest eigenvalues: [1] 0.24025026 0.23284841 0.21419365 0.18911631 0.13054411 0.01454168 [7] -0.13678224 -0.19889759 -0.32694998 -1.22316880 Largest eigenvalues: [1] 64079599 59956866 57537982 55733631 54838047 53561966 51793740 51766962 [9] 51707695 50824179 Smallest eigenvalues: [1] 0.41558011 0.37971485 0.23767634 0.07841913 0.07488108 0.04916357 [7] -0.02906305 -0.08548154 -0.30606844 -2.11074582 Largest eigenvalues: [1] 63827165 60265287 57422937 55607886 55498858 53761653 52625950 51818676 [9] 51735138 51284014 Smallest eigenvalues: [1] 0.206281423 0.186940906 0.184822632 0.164652584 0.156494196 [6] 0.147955263 0.058202108 -0.007530551 -0.279125147 -0.352152164 Largest eigenvalues: [1] 63593910 59314045 56383037 55532901 54778798 53085053 51773136 51495649 [9] 50830776 50198942 Smallest eigenvalues: [1] 0.47735267 0.38922739 0.38311668 0.37983251 0.34968656 0.28385840 [7] 0.19040160 0.16099142 -0.08795911 -0.44315592 Largest eigenvalues: [1] 64537503 60757877 57781254 55942695 55358972 53760801 52792436 52172156 [9] 52105396 51884014 Smallest eigenvalues: [1] 0.36681956 0.33198055 0.33129214 0.32368534 0.24858332 0.21126190 [7] 0.20711594 0.19122726 -0.08568089 -1.58808715 Largest eigenvalues: [1] 64961779 60717350 58030721 55773400 55687200 54230392 52235425 52002581 [9] 51934151 51336714 Smallest eigenvalues: [1] 0.23151387 0.16549267 0.15482562 0.08237195 0.03596431 -0.06702173 [7] -0.37048212 -0.38894702 -1.34481634 -1.70611943 Largest eigenvalues: [1] 64597605 59563841 56882993 55986066 54643173 53036149 52238462 51993337 [9] 51601370 51022888 Smallest eigenvalues: [1] 0.43433141 0.41408769 0.29875081 0.29814096 0.23928795 0.23167230 [7] 0.18174241 0.16648653 -0.06203392 -1.23436719 Largest eigenvalues: [1] 64440736 60560603 57212631 56259889 55598767 53962329 52232686 52090257 [9] 51934081 51051546 Smallest eigenvalues: [1] 0.3042010065 0.2028350908 0.1740175163 0.1612815640 0.1369131970 [6] 0.0001836193 -0.0677540862 -0.2490146759 -0.4799055444 -1.0698131028 Largest eigenvalues: [1] 64993726 60428037 57374522 56547352 54849189 53550509 52484664 52412518 [9] 51789101 51646571 Smallest eigenvalues: [1] 0.27330582 0.23265980 0.20692219 0.12274527 0.07847066 -0.19807447 [7] -0.25987368 -0.30761489 -0.51152650 -1.38724883 Largest eigenvalues: [1] 64121480 59235452 57025321 55467561 54263155 53170667 51844510 51643615 [9] 51464198 50938521 Smallest eigenvalues: [1] 0.22199018 0.21752864 0.17762979 0.16634727 0.12907103 -0.04799962 [7] -0.09461652 -0.13949955 -0.17537962 -1.50600064 Largest eigenvalues: [1] 64803510 60825577 57752098 56073264 55661494 54323780 52679780 52602585 [9] 52017695 51827638 Smallest eigenvalues: [1] 0.529283596 0.519283179 0.490264063 0.434428678 0.422483895 [6] 0.342396511 0.313743248 0.261834375 0.078963518 -0.009048804 Largest eigenvalues: [1] 62319757 59863546 56791761 54995234 54701300 53307653 51698147 51593220 [9] 50666779 50490874 Smallest eigenvalues: [1] 0.37679206 0.36717120 0.32350101 0.31689581 0.29871551 [6] 0.25686390 0.25632731 -0.01333862 -0.06789774 -10.12314265 Largest eigenvalues: [1] 64411516 59932779 57280277 55653920 55068576 53505755 52217133 51758458 [9] 51549442 50961953 Smallest eigenvalues: [1] 0.33992151 0.33773102 0.33052832 0.24759088 0.17865735 0.16725219 [7] 0.13009824 0.12557393 0.06940252 -0.05708416 Largest eigenvalues: [1] 62687074 60046225 57096819 55454949 55099931 53311649 52429309 52254927 [9] 51307310 51079840 Smallest eigenvalues: [1] 0.3734285 0.3578477 0.3031081 0.2387319 0.2306287 0.2039266 [7] 0.1485060 -0.1171986 -0.3440188 -1.6214314 Largest eigenvalues: [1] 65486043 60113924 57079185 56666044 55185757 53628727 52574929 52359392 [9] 52009107 51585582 Smallest eigenvalues: [1] 0.49486609 0.47791572 0.45526315 0.38861004 0.26367715 0.24308695 [7] 0.16907081 0.12584112 0.02471961 -0.01684104 Largest eigenvalues: [1] 62945545 60794518 57637850 56261031 54882770 54402627 52808606 52517634 [9] 51566391 51069462 Smallest eigenvalues: [1] 0.40440121 0.33971828 0.32780829 0.26849468 0.18441321 0.14547299 [7] 0.03445263 -0.35447099 -0.44357899 -4.96304851 Largest eigenvalues: [1] 65527053 60207613 57375006 56259761 55115688 53212988 52481602 52032514 [9] 51617348 51241593 Smallest eigenvalues: [1] 0.2201364 0.1930468 0.1874791 -0.1227888 -0.1273022 -0.2719032 [7] -0.2880179 -0.3875469 -0.4994241 -1.0144298 Largest eigenvalues: [1] 65057256 61275334 57637187 56391357 56306501 54331565 53877199 52564757 [9] 52190753 51824437 Smallest eigenvalues: [1] 0.4518062 0.3811479 0.3427248 0.3200841 0.2817578 0.2711405 [7] 0.2704352 0.1788838 -0.2115723 -0.4633926 Largest eigenvalues: [1] 64165066 60755183 58081525 56166649 55246195 53722459 52005370 51939202 [9] 51843830 50931778 Smallest eigenvalues: [1] 0.25074725 0.20080264 0.10458999 0.08528284 0.07400013 0.01865420 [7] -0.02934871 -0.12047732 -0.15615536 -3.60260821 Largest eigenvalues: [1] 65005210 59847985 57578032 56482285 55144388 53920519 52943505 52327741 [9] 52276216 51892719 Smallest eigenvalues: [1] 0.45241489 0.44066831 0.35509133 0.32710229 0.31067170 0.25264288 [7] 0.18197227 -0.07615371 -0.23499493 -2.00386152 Largest eigenvalues: [1] 65575740 59738799 56726747 56287922 54373976 52617790 52310861 51390303 [9] 51134809 50635299 Smallest eigenvalues: [1] 0.4649903 0.4474241 0.4294076 0.3502424 0.3471955 0.2751184 [7] 0.2261942 0.1726147 0.1328097 -0.3506693 Largest eigenvalues: [1] 64730132 59805212 57428042 55376687 55297960 53809419 51715412 51587904 [9] 51486614 50723969 Smallest eigenvalues: [1] 0.53888156 0.45745730 0.39162100 0.36546596 0.32729226 0.24969499 [7] 0.22215482 0.09068120 0.03596904 -0.16543456 Largest eigenvalues: [1] 64285560 60171025 57302773 55878871 55708304 54134687 52378623 52314474 [9] 51809959 51710390 Smallest eigenvalues: [1] 0.30722470 0.26472251 0.20720361 0.17229991 0.08035100 [6] 0.06282899 -0.13471021 -0.24564233 -0.84712211 -19.78156914 Largest eigenvalues: [1] 63373225 60139956 57612673 55372237 55048578 53712521 52590324 51754877 [9] 51208079 50960488 Smallest eigenvalues: [1] 0.45094110 0.43401422 0.40202821 0.37104549 0.28886965 0.28196224 [7] 0.19893324 0.14721583 0.05688805 -0.63896127 Largest eigenvalues: [1] 65752212 59703940 57233182 56738997 54613908 53095906 52639259 52129237 [9] 51608316 51128829 Smallest eigenvalues: [1] 0.538572136 0.515976379 0.469945128 0.430167322 0.366027608 [6] 0.317178642 0.142653151 0.084944324 0.041586483 -0.008741183 Largest eigenvalues: [1] 64580174 60202693 57517011 55442585 55231930 53796502 52481055 52135800 [9] 51571013 51344194 Smallest eigenvalues: [1] 0.36606927 0.35714062 0.29389149 0.23647287 0.21072451 0.18678329 [7] 0.09481632 -0.06747963 -0.23553946 -1.14394497 Largest eigenvalues: [1] 64461719 59735997 56821507 56081272 54957468 53379231 52166592 52112757 [9] 51622284 51044612 Smallest eigenvalues: [1] 0.46249793 0.43717746 0.40706058 0.30474117 0.27275971 0.26185734 [7] 0.22445666 0.19572387 0.03786895 -1.21038559 Largest eigenvalues: [1] 63452371 59579523 57298204 55281584 54737329 53529528 52205879 51839523 [9] 51449580 51030156 Smallest eigenvalues: [1] 0.44583460 0.43792066 0.38713001 0.34232814 0.32319399 0.30532744 [7] 0.20429410 0.03224634 -0.10057823 -0.38382236 Largest eigenvalues: [1] 62820107 59663631 57056598 55572069 54853961 53197441 51612340 51509818 [9] 51435912 50413943 Smallest eigenvalues: [1] 0.48627473 0.48486213 0.44672818 0.33133222 0.29116410 0.24938516 [7] 0.17885290 0.15383709 0.03918108 -0.32173457 Largest eigenvalues: [1] 64044075 60455779 57302207 55913636 55661146 53944846 52678631 52321508 [9] 52078249 51483432 Smallest eigenvalues: [1] 0.5002047 0.4877379 0.4363611 0.3618692 0.2871384 0.2837144 [7] 0.2813088 0.2140507 -0.4797941 -0.9148599 Largest eigenvalues: [1] 63638083 59431396 56612639 55357256 54698638 52886140 52464489 51393630 [9] 51193909 50785635 Smallest eigenvalues: [1] 0.40686541 0.40339525 0.38322734 0.35472292 0.31792274 0.14749524 [7] 0.10558648 0.01705676 -0.01633554 -1.35660784 Largest eigenvalues: [1] 65858758 59719838 57339255 56055788 54743702 53212222 52241443 51955715 [9] 51846048 50763179 Smallest eigenvalues: [1] 0.43457226 0.39821612 0.39522916 0.33260903 0.30360549 0.27909684 [7] 0.09056232 0.07132009 -0.03331028 -0.15457582 Largest eigenvalues: [1] 64720423 59776526 57054000 55910283 55196154 53571753 51959316 51679796 [9] 51182446 50133327 Smallest eigenvalues: [1] 0.39260874 0.33435365 0.30692710 0.30182919 0.18902775 0.18174103 [7] 0.12612453 -0.01734765 -0.23787213 -1.24284197 Largest eigenvalues: [1] 63199803 60239464 57177048 55512057 54614668 53577085 51846545 51628947 [9] 51002896 50764446 Smallest eigenvalues: [1] 0.50145166 0.48650096 0.38400414 0.34200567 0.24375922 0.17251154 [7] 0.15953227 0.12035749 0.02524313 -0.77626865 Largest eigenvalues: [1] 62208651 59439404 56257202 54771859 54608922 52944998 51956172 51311175 [9] 50736905 50573517 Smallest eigenvalues: [1] 0.56872319 0.55253719 0.52510494 0.38457499 0.37944957 0.32946291 [7] 0.14578330 0.06764163 -0.02156755 -0.08872731 Largest eigenvalues: [1] 65497041 59685859 56909482 56792229 54671221 52837401 52798023 51602580 [9] 51214826 50555018 Smallest eigenvalues: [1] 0.45195098 0.33012824 0.32135000 0.24388514 0.20623307 0.06529955 [7] 0.04877222 -0.10096606 -0.42589629 -1.64607516 Largest eigenvalues: [1] 65073717 61262736 57555699 57004377 56014142 54035441 53623577 52585375 [9] 52541897 52021777 Smallest eigenvalues: [1] 0.36025654 0.26378349 0.21604217 0.21202484 0.10607797 0.08405659 [7] -0.07731024 -0.60904395 -0.67791686 -1.48559029 Largest eigenvalues: [1] 66083921 59610777 56943449 56626455 54251470 52778248 52755492 51933327 [9] 51177987 51122943 Smallest eigenvalues: [1] 0.49283605 0.48350648 0.37031427 0.34334530 0.34313966 0.24508915 [7] 0.22922330 0.02242962 -0.07046072 -0.09086812 Largest eigenvalues: [1] 64279055 59176574 56610448 55358905 54514337 52907435 51709124 51318291 [9] 50987734 50327076 Smallest eigenvalues: [1] 0.59273904 0.45494010 0.43849772 0.42920931 0.31278377 0.31257013 [7] 0.26006999 0.15085641 -0.01491967 -0.18238095 Largest eigenvalues: [1] 63841274 59410326 56573212 55552144 54267231 52710932 51581156 51387589 [9] 50842338 49968115 Smallest eigenvalues: [1] 0.32548894 0.28259775 0.26385580 0.25170916 0.18768399 0.17611072 [7] 0.13279673 0.05586095 0.01349406 -0.62425734 Largest eigenvalues: [1] 65491052 60679702 58281654 56793204 55238631 54039033 52738094 52398507 [9] 52174768 51299871 Smallest eigenvalues: [1] 0.26999467 0.24067227 0.18690195 0.17381151 0.15689405 0.06549953 [7] 0.02325153 -0.01391736 -0.02708347 -1.39803260 Largest eigenvalues: [1] 65084599 59667335 56795187 55302314 54541184 52989902 51781746 51415711 [9] 51288702 50928691 Smallest eigenvalues: [1] 0.481809313 0.463455723 0.380058870 0.303092990 0.297394438 [6] 0.296393546 0.260159155 0.245311660 0.001545766 -5.653291840 Largest eigenvalues: [1] 65444898 60920182 58162050 56492742 55877988 54191029 52776147 52371895 [9] 52288088 51327756 Smallest eigenvalues: [1] 0.42724661 0.36254226 0.26973931 0.24610441 0.18356294 0.17923246 [7] 0.11800548 0.09199347 -0.04562304 -2.16147899 Largest eigenvalues: [1] 64443860 59692638 56612346 55302251 54601411 53081073 51565075 51394645 [9] 51080771 50329756 Smallest eigenvalues: [1] 0.127079620 0.121829523 -0.009105345 -0.098734966 -0.175533379 [6] -0.252872943 -0.275911775 -0.311978659 -0.407907347 -2.161574917 Largest eigenvalues: [1] 65166770 60394479 57775083 55548521 55184248 53636282 52218048 51709664 [9] 51565684 51504031 Smallest eigenvalues: [1] 0.498621018 0.482464932 0.464719120 0.367635146 0.357574127 [6] 0.281352521 0.156715382 0.137070219 -0.002578572 -0.026560631 Largest eigenvalues: [1] 63739908 60064686 56938842 55368735 55233402 53695629 52270016 52120536 [9] 51489855 51181683 Smallest eigenvalues: [1] 0.4550115 0.4339077 0.4096776 0.4083677 0.2809894 0.2704890 [7] 0.2332062 0.1926729 0.1642633 -0.3350256 Largest eigenvalues: [1] 65597075 60361315 57620003 56372938 54974286 53558960 52533581 51877096 [9] 51684126 51062125 Smallest eigenvalues: [1] 0.59293228 0.58439590 0.46079415 0.45680111 0.32576455 0.30668977 [7] 0.26509910 0.22948079 0.08844987 -0.19775837 Largest eigenvalues: [1] 66080229 60433448 57848196 56491531 55229555 53883980 52610828 52405954 [9] 51883012 51441355 Smallest eigenvalues: [1] 0.37981832 0.36038541 0.35522910 0.32377308 0.27366214 0.22163999 [7] 0.17251062 0.13792477 -0.08273076 -0.55500850 Largest eigenvalues: [1] 65121254 60782164 58069287 56509829 55274120 53986842 52427337 52286661 [9] 52056309 51143008 Smallest eigenvalues: [1] 0.4922655 0.4512300 0.4361336 0.3612484 0.3577866 0.3213488 [7] 0.3003183 0.2121997 0.1652579 -0.2157578 Largest eigenvalues: [1] 64907340 59573935 56568121 56394720 54398209 52937925 52218787 51739831 [9] 51448563 50468316 Smallest eigenvalues: [1] 0.5408972 0.5211180 0.5062630 0.4059827 0.3587215 0.3547026 [7] 0.1936218 0.1909158 0.1808374 -0.1337813 Largest eigenvalues: [1] 63808887 60205071 56991351 55354761 55284676 53747266 52290576 52010319 [9] 51451656 51267976 Smallest eigenvalues: [1] 0.3447919987 0.3307802435 0.2989218221 0.2922549215 0.2223076358 [6] 0.1546549790 0.1139861743 0.0701401505 0.0005542438 -0.0658164069 Largest eigenvalues: [1] 62031393 60336994 57417077 55937013 55018472 54168102 52646816 52352086 [9] 51505789 51012184 Smallest eigenvalues: [1] 0.6018108 0.5702971 0.5446860 0.4811291 0.4214358 0.4008453 [7] 0.3032235 0.2026565 0.1251318 -0.6339919 Largest eigenvalues: [1] 64140185 60661946 57032731 55678399 55601213 53980704 52335225 52178298 [9] 51534697 51069349 Smallest eigenvalues: [1] 0.4444439 0.4202566 0.3568545 0.3111323 0.2645969 0.2453223 [7] 0.1863267 0.1122573 0.1027479 -0.2382730 Largest eigenvalues: [1] 65917226 60080011 57518928 57227433 54856524 53449453 53203666 52068827 [9] 52001653 51138955 Smallest eigenvalues: [1] 0.36775398 0.36635231 0.28628080 0.22434271 0.14659257 0.10947501 [7] 0.07425764 -0.13103102 -0.46137337 -8.81269989 Largest eigenvalues: [1] 65632878 60315777 57704361 56882175 55055499 53485093 52860971 52488291 [9] 52332170 51832382 Smallest eigenvalues: [1] 0.41436564 0.38280502 0.36637619 0.29972288 0.21380625 0.19608325 [7] 0.13019916 0.02778648 -0.26604737 -0.36041729 Largest eigenvalues: [1] 63463811 60308786 56959079 55314477 54933507 53235613 52011915 51545353 [9] 51359442 51117125 Smallest eigenvalues: [1] 0.42499966 0.40481843 0.37754132 0.33857223 0.19431705 0.18293681 [7] -0.08745294 -0.22701228 -0.22901659 -1.85418629 Largest eigenvalues: [1] 64778842 59975199 57334997 56085416 54691803 53210121 52154412 52089627 [9] 51865965 51359928 Smallest eigenvalues: [1] 0.43607020 0.38846239 0.37169210 0.32916283 0.26544295 0.25766863 [7] 0.23214259 0.19554605 -0.01945274 -0.23953616 Largest eigenvalues: [1] 63577978 59508908 57116957 55813181 54230290 52799328 51803495 51498936 [9] 51095340 50431225 Smallest eigenvalues: [1] 0.382521787 0.303025366 0.233012294 0.222400318 0.217929149 [6] 0.146430846 0.003283711 -0.071249471 -0.364714792 -2.076921842 Largest eigenvalues: [1] 63389438 60524476 57270817 55576869 54974677 53437762 52024739 51993810 [9] 51715772 51310069 Smallest eigenvalues: [1] 0.35367247 0.34057294 0.30666115 0.23073180 0.22192793 0.18926718 [7] 0.18611158 0.05033477 -0.67011418 -1.04611634 Largest eigenvalues: [1] 64474348 59593010 57349514 56989253 54446650 52950565 52602283 52560805 [9] 51821221 51089856 Smallest eigenvalues: [1] 0.18523578 0.16596405 0.09903060 0.07801804 0.07507484 0.04546843 [7] 0.01899126 -0.02363648 -0.57226297 -1.83073925 Largest eigenvalues: [1] 66504444 61601941 58788573 57689326 55697108 54093670 53626734 52955438 [9] 52543049 52223916 Smallest eigenvalues: [1] 0.4544503 0.4184977 0.4027554 0.3353646 0.3245670 0.2896932 [7] 0.2108479 0.1587453 0.1257685 -0.1317678 Largest eigenvalues: [1] 65259073 60189300 57816812 56136084 54910889 53332152 52055641 52008840 [9] 51532561 51196078 Smallest eigenvalues: [1] 0.45254930 0.44487126 0.39384401 0.38563752 0.34448654 0.29665333 [7] 0.19905804 0.15241638 0.00551193 -0.03876237 Largest eigenvalues: [1] 65927861 60712931 57938491 56459590 55520595 53970151 52773381 52682583 [9] 52463471 51814417 Smallest eigenvalues: [1] 0.410698714 0.408099959 0.243021489 0.232795109 0.127629407 [6] 0.083217061 0.003270844 -0.155305548 -0.395444815 -2.934279357 Largest eigenvalues: [1] 65876519 60353230 57619607 56827282 55201571 53869789 52895199 52133512 [9] 52105097 51236102 Smallest eigenvalues: [1] 0.181022704 0.174913007 0.150845916 0.042466630 -0.009345051 [6] -0.096044263 -0.183298468 -0.187795549 -0.836485269 -3.559519544 Largest eigenvalues: [1] 62707691 59235668 56963571 54769921 54040168 53213604 51564434 51096805 [9] 50516481 50315509 Smallest eigenvalues: [1] 0.165680136 0.146564132 0.112689155 0.046108623 -0.002610232 [6] -0.023676892 -0.124903852 -0.136475594 -0.232947222 -0.383598663 Largest eigenvalues: [1] 64922418 60290803 57654552 55311559 54784116 53417417 52095025 51496364 [9] 51305503 51217163 Smallest eigenvalues: [1] 0.44105618 0.39454040 0.32722464 0.30564660 0.28974343 0.21912103 [7] 0.12869477 0.02467714 -0.10971108 -2.06292443 Largest eigenvalues: [1] 65484262 59849210 57211460 56312252 54694300 53293779 52426081 51836154 [9] 51818290 51009001 Smallest eigenvalues: [1] 0.32180552 0.18214718 0.13225753 0.10831086 0.03874408 -0.04069816 [7] -0.15856280 -0.24018360 -0.87680988 -1.68601624 Largest eigenvalues: [1] 64515020 59466898 56478765 55719171 54747729 52889345 51884086 51712812 [9] 51281814 50690846 Smallest eigenvalues: [1] 0.47174664 0.47005563 0.34241999 0.33970331 0.28957042 0.19171958 [7] 0.04497320 0.04476324 -0.04559572 -0.31645563 Largest eigenvalues: [1] 64531091 60184811 57181651 56350083 54713090 53098936 52418216 52223430 [9] 51552641 51090515 Smallest eigenvalues: [1] 0.41526513 0.39880820 0.34388130 0.27121541 0.24190545 0.18419011 [7] 0.07437829 -0.16510526 -0.21212665 -4.52041256 Largest eigenvalues: [1] 62207773 59355186 55921699 54675618 54162259 52702627 51450199 50723030 [9] 50231418 49925273 Smallest eigenvalues: [1] 0.37074429 0.34164873 0.30671791 0.27714647 0.22234495 0.19320356 [7] 0.16831436 0.07345757 0.04423442 -1.44009343 Largest eigenvalues: [1] 63990438 59830093 57168527 55672086 55412440 53844115 52520037 51969896 [9] 51625410 51474002 Smallest eigenvalues: [1] 0.30022882 0.27236204 0.22714886 0.19124063 0.11819728 0.07276478 [7] -0.07348596 -0.20636960 -0.21830364 -1.29573249 Largest eigenvalues: [1] 64236562 59801849 56369385 55094268 54736682 52852062 51490881 51162714 [9] 51105142 50595417 Smallest eigenvalues: [1] 0.09820088 0.01650463 -0.07651741 -0.13403839 -0.15289827 -0.22207786 [7] -0.39813064 -0.48560551 -0.91696221 -3.76682158 Largest eigenvalues: [1] 62954386 59115222 56085525 54841022 54356505 52832332 51992030 51445482 [9] 50825124 50507288 Smallest eigenvalues: [1] 0.420085508 0.393832512 0.376946216 0.357338459 0.277455977 [6] 0.207533793 0.080876851 0.008207197 -0.168546993 -0.398576622 Largest eigenvalues: [1] 64370745 60413383 57136266 56321755 55023929 53177864 52610524 52328249 [9] 51732811 51464329 Smallest eigenvalues: [1] 0.4724632 0.4370566 0.4265297 0.4231744 0.3627276 0.3252239 [7] 0.1988408 0.1272765 -0.3075132 -0.9177189 Largest eigenvalues: [1] 63308648 60185682 57366272 55834980 54989849 53201688 51978565 51913818 [9] 51804414 50900120 Smallest eigenvalues: [1] 0.34648664 0.33279024 0.30633631 0.29363954 0.12753658 0.11236166 [7] -0.01674858 -0.06218904 -0.20278956 -1.65584630 Largest eigenvalues: [1] 62864323 60792602 57091288 55771527 55201640 53898426 52213670 51827805 [9] 51245487 50946048 Smallest eigenvalues: [1] 0.35996701 0.34816292 0.30543824 0.28775183 0.24654443 0.22504584 [7] -0.07327008 -0.08201719 -0.92335522 -1.33899399 Largest eigenvalues: [1] 63152375 59536511 56998389 55489336 54728026 53018664 51765333 51693990 [9] 51507978 50776270 Smallest eigenvalues: [1] 0.34145843 0.30525460 0.24207377 0.19609694 0.18092572 0.07296567 [7] 0.04392425 -0.07557654 -0.20843504 -1.00644044 Largest eigenvalues: [1] 64191288 60468457 57349626 55987471 55267367 53752561 52402743 52337988 [9] 51930716 51342907 Smallest eigenvalues: [1] 0.16480505 0.10501115 0.09733584 -0.05264161 -0.11341967 -0.54094444 [7] -0.62447927 -1.04296375 -1.10775942 -1.28413435 Largest eigenvalues: [1] 65721208 59250519 56443440 55962739 54075474 52612083 52042557 51583471 [9] 51297542 50731930 Smallest eigenvalues: [1] 0.4553532 0.4397757 0.4357501 0.2878770 0.2780496 0.2022769 [7] 0.1498324 0.1361284 0.1015900 -0.9212881 Largest eigenvalues: [1] 64679249 60718639 57771459 55864558 55720175 54153124 53002686 52082547 [9] 51922089 51684424
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 3.273444 | 0.7430787 | 16.39471 | 0.035 | 2.593625 | 2.965928 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + speed + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
speed = speed_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_speed_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
speed = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 19. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 496 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.4111067859 0.4060596198 0.3915250907 0.3667542688 0.2747280854 [6] 0.1836739357 0.0994980542 0.0730505790 -0.0004004443 -0.0564971211 Largest eigenvalues: [1] 64776286 59806579 56995660 56046498 54865431 53214158 52133738 51963655 [9] 51377558 50380134 Smallest eigenvalues: [1] 0.41932427 0.35981599 0.35825030 0.32100910 0.31044862 0.31040949 [7] 0.21655105 0.11850137 0.09216851 -1.42811397 Largest eigenvalues: [1] 64114397 60417755 57701449 56477539 54715351 53279357 52419901 51941557 [9] 51841653 50940665 Smallest eigenvalues: [1] 0.34746559 0.30655599 0.26388856 0.19530274 0.17362013 0.05345603 [7] -0.03063299 -0.14074432 -0.86686973 -2.82532815 Largest eigenvalues: [1] 62446331 60010974 57464031 55380578 54991825 53699220 51963773 51925015 [9] 51193654 50702954 Smallest eigenvalues: [1] 0.456027527 0.439197069 0.414925503 0.401800672 0.318674363 [6] 0.263457887 0.199399706 0.107372129 0.002413811 -0.009647748 Largest eigenvalues: [1] 63269966 59621072 56521866 55407703 54652412 52835529 51487587 51384960 [9] 51348493 50284578 Smallest eigenvalues: [1] 0.34795582 0.30190306 0.29234353 0.27092669 0.23874343 0.20285868 [7] 0.13030180 -0.05677447 -0.13152799 -0.16863223 Largest eigenvalues: [1] 65182869 59492190 57147297 56272884 54754012 53274887 52349292 51851275 [9] 51358340 50870318 Smallest eigenvalues: [1] 0.42666426 0.39250159 0.34191829 0.34048308 0.27595871 0.25541766 [7] 0.24606421 0.18622557 0.09519852 -0.25319954 Largest eigenvalues: [1] 64686203 60943774 57505812 56899873 55617922 54073533 52933142 52670288 [9] 52074406 51595708 Smallest eigenvalues: [1] 0.38288370 0.36655658 0.32959381 0.26726602 0.26357324 0.24175543 [7] 0.05750062 0.04134855 -0.10808766 -0.55646867 Largest eigenvalues: [1] 65106461 60216870 57807132 57067224 54611099 53370733 52891045 52109430 [9] 52026742 51326348 Smallest eigenvalues: [1] 0.4100950 0.3926993 0.3489299 0.2395718 0.2204637 0.1803786 [7] 0.1548194 0.1356109 0.0586312 -0.8274448 Largest eigenvalues: [1] 65384400 60187214 57143720 56593391 54453800 52841008 52609853 52166583 [9] 51355190 51335870 Smallest eigenvalues: [1] 0.40967101 0.39961533 0.37790619 0.34270204 0.34030965 0.32247737 [7] 0.26907640 0.02517217 -0.01636911 -0.06923915 Largest eigenvalues: [1] 65261007 59384721 56838961 56379126 54043196 52775407 52173240 51685327 [9] 51038976 50707233 Smallest eigenvalues: [1] 0.5022787 0.4059451 0.3628788 0.3289123 0.2555456 0.2243377 [7] 0.1938979 0.1416800 0.1286817 -2.1010851 Largest eigenvalues: [1] 64431141 59590009 57218222 56191284 54200245 52453528 52103090 51546390 [9] 51365994 50771667 Smallest eigenvalues: [1] 0.32753087 0.28660565 0.23819976 0.21831565 0.13671448 0.11018802 [7] 0.09660409 0.09518589 0.06379272 -0.39374274 Largest eigenvalues: [1] 64253153 59994854 57599777 55658141 54809574 53616891 52437973 51884816 [9] 51823181 51580091 Smallest eigenvalues: [1] 0.40346117 0.39854181 0.38753630 0.25290181 0.20491381 0.18177633 [7] 0.04344643 0.01677451 -0.03913939 -0.17609229 Largest eigenvalues: [1] 64775179 60637979 57621838 56565725 54976012 53429516 52599335 51968080 [9] 51857839 50621840 Smallest eigenvalues: [1] 0.48112129 0.46662833 0.43584216 0.42275464 0.33599547 0.30974390 [7] 0.05678591 0.03898816 -0.13860770 -2.91531114 Largest eigenvalues: [1] 64691794 60828389 57245667 56589811 55441208 53693200 53431834 52586481 [9] 51670160 51471212 Smallest eigenvalues: [1] 0.36614103 0.34388287 0.26465753 0.25689074 0.25089086 0.14117391 [7] 0.09406132 0.03769098 -0.23609521 -3.54391180 Largest eigenvalues: [1] 63025192 60080884 57177815 55389350 55252021 53771531 52270610 52225026 [9] 51341969 51107016 Smallest eigenvalues: [1] 0.44061106 0.38370316 0.32256110 0.29240347 0.25207303 0.23990358 [7] 0.22538252 0.20540340 -0.02396898 -0.05299193 Largest eigenvalues: [1] 65092697 59752620 57118382 56652411 54489553 52929063 52645662 51693008 [9] 51683653 50864064 Smallest eigenvalues: [1] 0.46684848 0.46455623 0.44385813 0.38111165 0.33488923 0.24463498 [7] 0.06157924 0.04126850 -0.12465960 -0.15389065 Largest eigenvalues: [1] 64854299 59600960 56703000 56264249 54459487 52700279 52238290 52182457 [9] 51559931 51218870 Smallest eigenvalues: [1] 0.25669589 0.22820437 0.21415073 0.09354814 -0.03540017 -0.06424339 [7] -0.14584829 -0.33104255 -0.42264955 -2.73951310 Largest eigenvalues: [1] 65918448 59534026 56704235 56469173 54446355 52829444 52786999 51674873 [9] 51206189 50452932 Smallest eigenvalues: [1] 0.48311108 0.46754444 0.42026058 0.39779941 0.35393456 0.34280085 [7] 0.21703309 0.09933597 -0.03776027 -0.85445499 Largest eigenvalues: [1] 62832385 59970809 56542783 55234557 54897699 53438640 52265579 51362351 [9] 50940999 50442493 Smallest eigenvalues: [1] 0.37036520 0.35845806 0.21320802 0.20693907 0.12495424 0.03973884 [7] -0.04189556 -0.13963061 -0.30328702 -0.53304849 Largest eigenvalues: [1] 65649012 60560699 57382592 56559344 55807553 53892536 52678825 52549933 [9] 52407890 51384984 Smallest eigenvalues: [1] 0.40798411 0.39577985 0.27992797 0.27524419 0.26917476 0.22259952 [7] 0.21085507 0.01762706 -0.19089999 -0.64791046 Largest eigenvalues: [1] 66148246 59936532 56938692 56737207 54361291 53024794 52703894 52052551 [9] 51180755 51025623 Smallest eigenvalues: [1] 0.41859956 0.38661586 0.38539630 0.31270567 0.28355908 0.18329513 [7] 0.13084286 -0.07979516 -0.30269587 -1.75181268 Largest eigenvalues: [1] 63312075 59819165 56820222 54857803 54792932 53382808 52040556 51966322 [9] 51026025 50824184 Smallest eigenvalues: [1] 0.45065580 0.44408923 0.39251473 0.28796502 0.24931205 0.21483115 [7] 0.18864842 0.11894359 -0.06480995 -2.45543060 Largest eigenvalues: [1] 65316430 60383288 57671272 56991201 54726515 53389863 52828170 52095731 [9] 51723794 51125035 Smallest eigenvalues: [1] 0.4683560 0.3985859 0.3958591 0.3198591 0.3148761 0.2789644 [7] 0.2765103 0.1530935 -0.6180494 -1.1234251 Largest eigenvalues: [1] 64901428 59732531 56683090 56446438 54166473 52547745 52419617 51279064 [9] 51116933 50252196 Smallest eigenvalues: [1] 0.40889761 0.40548754 0.38093545 0.32265653 0.31419768 0.29392001 [7] 0.28559350 0.22841887 0.04085756 -0.03215193 Largest eigenvalues: [1] 63714213 59722760 56863218 55605542 54407699 52706481 51678167 51332580 [9] 51269465 50370549 Smallest eigenvalues: [1] 0.430266651 0.407953318 0.407932440 0.365711687 0.361813138 [6] 0.312648265 0.265442346 0.218579524 -0.006299881 -0.159976375 Largest eigenvalues: [1] 63342268 59943320 57077323 55388994 54915008 53239025 51780660 51701445 [9] 51469768 50864582 Smallest eigenvalues: [1] 0.5087335 0.4917932 0.4690036 0.4529612 0.4189303 0.3891217 [7] 0.3818905 0.1945198 0.1553195 -0.2295465 Largest eigenvalues: [1] 64786430 60109120 56822273 56003811 54638389 52698395 52101328 51775439 [9] 51393498 50974535 Smallest eigenvalues: [1] 0.28533345 0.23417890 0.22138217 0.20451751 0.14382624 0.10672599 [7] -0.03808189 -0.54828249 -0.72582920 -1.46781903 Largest eigenvalues: [1] 65740527 60518065 57842226 56957398 55095913 53048971 53043423 52949699 [9] 51849419 51749296 Smallest eigenvalues: [1] 0.3645848496 0.3614161559 0.3261276958 0.2835010152 0.2314311827 [6] 0.2242678111 0.1778167700 0.0959320039 0.0008347958 -0.1527933507 Largest eigenvalues: [1] 63239619 60502852 57679271 55495275 55389795 54022119 52579505 52134410 [9] 51511486 51035661 Smallest eigenvalues: [1] 0.337408164 0.330771843 0.244612008 0.238668427 0.219901188 [6] 0.182588058 0.180819122 0.068154489 0.029216102 -0.001743209 Largest eigenvalues: [1] 64893718 59187935 56707445 56138859 54313201 52755766 52136583 51761702 [9] 51019511 50706542 Smallest eigenvalues: [1] 0.417875053 0.386816177 0.330835252 0.307963965 0.200738602 [6] 0.151420132 0.116478234 0.109863568 0.005544936 -0.020929634 Largest eigenvalues: [1] 63371402 59345571 56994568 55449610 54622016 52943287 51638224 51549504 [9] 51474957 50632506 Smallest eigenvalues: [1] 0.33566072 0.27121461 0.24859670 0.22550764 0.18029414 0.11280523 [7] 0.10655890 0.06922503 0.04628951 -0.37365294 Largest eigenvalues: [1] 61588691 59009095 56166019 54601949 54102143 52230984 50956356 50813038 [9] 50559184 49634210 Smallest eigenvalues: [1] 0.2935846 0.2455671 0.2241380 0.1885087 0.1504163 0.1423864 [7] 0.1340019 -0.4380236 -0.4785979 -5.0220223 Largest eigenvalues: [1] 63855459 60582627 57544086 56534516 55535467 54802364 52893934 51948811 [9] 51657106 51170757 Smallest eigenvalues: [1] 0.37900212 0.34292936 0.25403431 0.23092215 0.21864850 0.20914778 [7] 0.15253268 0.07504411 0.04965593 -0.01201788 Largest eigenvalues: [1] 63424796 60683036 57534926 55960092 54988766 53556368 51983129 51920619 [9] 51903241 50633303 Smallest eigenvalues: [1] 0.36845861 0.36218236 0.34715168 0.29601468 0.27956358 0.25117287 [7] 0.22010688 0.21475405 -0.02979225 -0.51878155 Largest eigenvalues: [1] 63720488 60094697 57397907 56148258 54997583 53337317 52563635 52172712 [9] 51524321 51026322 Smallest eigenvalues: [1] 0.40641253 0.37725052 0.36152601 0.34473107 0.31464252 0.29481929 [7] 0.14523208 0.07203331 0.02375869 -0.38660684 Largest eigenvalues: [1] 62686817 59129639 56076682 55559913 54234740 52377899 51453696 51177205 [9] 51036717 49891869 Smallest eigenvalues: [1] 0.47386376 0.44647779 0.41744761 0.30609730 0.25286853 0.22763894 [7] 0.10418029 0.05621746 -0.05317571 -0.17907467 Largest eigenvalues: [1] 64617178 60278766 57683557 56755755 54833653 53126542 52650332 52110486 [9] 51791825 50977613 Smallest eigenvalues: [1] 0.38697427 0.37851103 0.34798907 0.29813017 0.24645090 0.20580741 [7] -0.09538171 -0.34392516 -0.35418749 -2.51850878 Largest eigenvalues: [1] 65195565 59431694 56620593 56394111 54210596 52517191 52259828 51903675 [9] 51134386 50770169 Smallest eigenvalues: [1] 0.30460289 0.24902795 0.24378799 0.24056480 0.21196222 0.08181235 [7] 0.06595614 0.01182288 -0.10864379 -0.50939880 Largest eigenvalues: [1] 63897877 58969414 56345817 55609982 54132315 52283775 51549099 51408710 [9] 51056792 50116509 Smallest eigenvalues: [1] 0.46472842 0.39754446 0.38327359 0.33155064 0.30238399 0.20216482 [7] 0.14200928 0.04891835 -0.07681344 -0.21892836 Largest eigenvalues: [1] 65738328 61193814 57482269 56913549 55845190 54089362 53009626 52892388 [9] 52171353 51921838 Smallest eigenvalues: [1] 0.47253552 0.42018637 0.39705278 0.33586691 0.31965066 0.25882492 [7] 0.19703330 0.15759150 0.04297667 -3.93959590 Largest eigenvalues: [1] 64697851 61135291 57808662 56035212 56010846 54151177 52771924 52316137 [9] 52235069 51660277 Smallest eigenvalues: [1] 0.47403206 0.46325011 0.39645051 0.35196463 0.34587219 0.26327375 [7] 0.22499491 0.19503739 0.09328555 -0.07000572 Largest eigenvalues: [1] 63590085 59935078 56910186 55355015 55053166 53296053 52119637 51472066 [9] 51453457 50936874 Smallest eigenvalues: [1] 0.5042682 0.4957445 0.4711529 0.4002012 0.3733133 0.2939521 [7] 0.2819625 0.2229576 0.1654210 -0.1289347 Largest eigenvalues: [1] 65137782 59851491 56995899 55903658 55038764 53257397 52140155 51609227 [9] 51549448 50369119 Smallest eigenvalues: [1] 0.38142517 0.37274411 0.35776423 0.17734417 0.17006631 0.10158363 [7] -0.01243380 -0.06234247 -0.24472521 -0.54180621 Largest eigenvalues: [1] 65193181 59765852 56988311 56971148 54439948 52988641 52843269 51891463 [9] 51769392 50924555 Smallest eigenvalues: [1] 0.52890241 0.50520436 0.43107167 0.36139184 0.35691020 0.34803100 [7] 0.30239200 0.22797505 0.01712836 -1.72110422 Largest eigenvalues: [1] 63312265 60028109 56795456 55474236 55066779 53629254 52138711 51475981 [9] 51198505 50604615 Smallest eigenvalues: [1] 0.57259226 0.52724697 0.41433012 0.38918462 0.34405067 0.29060570 [7] 0.25968765 0.21073526 0.16407224 -0.06270084 Largest eigenvalues: [1] 63061481 60093141 56929986 55620924 54844072 53210847 51798200 51659437 [9] 51561301 50744667 Smallest eigenvalues: [1] 0.4629470 0.3735626 0.3428416 0.3177159 0.3076850 0.2051303 [7] 0.1756806 0.1749230 0.1584508 -0.6929274 Largest eigenvalues: [1] 63622784 59299134 56581855 55124306 54872565 53218955 51656725 51211841 [9] 50892179 50080756 Smallest eigenvalues: [1] 0.43787493 0.42586114 0.34936057 0.30228151 0.26226710 0.25898663 [7] 0.24720131 0.12523122 0.06132591 -0.03893736 Largest eigenvalues: [1] 63210731 58994405 56485940 55125110 54112918 52606117 51397917 51161450 [9] 51120059 50186689 Smallest eigenvalues: [1] 0.423535025 0.399340685 0.350846534 0.348249226 0.279995345 [6] 0.144745777 0.136606622 0.007269806 -0.003594220 -0.140345556 Largest eigenvalues: [1] 61914811 59257636 56322632 55120593 53973184 53275122 51750323 51367791 [9] 50324151 50084642 Smallest eigenvalues: [1] 4.163020e-01 3.837330e-01 3.542165e-01 2.693236e-01 2.347104e-01 [6] 2.012945e-01 1.823881e-01 1.405314e-01 8.516289e-02 -2.344407e-05 Largest eigenvalues: [1] 63208380 60061732 56880170 55607659 54978209 53328298 52656110 52041426 [9] 51680873 51482270 Smallest eigenvalues: [1] 0.33215143 0.27876901 0.27561970 0.25239191 0.24495329 0.23861548 [7] 0.19227594 0.16427481 -0.09162574 -0.09464162 Largest eigenvalues: [1] 63229112 58816289 56374734 54726694 54676849 52898033 51416744 50916668 [9] 50855595 50133268 Smallest eigenvalues: [1] 0.4147003164 0.4039546899 0.3911389589 0.3379692885 0.2910189415 [6] 0.2685145538 0.1562274291 0.1184301786 -0.0001589854 -0.6446075474 Largest eigenvalues: [1] 65578304 60348906 57553373 56778727 54783787 53229979 52896141 51937282 [9] 51467342 50908595 Smallest eigenvalues: [1] 0.4157501 0.4153980 0.4004454 0.3988825 0.3227513 0.2862461 [7] 0.2703148 0.2072963 -0.1682199 -0.7203737 Largest eigenvalues: [1] 64269381 60742275 57354458 56683065 55191957 53510756 52607619 52499626 [9] 52049502 51364003 Smallest eigenvalues: [1] 0.513935574 0.449616132 0.414397072 0.412105909 0.397535673 [6] 0.348660922 0.234639311 0.200582564 0.006845092 -0.184814437 Largest eigenvalues: [1] 64396621 59730961 57313462 55661346 54707706 53632760 52029463 51760870 [9] 51477575 50856704 Smallest eigenvalues: [1] 0.42395456 0.35746282 0.34650781 0.25418387 0.16691537 0.13977310 [7] 0.10221085 -0.03885257 -0.05896622 -0.07901664 Largest eigenvalues: [1] 62299054 60506216 57084514 55562827 55136925 53786765 52523373 52490245 [9] 51307302 51129061 Smallest eigenvalues: [1] 0.42714140 0.40437521 0.35513403 0.32138062 0.30815829 0.29377149 [7] 0.21810485 0.14733562 0.06677596 -1.57385290 Largest eigenvalues: [1] 64915524 60290007 57258047 56045798 55454941 53903655 52230443 52059623 [9] 52011283 51308714 Smallest eigenvalues: [1] 0.4375071 0.4163303 0.3892812 0.3629351 0.3431135 0.2732576 [7] 0.2542686 0.2375373 0.1760501 -0.3738515 Largest eigenvalues: [1] 65797041 60336589 57253003 57110398 54300392 53106568 52568494 51855116 [9] 51331634 51059262 Smallest eigenvalues: [1] 0.309308394 0.280202595 0.224181619 0.153702976 0.104855876 [6] 0.094462373 0.048514453 0.001636483 -0.146414654 -0.308949610 Largest eigenvalues: [1] 63937953 60589349 57127462 56005491 55178997 53542959 53027880 52091574 [9] 51795621 51716421 Smallest eigenvalues: [1] 0.47821198 0.44648237 0.43950381 0.42388484 0.41408850 0.37335460 [7] 0.21289649 0.03040335 -0.02260064 -0.14560059 Largest eigenvalues: [1] 64905274 59984785 57022605 56299374 54535734 52642684 52442960 51463678 [9] 51007285 50250031 Smallest eigenvalues: [1] 0.4770757 0.4389563 0.3958883 0.2874747 0.2529428 0.2488271 [7] 0.1948643 0.1788865 0.1313565 -0.1380460 Largest eigenvalues: [1] 64666835 60249432 57849938 56393640 54840400 53482917 52588832 52420611 [9] 51935029 51683320 Smallest eigenvalues: [1] 0.4559853 0.4135622 0.3302414 0.3089361 0.2851032 0.2386932 [7] 0.2236101 0.1522095 -0.8410498 -5.4109808 Largest eigenvalues: [1] 66596712 59870452 57315632 56722126 54228914 53291565 52493670 51731060 [9] 51214712 50689076 Smallest eigenvalues: [1] 0.37463844 0.35407140 0.33249877 0.29121754 0.28514685 0.26966769 [7] 0.20700293 0.13063432 0.06274704 -0.59291370 Largest eigenvalues: [1] 64028069 59466943 56448107 56276999 54472723 52736518 52062873 51776550 [9] 51710027 50841575 Smallest eigenvalues: [1] 0.45370720 0.41746077 0.38474299 0.30601530 0.30575321 0.24755227 [7] 0.23548911 0.12005640 -0.07512968 -1.33675093 Largest eigenvalues: [1] 65626744 60850485 57794433 56981762 55660667 53989801 53198138 53055165 [9] 52150807 51730168 Smallest eigenvalues: [1] 0.38659604 0.34104758 0.33047231 0.29781052 0.21338135 0.18997626 [7] 0.05679216 -0.11263587 -1.10506400 -1.52074106 Largest eigenvalues: [1] 63054991 60153707 56968472 55855674 55266404 53533718 52268163 52001163 [9] 51600067 50997361 Smallest eigenvalues: [1] 0.50060689 0.45660494 0.41715382 0.41137887 0.38002651 0.34964750 [7] 0.20837024 0.18424049 0.02820403 -1.85161083 Largest eigenvalues: [1] 63295154 59861234 56645150 54947579 54661893 52952763 51513694 51107188 [9] 51038847 50332309 Smallest eigenvalues: [1] 0.4770865 0.4483542 0.4173920 0.3905126 0.3798266 0.3792588 [7] 0.2378632 0.1712681 -0.4537652 -1.0035315 Largest eigenvalues: [1] 65079455 59802719 57286363 56359055 54542118 52903017 52319485 51994926 [9] 51904962 51150141 Smallest eigenvalues: [1] 0.4749295 0.4102342 0.3931711 0.3399493 0.3040926 0.2530724 [7] 0.1707636 0.1688260 -0.0674789 -5.3894161 Largest eigenvalues: [1] 65686553 60376660 57941207 57060740 55241484 53788840 52990489 52644283 [9] 52373160 51623773 Smallest eigenvalues: [1] 0.05784091 0.02952196 0.01261396 -0.03971815 -0.10855747 -0.21352522 [7] -0.30843741 -0.62711038 -0.77494692 -1.95812448 Largest eigenvalues: [1] 66206502 59817238 57267568 57081256 54279468 53056365 53024913 51934690 [9] 51886921 51183354 Smallest eigenvalues: [1] 0.4387407 0.4062699 0.3853362 0.3184361 0.2886097 0.2858855 [7] 0.2385515 0.2375246 0.1293310 -4.7552705 Largest eigenvalues: [1] 65948819 59714655 57183056 57030250 54700796 53084953 52969253 52158724 [9] 51814698 51246049 Smallest eigenvalues: [1] 0.45539080 0.34197461 0.33845521 0.31480683 0.27999123 0.20581157 [7] 0.18201863 0.16258885 0.02738596 -0.01186590 Largest eigenvalues: [1] 63342308 60708724 57505649 55570253 55506964 53929813 52263287 51794836 [9] 51606952 51014797 Smallest eigenvalues: [1] 0.394497530 0.381129220 0.266990056 0.233745799 0.206133045 [6] 0.155111969 0.084627541 0.023333878 -0.007756513 -0.032460323 Largest eigenvalues: [1] 64623753 60925903 57964271 56969706 54617420 53308408 52809280 51893762 [9] 51655611 50917559 Smallest eigenvalues: [1] 0.42118161 0.34597774 0.32546703 0.20560167 0.20216586 0.19148582 [7] 0.17773152 0.08563578 -0.46133472 -0.51239087 Largest eigenvalues: [1] 63795689 59739643 56690781 55656712 54932216 53460686 52452321 51937507 [9] 51631518 51349230 Smallest eigenvalues: [1] 0.40511651 0.40389447 0.37068046 0.34024774 0.32062752 0.21066618 [7] 0.15957844 0.05668655 -0.01959660 -0.06373214 Largest eigenvalues: [1] 62521052 59354904 56748330 55179535 54739505 52799342 51675347 51599739 [9] 51125288 50577512 Smallest eigenvalues: [1] 0.54264528 0.50092400 0.47570980 0.43237444 0.39971448 0.34315201 [7] 0.32916607 0.23155452 0.18255630 -0.08849715 Largest eigenvalues: [1] 62958704 60642463 57290614 55439755 55368675 53617192 52378322 52098263 [9] 51465661 50922475 Smallest eigenvalues: [1] 0.48493551 0.47455061 0.40050141 0.29050258 0.25940824 0.23842616 [7] 0.23531196 0.22731032 -0.04005743 -0.18128685 Largest eigenvalues: [1] 65224287 60974191 58090111 57048375 55320195 53780563 53064111 52663689 [9] 52273230 51491540 Smallest eigenvalues: [1] 0.55489215 0.53206278 0.52033071 0.47228161 0.42434380 0.39763010 [7] 0.37059699 0.31041877 0.15222602 -0.04864723 Largest eigenvalues: [1] 65768202 60154193 57263187 56555667 54450551 52723593 52646440 52110896 [9] 51202982 51129351 Smallest eigenvalues: [1] 0.3300423 0.3296091 0.3001157 0.2585520 0.2250404 0.2173399 [7] 0.1344559 -0.1556361 -0.2503543 -3.9281720 Largest eigenvalues: [1] 62939742 59527136 56926141 55654634 55192152 53445833 51889388 51685488 [9] 51556724 50513184 Smallest eigenvalues: [1] 0.30033249 0.25172429 0.19605676 0.17847207 0.09115679 0.05481704 [7] 0.04101656 0.01562529 -0.82241850 -4.47677978 Largest eigenvalues: [1] 64874073 59461977 56574650 56187258 54608269 52978057 52163514 51352543 [9] 51282230 50458182 Smallest eigenvalues: [1] 0.38865787 0.34726590 0.30768725 0.28431863 0.26403695 0.23211328 [7] 0.18397852 0.16484702 0.04968852 -0.26449748 Largest eigenvalues: [1] 61386416 59578826 56754557 55184652 54145391 53244921 51886943 51061337 [9] 50320485 50262684 Smallest eigenvalues: [1] 0.34104983 0.32610285 0.29095574 0.27022214 0.26569540 0.20892956 [7] 0.19145478 0.07754775 0.06867515 -1.20845806 Largest eigenvalues: [1] 64413442 59454864 56957389 55325678 55201264 53412482 51741070 51627566 [9] 50790370 50258723 Smallest eigenvalues: [1] 0.46315197 0.40150090 0.39414803 0.35436059 0.34697991 0.23998470 [7] 0.21091155 0.19262153 0.09640275 -0.01958691 Largest eigenvalues: [1] 63024552 59431094 56797882 54923387 54688887 53168965 51653565 51591610 [9] 51034663 50757027 Smallest eigenvalues: [1] 0.3881591 0.3840806 0.3614975 0.3052538 0.2894149 0.1820190 [7] 0.1152468 -0.1138531 -0.1644902 -0.1752864 Largest eigenvalues: [1] 64990633 60785142 58388146 55848438 55316000 53721633 52547209 52414458 [9] 52057515 51834471 Smallest eigenvalues: [1] 0.36033977 0.33333958 0.30786123 0.22595951 0.20053913 0.03342066 [7] 0.01975513 -0.25250002 -0.25489441 -0.80448272 Largest eigenvalues: [1] 63687493 59376285 57282945 56063134 54275990 52727241 52018724 51564004 [9] 51455906 50547549 Smallest eigenvalues: [1] 0.5727016 0.5492716 0.5140339 0.5054864 0.4769919 0.4218387 [7] 0.3548869 0.3207122 0.2406381 -2.3514650 Largest eigenvalues: [1] 64423801 60060008 57177027 56197578 54621647 52745500 52184481 51614125 [9] 51445337 50622501 Smallest eigenvalues: [1] 0.4515304 0.4245778 0.4050474 0.3938016 0.3802573 0.3169860 [7] 0.3143473 0.2583652 0.1878882 -0.1361578 Largest eigenvalues: [1] 62814752 59900893 56743619 55340590 54486987 52802739 51544732 51311213 [9] 51200714 50375242 Smallest eigenvalues: [1] 0.44356768 0.42046722 0.39950031 0.32870009 0.27196653 0.12560192 [7] 0.09464374 0.06988762 -0.00171136 -0.05019119 Largest eigenvalues: [1] 64132448 59781318 57110843 56383614 54761570 53001506 52282623 52098521 [9] 51712448 50714730 Smallest eigenvalues: [1] 0.49438405 0.38946797 0.34314212 0.34017865 0.32713573 0.32277015 [7] 0.18083315 0.02447813 0.02023877 -0.15580430 Largest eigenvalues: [1] 63568568 59220209 56877904 54653450 54109074 52544329 51248206 51018887 [9] 50925513 50444026 Smallest eigenvalues: [1] 0.441213482 0.402187823 0.360054823 0.343298783 0.278579172 [6] 0.238515338 0.123659971 0.006826894 -0.020851861 -0.141814677 Largest eigenvalues: [1] 61651023 59652665 56786901 54878602 54452827 53338772 51918450 51387919 [9] 50480596 50331876 Smallest eigenvalues: [1] 0.3877520 0.3760961 0.3414564 0.2800164 0.2292212 0.2151944 [7] 0.1657069 0.1569507 0.1014188 -1.6737793 Largest eigenvalues: [1] 62767736 58823411 56322571 54968439 53912538 52535779 51207713 50984160 [9] 50920675 50143326 Smallest eigenvalues: [1] 0.40413041 0.37107023 0.34796408 0.30040353 0.29680009 0.18375282 [7] 0.12303743 -0.08728291 -0.37144939 -5.39282504 Largest eigenvalues: [1] 62556374 59968023 57365673 55205314 54800629 53256619 51601316 51377913 [9] 51367763 50564854 Smallest eigenvalues: [1] 0.27247301 0.24561616 0.22882619 0.16914650 0.07215156 0.04366907 [7] 0.01613879 0.01025008 -0.03466485 -0.67967206 Largest eigenvalues: [1] 64452351 60932428 57664256 55994006 55930112 54006657 53073763 52262155 [9] 52088678 51815908 Smallest eigenvalues: [1] 0.3426507 0.3272725 0.3152655 0.2504503 0.2025221 0.1619278 [7] 0.1159838 0.1037998 -0.1736154 -0.5895960 Largest eigenvalues: [1] 67211058 60168152 57837245 57313590 54546741 53800700 52795025 52218388 [9] 51265936 51109886 Smallest eigenvalues: [1] 0.5213977 0.4707618 0.4384802 0.4284494 0.4211158 0.3637000 [7] 0.3120819 0.3117351 0.2867010 -0.3436925 Largest eigenvalues: [1] 65104927 60196287 57651473 56533494 54727265 53278819 52557329 51834401 [9] 51662417 50788674 Smallest eigenvalues: [1] 0.419861415 0.378044758 0.375408021 0.373814674 0.348674096 [6] 0.315929850 0.203400380 0.070829478 -0.006275546 -3.475224676 Largest eigenvalues: [1] 63873301 60584258 57021513 55899508 55695041 53760897 52429273 52300099 [9] 51920751 51409538 Smallest eigenvalues: [1] 0.282628072 0.279136691 0.269935974 0.230440702 0.181195615 [6] 0.075532723 -0.008834248 -0.266524326 -0.302874711 -3.178384059 Largest eigenvalues: [1] 61257017 59772518 56841432 54579859 54165949 53125736 51372423 51212731 [9] 50365860 50137497 Smallest eigenvalues: [1] 0.5770307 0.5518265 0.4480035 0.3917223 0.3914581 0.3000425 [7] 0.2956454 0.2344597 0.2169452 -1.2452503 Largest eigenvalues: [1] 66800240 60316173 57954366 57523528 54946296 53655724 52829071 52581605 [9] 51583791 51472788 Smallest eigenvalues: [1] 0.49971376 0.41094068 0.41070446 0.39090868 0.38785315 0.31521481 [7] 0.24441046 0.08525905 -0.03795092 -0.26106001 Largest eigenvalues: [1] 65880126 60399752 57582090 57368490 54628447 53423525 52714113 52092630 [9] 51583037 50978100 Smallest eigenvalues: [1] 0.4741982 0.4243970 0.4105458 0.4047667 0.2823013 0.2792638 [7] 0.1988400 0.1740771 -0.1861228 -2.4816150 Largest eigenvalues: [1] 65308973 61228708 57381934 56254641 55678196 53732927 53299441 52485245 [9] 52103898 51787031 Smallest eigenvalues: [1] 0.47454213 0.45891185 0.42725572 0.34099575 0.22886042 0.22066373 [7] 0.21248619 0.15628414 0.06437691 -5.19893093 Largest eigenvalues: [1] 64217030 59344675 56778044 55720375 54378806 52640763 51843352 51336131 [9] 50828638 50041225 Smallest eigenvalues: [1] 0.29297725 0.28043615 0.28037020 0.27389825 0.26965176 0.16793444 [7] 0.08639555 0.01533882 -0.05557310 -0.17052829 Largest eigenvalues: [1] 63259686 60847492 57501259 55965853 55351122 53859808 52272128 51901143 [9] 51804168 50700061 Smallest eigenvalues: [1] 0.23676217 0.20308198 0.15102903 0.14670640 0.01808751 -0.02944477 [7] -0.03503629 -0.18284821 -0.48185254 -3.46820603 Largest eigenvalues: [1] 62258108 58723590 56235991 55143845 53705898 52044222 51125190 51024809 [9] 50885708 50086042 Smallest eigenvalues: [1] 0.50613441 0.49117951 0.44386310 0.41918374 0.29258286 0.29014648 [7] 0.28964740 0.27785474 0.01645168 -0.08981621 Largest eigenvalues: [1] 63961524 59855917 56487649 55730013 54750051 53121008 51724709 51687729 [9] 51380431 50430069 Smallest eigenvalues: [1] 0.248427886 0.243321433 0.196383449 0.192962959 0.173939308 [6] 0.133182304 0.044087191 0.028209020 0.004579953 -0.004315265 Largest eigenvalues: [1] 64849236 59130549 56498432 56324704 53958165 52586604 52272278 51170907 [9] 50651078 50039970 Smallest eigenvalues: [1] 0.5358907 0.4709333 0.4434988 0.4271307 0.3459811 0.3011736 [7] 0.2720542 0.2438596 0.2149343 -0.1345852 Largest eigenvalues: [1] 65061266 60799338 57630644 56641802 55476500 53561575 52928370 52677211 [9] 52102212 51663789 Smallest eigenvalues: [1] 0.4669376 0.4262264 0.4222228 0.4110763 0.4098774 0.3357056 [7] 0.3162517 0.2903874 0.1181259 -0.2042448 Largest eigenvalues: [1] 62702205 59717564 56833266 54949744 54740071 53367135 51829026 51271738 [9] 51075252 50382148 Smallest eigenvalues: [1] 0.3564605 0.3379122 0.2666972 0.2577763 0.1975894 0.1799183 [7] 0.1646375 0.1571492 0.0495473 -0.1143141 Largest eigenvalues: [1] 62415326 60130318 56962788 55511463 54694636 53438410 52249442 51903216 [9] 51220832 50930486 Smallest eigenvalues: [1] 0.34817203 0.34478925 0.25536370 0.23282984 0.03256536 0.02003475 [7] -0.08669589 -0.15071883 -0.33437422 -2.73316779 Largest eigenvalues: [1] 64184380 60399753 57474712 56031828 55255020 53614193 52447999 52191569 [9] 51848394 51482291 Smallest eigenvalues: [1] 0.4002912 0.3920378 0.3803596 0.3319668 0.2603523 0.2557682 [7] 0.1833026 0.1692031 0.1038402 -0.2996123 Largest eigenvalues: [1] 65166026 61031786 57493028 57440839 55173659 53428531 53201509 52433327 [9] 52221193 51189900 Smallest eigenvalues: [1] 0.4773357 0.4322349 0.4277388 0.4074611 0.3379200 0.3224901 [7] 0.2508553 0.1897822 0.1633150 -0.2071923 Largest eigenvalues: [1] 64811912 60389184 57360359 56115393 55169470 53518990 52231843 52114082 [9] 52062995 51019275 Smallest eigenvalues: [1] 0.50790366 0.49553333 0.46245753 0.41270948 0.37911392 0.32490067 [7] 0.23257606 0.23211016 0.08148267 -0.04511486 Largest eigenvalues: [1] 64444705 60608707 57239046 56044315 54796436 53161129 52143397 52087485 [9] 51566364 51115935 Smallest eigenvalues: [1] 0.5612749 0.5359034 0.5253435 0.4658084 0.4478112 0.3726987 [7] 0.3456432 0.3369135 0.2894344 -1.4250324 Largest eigenvalues: [1] 63692022 60501164 57480760 55641568 55586480 53940256 52347555 52291657 [9] 51739695 51293942 Smallest eigenvalues: [1] 0.34655462 0.34385016 0.32608559 0.29230773 0.15530102 0.14938306 [7] 0.12599973 -0.09265381 -1.48306356 -5.13933612 Largest eigenvalues: [1] 63210911 60523521 56831054 55786968 55023987 53218020 52059341 51741703 [9] 51513400 50678949 Smallest eigenvalues: [1] 0.55210557 0.53274515 0.39634421 0.37393257 0.33599339 0.33547757 [7] 0.30088601 0.20839500 0.15654078 -0.04782717 Largest eigenvalues: [1] 63670765 59841913 57095141 55264414 54971001 53383251 51733768 51704545 [9] 51483539 50802676 Smallest eigenvalues: [1] 0.41081868 0.35789094 0.32431733 0.25331339 0.24594816 0.20196975 [7] 0.06648996 -0.25247954 -0.29926274 -2.10070285 Largest eigenvalues: [1] 64479788 59503616 56505641 54903711 54515314 52820223 51846282 51736510 [9] 51121159 50973167 Smallest eigenvalues: [1] 0.5588531 0.5565010 0.5478989 0.5245142 0.4885647 0.3853234 [7] 0.3453767 0.3385378 0.3300172 -0.9846933 Largest eigenvalues: [1] 64571054 60221812 56952203 56406567 55106991 53019567 52509069 52414262 [9] 51271921 51153828 Smallest eigenvalues: [1] 0.45326344 0.44126318 0.43210967 0.38033081 0.35906289 0.35556418 [7] 0.33805985 0.26565419 0.04989744 -0.28649507 Largest eigenvalues: [1] 63905414 60473745 57157903 55718577 55653370 53896673 51912006 51873557 [9] 51787004 50914756 Smallest eigenvalues: [1] 0.375933796 0.357535298 0.317645466 0.290888206 0.287197275 [6] 0.216235857 0.179441355 0.139911031 0.009581873 -0.010343354 Largest eigenvalues: [1] 62987539 59705183 56949430 55695002 54302762 53126617 51754630 51684240 [9] 51540785 50937803 Smallest eigenvalues: [1] 0.4989466 0.4439029 0.4260818 0.4111692 0.3944669 0.3718408 [7] 0.3592386 0.3329371 0.2462802 -2.5850923 Largest eigenvalues: [1] 63471358 59125182 56354942 54955889 54384338 52444011 51157702 51052770 [9] 50996951 50136678 Smallest eigenvalues: [1] 0.350482800 0.334216462 0.306708386 0.237499496 0.204614811 [6] 0.164931184 0.000620337 -0.056680235 -0.225653384 -0.748413086 Largest eigenvalues: [1] 64340358 60229812 57403027 55533234 54710753 53271723 51853251 51842995 [9] 51602765 50963871 Smallest eigenvalues: [1] 0.38106906 0.36502182 0.29874376 0.24322162 0.23465017 0.22239371 [7] 0.18785561 0.12854075 0.11143335 -0.02587055 Largest eigenvalues: [1] 62923039 59824114 57215507 55705231 55048949 53373988 52009795 51792748 [9] 51610529 50688017 Smallest eigenvalues: [1] 0.25594940 0.25352542 0.20925942 0.18340075 0.16309732 0.09991428 [7] 0.07994251 -0.09777252 -0.15790057 -0.30520783 Largest eigenvalues: [1] 62953180 59296101 56425221 54775886 54228180 53132707 51901829 51086362 [9] 50610786 50451629 Smallest eigenvalues: [1] 0.45265675 0.37653387 0.36834970 0.35151217 0.26993865 0.19171175 [7] 0.17288609 0.11440164 0.09632834 -0.07923113 Largest eigenvalues: [1] 64437847 60127334 56916808 56643667 55098444 53158446 52527415 52453714 [9] 52174719 51357155 Smallest eigenvalues: [1] 0.4160336 0.3826172 0.3617871 0.3091674 0.2775094 0.2728752 [7] 0.2174199 0.1582686 0.1249701 -1.0470558 Largest eigenvalues: [1] 65223701 60419950 57117786 56831839 55325708 53515005 52771579 52255756 [9] 52215799 51339682 Smallest eigenvalues: [1] 0.5657418 0.4635853 0.4614540 0.4474245 0.3572797 0.3342631 [7] 0.3295908 0.2744666 -0.1018610 -0.1026448 Largest eigenvalues: [1] 63971440 59693029 56394983 55291144 54636746 52738955 51484399 51433412 [9] 51312340 50484840 Smallest eigenvalues: [1] 0.41424884 0.40433995 0.37400008 0.25853790 0.20621991 0.20032496 [7] 0.08329316 0.06992070 0.04101541 -0.15343428 Largest eigenvalues: [1] 62635686 60016299 56686036 55483228 54534221 53617484 52304692 51748725 [9] 50862412 50719428 Smallest eigenvalues: [1] 0.5334944 0.5115820 0.5049301 0.4543785 0.4254876 0.3626894 [7] 0.3127751 0.3032202 0.2164003 -2.7029730 Largest eigenvalues: [1] 64380181 60486534 56944037 56306504 55270629 53268230 52250087 52160096 [9] 51569097 50776476 Smallest eigenvalues: [1] 0.29072874 0.23287835 0.19129834 0.17457923 0.16019336 0.13673828 [7] 0.12871361 -0.02144208 -0.31162891 -0.62560096 Largest eigenvalues: [1] 64870252 60114606 56719741 56292118 55076071 53409337 52507852 52361203 [9] 51779929 51059506 Smallest eigenvalues: [1] 0.41188949 0.35505182 0.30752965 0.30326280 0.26482320 0.22502483 [7] 0.19528615 0.11011382 -0.04549129 -0.44046956 Largest eigenvalues: [1] 65867372 59586229 57621231 56070963 54556516 53056541 52303459 51915895 [9] 51817845 51363636 Smallest eigenvalues: [1] 0.4659042 0.3374656 0.3291542 0.3060817 0.2766187 0.2653688 [7] 0.2411973 0.1925782 -0.1095380 -0.3198741 Largest eigenvalues: [1] 64551544 60284695 57858394 55990424 55424467 54107168 52204372 52111868 [9] 51788471 50899960 Smallest eigenvalues: [1] 0.27562717 0.26891897 0.25174171 0.19222617 0.13113442 0.11615997 [7] 0.06624774 -0.03770178 -0.16346759 -0.24808153 Largest eigenvalues: [1] 63418185 59998394 57062633 55871883 54834082 53281010 52310525 51856968 [9] 51804878 51287640 Smallest eigenvalues: [1] 0.42738336 0.42591558 0.35928664 0.34219982 0.26651808 0.18232250 [7] 0.17615264 0.14551789 0.11658508 -0.09916294 Largest eigenvalues: [1] 65950767 59945301 57396804 56632060 54674904 53176559 52706504 51697866 [9] 51534714 50680063 Smallest eigenvalues: [1] 0.29942865 0.28905598 0.26138978 0.24718670 0.20226184 0.12294696 [7] 0.07168579 0.04922947 -0.18015582 -0.81582743 Largest eigenvalues: [1] 65332109 59668015 56910747 56872076 54326135 52911123 52669904 52150774 [9] 51292458 51106581 Smallest eigenvalues: [1] 0.52447316 0.47972043 0.46426207 0.46380191 0.43599805 0.39567602 [7] 0.21026910 0.16457606 -0.06039464 -0.06327350 Largest eigenvalues: [1] 65617452 60269158 57088453 56144673 54759249 52878128 52348133 51649140 [9] 51532915 50661340 Smallest eigenvalues: [1] 0.23942874 0.17651654 0.14249827 0.13202542 0.11534802 0.06752890 [7] 0.06106508 0.04564529 -0.22124934 -0.48210028 Largest eigenvalues: [1] 64581802 60867241 57528691 56454189 55350422 53722351 52425744 52291580 [9] 52126968 51500843 Smallest eigenvalues: [1] 0.409211467 0.402491613 0.373694249 0.319309942 0.263419237 [6] 0.223992995 0.014341119 0.003170013 -0.258042811 -0.545635353 Largest eigenvalues: [1] 64255836 58611573 56023519 55130481 53605190 51788496 51213976 50725944 [9] 50529430 50040484 Smallest eigenvalues: [1] 0.50454111 0.46195100 0.44234163 0.40015859 0.36645976 0.18381692 [7] 0.12772568 0.08965871 -0.06893770 -0.30760598 Largest eigenvalues: [1] 65251042 59596176 56614368 56580237 54249189 52385200 52322695 51348742 [9] 51293314 50471448 Smallest eigenvalues: [1] 0.31097468 0.27989480 0.23952482 0.21417065 0.21076989 0.18889046 [7] 0.16752048 0.09886603 -0.48717312 -1.16803782 Largest eigenvalues: [1] 65918057 60955064 57531931 57493382 55723497 53545038 53487643 53031926 [9] 52438267 51909198 Smallest eigenvalues: [1] 0.5347585 0.4962192 0.4255062 0.4047164 0.3692113 0.3375820 [7] 0.1765398 0.1406169 0.1035736 -0.1270950 Largest eigenvalues: [1] 63940892 59953786 56838897 55605485 54927820 53288604 51981493 51692192 [9] 51656494 50943779 Smallest eigenvalues: [1] 0.48618303 0.47693342 0.37951685 0.35497047 0.31433391 0.24618331 [7] 0.19677847 0.12570931 -0.04603824 -2.70202496 Largest eigenvalues: [1] 64417458 59837771 57264574 55969609 54538839 52879705 52133972 51686824 [9] 51297385 50451719 Smallest eigenvalues: [1] 0.5427545 0.5323213 0.5031192 0.4519202 0.4153887 0.4069469 [7] 0.3799532 0.3327700 0.1820873 -0.1219847 Largest eigenvalues: [1] 63735594 60097533 57089637 55743636 54875691 53417459 51798248 51660182 [9] 51351787 50335888 Smallest eigenvalues: [1] 0.42717029 0.38094080 0.32333697 0.30030779 0.29063465 0.27173922 [7] 0.15401350 0.02718579 -0.09521869 -1.21557704 Largest eigenvalues: [1] 65557926 60126774 57418143 55929693 55312638 53846228 52168909 52116231 [9] 51828579 51154824 Smallest eigenvalues: [1] 0.52954933 0.50364698 0.45379738 0.44857760 0.42567845 0.38853342 [7] 0.37767700 0.24280915 0.09184402 -0.26225527 Largest eigenvalues: [1] 65057042 60817518 57341751 57339614 54977045 53099162 53088693 52416216 [9] 51891920 51152261 Smallest eigenvalues: [1] 0.47676592 0.40378951 0.35269869 0.34613978 0.33166163 0.29253198 [7] 0.25704289 0.16549965 0.05799535 -0.01630693 Largest eigenvalues: [1] 64683309 59312175 56287695 55929348 54314478 52722339 51994006 51350820 [9] 51325661 50553036 Smallest eigenvalues: [1] 0.5073037 0.4522031 0.3818365 0.3621858 0.3617883 0.3377283 [7] 0.2809963 0.2096979 -0.1787391 -1.2845520 Largest eigenvalues: [1] 64802861 60475512 57086631 56363785 55170281 53430022 52290035 51869812 [9] 51746509 50802714 Smallest eigenvalues: [1] 0.30121826 0.27099400 0.25932784 0.18160536 0.14910535 0.11057145 [7] 0.07840236 -0.17346582 -0.41175763 -0.66080469 Largest eigenvalues: [1] 66198288 60254655 57749206 57107450 54680851 53298514 53172401 51854172 [9] 51794194 50868717 Smallest eigenvalues: [1] 0.332561804 0.310327261 0.234901611 0.187475054 0.180170886 [6] 0.110566983 0.094393847 0.002502927 -0.006820422 -1.199379987 Largest eigenvalues: [1] 63849965 59470350 56687821 55715458 54801608 52739169 51763127 51715845 [9] 51708859 50967127 Smallest eigenvalues: [1] 0.50999921 0.48427337 0.38216766 0.31021745 0.29265576 0.27097036 [7] 0.27060036 0.01992409 -0.01046537 -0.02088294 Largest eigenvalues: [1] 64375007 60012951 57179871 56609076 54748825 52939657 52504509 52081094 [9] 51484969 50802789 Smallest eigenvalues: [1] 0.3315742 0.3101312 0.2919505 0.2493203 0.2309198 0.1793975 [7] 0.1331548 -0.0929467 -0.3174801 -0.9253021 Largest eigenvalues: [1] 64540686 61134227 58002340 56442246 55891066 54055955 53156787 52821624 [9] 52425341 52095934 Smallest eigenvalues: [1] 0.42769089 0.41339694 0.40684762 0.37344477 0.34179767 0.23001413 [7] 0.09815963 0.07755874 0.04446335 -0.08367472 Largest eigenvalues: [1] 64052760 59496140 56652988 55528109 54111435 52387599 51544405 51203085 [9] 51087690 50317411 Smallest eigenvalues: [1] 0.46702998 0.38863824 0.34560776 0.34271825 0.30671153 0.26041598 [7] 0.23690849 0.23114173 0.01155683 -1.37711687 Largest eigenvalues: [1] 63058859 60057280 57348262 55837121 54849419 54209392 52661456 51431591 [9] 51083422 50904534 Smallest eigenvalues: [1] 0.40329994 0.38167413 0.33441614 0.32431277 0.29996045 0.27877185 [7] 0.27107046 0.15097807 0.03485868 -0.49860524 Largest eigenvalues: [1] 65645306 60630493 57742387 56901914 55243188 53691589 52950037 52441033 [9] 52268909 51424201 Smallest eigenvalues: [1] 0.43270039 0.41508788 0.40370674 0.39151875 0.34197521 0.26516462 [7] 0.25379765 0.24191011 0.14626610 -0.07802057 Largest eigenvalues: [1] 62186020 59778345 56776566 54809062 54235535 52722520 51133921 51047573 [9] 50880643 50122481 Smallest eigenvalues: [1] 0.40581734 0.36008267 0.32632249 0.31615059 0.27311864 0.23838390 [7] 0.21197199 0.10693850 0.03298843 -0.48786478 Largest eigenvalues: [1] 66461087 61132142 57758045 57537067 55392971 53533293 53475558 53298905 [9] 52168236 51750259 Smallest eigenvalues: [1] 0.33798862 0.33350160 0.32367642 0.24976225 0.21313896 0.18427831 [7] 0.11491321 0.09639502 0.06794379 -0.08795605 Largest eigenvalues: [1] 64996760 60185786 57316037 56721282 55037070 53517572 52629413 52093354 [9] 51954334 51270225 Smallest eigenvalues: [1] 0.47990346 0.45709159 0.43070159 0.41197428 0.37093862 0.27102989 [7] 0.26656596 0.24417665 0.02223501 -0.17136428 Largest eigenvalues: [1] 64492383 60363583 57304388 56035519 55238382 53345425 52119218 52085773 [9] 51897495 50918669 Smallest eigenvalues: [1] 0.41877829 0.41447196 0.37515555 0.35777618 0.35464348 0.32437595 [7] 0.23704118 0.03877728 -0.03406485 -0.07046079 Largest eigenvalues: [1] 64504919 60302811 57710668 55825027 55066531 53678887 52220212 51945812 [9] 51909234 51022094 Smallest eigenvalues: [1] 0.44646009 0.41056660 0.40114501 0.35833293 0.29206463 0.29040661 [7] 0.27573772 0.26316542 0.22643311 -0.04504442 Largest eigenvalues: [1] 62802961 59942073 56741447 55079609 55032415 53280863 51551208 51524280 [9] 51149306 50470997 Smallest eigenvalues: [1] 0.50796688 0.45523848 0.44627339 0.41772109 0.32986013 0.30240848 [7] 0.25318194 0.18577283 0.09487684 -0.37937425 Largest eigenvalues: [1] 65701761 60680424 57484925 57023649 55353348 53660301 53152121 53052277 [9] 51673014 51252648 Smallest eigenvalues: [1] 0.39219512 0.33266557 0.30997414 0.29020731 0.27230677 0.24935759 [7] 0.24171324 0.12746831 0.04870696 -0.34468129 Largest eigenvalues: [1] 63777464 60361450 57255632 55932966 55239462 53637076 52013071 51943481 [9] 51910557 50755544 Smallest eigenvalues: [1] 0.48165712 0.47417802 0.31211785 0.30923073 0.30631704 0.27206626 [7] 0.26430906 0.22188948 0.17087950 -0.01100268 Largest eigenvalues: [1] 64185511 59677400 57154415 55824226 54243626 52889444 51910089 51412890 [9] 51088831 50625849 Smallest eigenvalues: [1] 0.4491140 0.4464624 0.3494821 0.2592410 0.2309093 0.2167945 [7] 0.1560999 -0.1374232 -0.8270159 -5.0634316 Largest eigenvalues: [1] 65597031 60651933 58016032 56740935 54895621 53195047 52774862 52159326 [9] 52113517 51586302 Smallest eigenvalues: [1] 0.29622484 0.23915821 0.23509350 0.23487333 0.16764420 0.15183665 [7] 0.14332240 0.12477499 -0.01985016 -0.03498369 Largest eigenvalues: [1] 63178213 60105040 57181904 56281338 54932369 54210849 52447885 51670601 [9] 50899631 50678038 Smallest eigenvalues: [1] 0.588385518 0.529411822 0.475822506 0.456254117 0.445050444 [6] 0.438608587 0.379695366 0.208796035 0.089453067 -0.002246488 Largest eigenvalues: [1] 66044248 60037349 57501698 56998809 54800453 53092749 52765833 52097725 [9] 51627944 51168662 Smallest eigenvalues: [1] 0.32927765 0.29881761 0.29527221 0.24803150 0.19902564 -0.02338507 [7] -0.06301828 -0.17670915 -0.55219787 -3.51883974 Largest eigenvalues: [1] 65513023 60265189 57276996 56321771 55491066 53808001 52523534 52161743 [9] 51906913 51066207 Smallest eigenvalues: [1] 0.5120147 0.4902305 0.4279274 0.3249458 0.3186632 0.2736615 [7] 0.2342692 0.1737507 0.1399606 -1.7090498 Largest eigenvalues: [1] 63528716 59484670 57129229 55601654 54543136 53150110 51758713 51603425 [9] 51365691 50577859 Smallest eigenvalues: [1] 0.5060602 0.4541361 0.3075310 0.3032671 0.2913096 0.2756836 [7] 0.2318237 0.2295834 0.2243743 -0.5578332 Largest eigenvalues: [1] 64970375 60145520 57462197 56262273 54930904 53570362 52234123 51884440 [9] 51468482 50674500 Smallest eigenvalues: [1] 0.30786794 0.29715886 0.28676674 0.24580613 0.23071977 0.14116524 [7] 0.11489875 0.10592681 0.01524733 -0.13985453 Largest eigenvalues: [1] 65226360 60289127 57669349 56336281 55162949 53374729 53130307 52598554 [9] 51744520 51582214 Smallest eigenvalues: [1] 0.44877412 0.42320217 0.41062041 0.29966239 0.27905187 0.08478913 [7] 0.06798686 0.03887282 -0.28346315 -0.33274652 Largest eigenvalues: [1] 64168026 59904256 56665032 55331946 54540515 53092721 51649508 51597945 [9] 51404244 50888228 Smallest eigenvalues: [1] 0.29852339 0.28700359 0.26902276 0.24486402 0.21711633 0.10498651 [7] 0.06584258 -0.04016976 -0.10621229 -0.63810147 Largest eigenvalues: [1] 64306733 59727134 57010731 55780813 54841150 53488188 51981938 51825529 [9] 51780404 51163424 Smallest eigenvalues: [1] 0.58756124 0.55031381 0.40203394 0.39449552 0.33908763 0.30757219 [7] 0.29281944 0.24704331 0.05327901 -0.12842555 Largest eigenvalues: [1] 64314663 60502582 57157259 55976922 55115413 53280331 52175693 52069018 [9] 51707675 50820973 Smallest eigenvalues: [1] 0.40169634 0.36238506 0.35380109 0.32671150 0.31461695 0.23331964 [7] 0.18580917 0.17222265 0.01182588 -0.33033398 Largest eigenvalues: [1] 65134397 60433704 58005429 56388136 55575484 54324000 52848194 52582932 [9] 52378177 51824302 Smallest eigenvalues: [1] 0.43948897 0.39629211 0.36047301 0.26414728 0.25710602 0.25483879 [7] 0.22808060 0.03166845 -0.18000824 -0.48135630 Largest eigenvalues: [1] 63773738 60273211 56488171 55576385 54764199 53014431 51612270 51452388 [9] 50920382 50173800 Smallest eigenvalues: [1] 0.4574529 0.4294386 0.3964928 0.3700166 0.3663983 0.2016658 [7] 0.1530145 0.1489632 -1.6178774 -2.2031930 Largest eigenvalues: [1] 65243289 59572539 56883002 56800788 54419113 52680525 52527658 52416351 [9] 51557262 51325714 Smallest eigenvalues: [1] 0.41786046 0.40295364 0.38707463 0.32375821 0.27768959 0.21925706 [7] 0.21455049 0.07039857 -0.03699965 -0.27624821 Largest eigenvalues: [1] 62196768 59658703 56314073 55309677 54479038 52683108 51967333 51512327 [9] 51222784 50730770 Smallest eigenvalues: [1] 0.3035823 0.2212409 0.2154011 0.2062859 0.1990763 0.1938541 [7] 0.1596840 0.0548550 0.0320958 -0.1692106 Largest eigenvalues: [1] 66142160 60332402 57794061 56567923 55050964 53472329 53008055 51920514 [9] 51701106 50833244 Smallest eigenvalues: [1] 0.45932737 0.39271114 0.38297706 0.34107954 0.29288405 0.27909868 [7] 0.25270731 0.16194959 0.15263188 -0.04051266 Largest eigenvalues: [1] 62832764 59342784 56727162 54970955 54508602 53012522 51722862 51357914 [9] 50962398 50382907 Smallest eigenvalues: [1] 0.47577080 0.47074609 0.44853104 0.44104044 0.42526933 0.41566454 [7] 0.29011880 0.21557019 0.00950453 -0.11174865 Largest eigenvalues: [1] 63632665 60300709 57342019 55695599 54911652 53369035 52058654 51862302 [9] 51608868 50778887 Smallest eigenvalues: [1] 0.47404903 0.45525679 0.42329400 0.36164076 0.35454958 0.26831721 [7] 0.19221343 0.04257136 -0.10671445 -6.96697582 Largest eigenvalues: [1] 63642147 59474460 56524493 55650766 54264493 52780178 51516685 51354372 [9] 51330918 50301659 Smallest eigenvalues: [1] 0.34612221 0.33736227 0.33315305 0.23277696 0.13115882 0.11311170 [7] 0.07567395 -0.35443778 -0.58975453 -3.44584909 Largest eigenvalues: [1] 63824244 60348349 57421645 55753516 55650829 53616359 52539408 51957746 [9] 51804787 51075666 Smallest eigenvalues: [1] 0.215741956 0.193440114 0.192256962 0.144103487 0.109000049 [6] -0.006112014 -0.217082728 -0.269809294 -0.428519875 -0.473183415 Largest eigenvalues: [1] 63399611 59326360 56294557 55566521 54667926 53074863 51880150 51571208 [9] 50821388 50195623 Smallest eigenvalues: [1] 0.39917552 0.39525696 0.33925254 0.29942161 0.29097067 0.27999483 [7] 0.19164328 0.17227190 -0.05526377 -1.26181739 Largest eigenvalues: [1] 64704102 60461461 57633976 56122917 54639881 53058217 52474655 52270723 [9] 51615739 51471803 Smallest eigenvalues: [1] 0.38868897 0.36877991 0.31140916 0.29722876 0.29043014 0.19141210 [7] 0.10573200 0.09423908 -0.11340411 -0.26125671 Largest eigenvalues: [1] 63890772 60417013 57135184 56600135 55584797 53640976 52608453 52356314 [9] 52308943 51198826 Smallest eigenvalues: [1] 0.5283175 0.4956874 0.4851959 0.4838516 0.4014163 0.3769120 [7] 0.3639069 0.3003085 0.1638212 -0.1029271 Largest eigenvalues: [1] 64838039 59949207 56973242 56953182 54194953 52719309 52438542 51342320 [9] 51157056 50101972 Smallest eigenvalues: [1] 0.37397298 0.35897612 0.35072556 0.32049585 0.31000401 0.27111053 [7] 0.21637655 0.12339520 -0.01119300 -0.03449607 Largest eigenvalues: [1] 64835509 60796951 57459527 57159236 55224446 53653997 52988938 52714353 [9] 52053021 51572485 Smallest eigenvalues: [1] 0.4237647 0.3942397 0.3548675 0.3528174 0.3031715 0.2709671 [7] 0.2147404 0.1376591 -0.3181742 -1.5986810 Largest eigenvalues: [1] 63529531 60489765 57367720 56159536 54893598 53217256 52247038 52230391 [9] 52078855 51147332 Smallest eigenvalues: [1] 0.44358032 0.38589475 0.37619039 0.28206063 0.26945306 0.20097575 [7] 0.18631274 0.08630402 0.08288487 -0.00694323 Largest eigenvalues: [1] 62165192 59133159 56218087 54379090 53997843 52482821 51146133 51078889 [9] 50565301 50362020 Smallest eigenvalues: [1] 0.46363012 0.35697754 0.30067607 0.29201585 0.29080292 0.26675858 [7] 0.21059676 0.03016882 -0.03019872 -0.09614621 Largest eigenvalues: [1] 64935858 60810406 57700579 56809224 55185833 53858493 52736293 52500808 [9] 52308451 51422649 Smallest eigenvalues: [1] 0.473970844 0.421234355 0.395283399 0.386577443 0.306521414 [6] 0.221815956 0.130092306 0.109075044 0.008464154 -0.074206859 Largest eigenvalues: [1] 63681412 60355025 57320650 55601879 55417537 53871513 52506467 52165013 [9] 51639563 51051069 Smallest eigenvalues: [1] 0.5000428 0.4191230 0.3895635 0.3802932 0.3013627 0.2857498 [7] 0.2754820 0.2668090 0.1170964 -0.1498062 Largest eigenvalues: [1] 61997183 59564069 56431249 54933208 54542058 53230276 51865863 51363860 [9] 50605070 50311315 Smallest eigenvalues: [1] 0.45335624 0.43025851 0.36416624 0.27939724 0.24438702 0.23138496 [7] 0.19645169 -0.03686460 -0.07908756 -0.12252773 Largest eigenvalues: [1] 65144966 60362593 57735024 56175889 55040973 53497948 52333859 51819611 [9] 51770744 50774426 Smallest eigenvalues: [1] 0.45074843 0.44143114 0.42290250 0.38807240 0.32599663 0.26255333 [7] 0.11050881 0.09203367 0.01680314 -0.16696491 Largest eigenvalues: [1] 63935309 59876959 57182240 55869605 54731559 53062138 51867907 51833400 [9] 51648071 50575471 Smallest eigenvalues: [1] 0.36401192 0.31918027 0.24459720 0.21421691 0.21335935 0.13611351 [7] 0.01837308 -0.14135963 -0.16466506 -1.15254031 Largest eigenvalues: [1] 63244794 59229842 56767267 55724536 54298440 52649063 52138534 51605013 [9] 51286795 50373537 Smallest eigenvalues: [1] 0.4458314 0.4119143 0.3856932 0.3483522 0.2662103 0.2541812 [7] 0.2349929 0.1373263 -0.3723466 -0.6398042 Largest eigenvalues: [1] 65727685 60366597 57809837 57326222 54590417 53548817 52492496 52204945 [9] 51347274 50923999 Smallest eigenvalues: [1] 0.48875719 0.44663210 0.38840025 0.36729165 0.31143062 0.30435465 [7] 0.18617017 0.16640290 -0.02860812 -0.04143211 Largest eigenvalues: [1] 63148506 60437476 57437841 56051470 54810058 54209097 52476003 52310780 [9] 51328712 51033940 Smallest eigenvalues: [1] 0.5351956 0.4427493 0.4338828 0.4209067 0.3734884 0.2995147 [7] 0.2585971 0.2077876 -0.1092852 -0.5931205 Largest eigenvalues: [1] 65111816 60474293 57298758 56486830 55216463 52993319 52567364 51987613 [9] 51730072 50999712 Smallest eigenvalues: [1] 0.46909584 0.40489763 0.36685301 0.34977575 0.33654319 0.24879438 [7] 0.23174085 0.19775960 0.16721987 -0.05690472 Largest eigenvalues: [1] 64908571 60900981 57236829 56486094 55807187 53833691 53615792 52527918 [9] 51872704 51592904 Smallest eigenvalues: [1] 0.3619604645 0.3147112281 0.2966078104 0.1212452143 0.0242330430 [6] 0.0119903666 -0.0006817226 -0.3637461561 -1.0601011343 -2.1250127537 Largest eigenvalues: [1] 63470445 60892853 57922165 55759763 55676635 54243466 52723418 52278691 [9] 51857004 51299359 Smallest eigenvalues: [1] 0.3229187 0.3141152 0.3130450 0.2973672 0.2477959 0.2316078 [7] 0.1887063 0.1586283 0.1404220 -0.1526431 Largest eigenvalues: [1] 65102605 59719498 57013797 56088033 54073234 52723526 52085322 51861673 [9] 51216363 51171907 Smallest eigenvalues: [1] 0.37139749 0.37015411 0.35523001 0.33940621 0.32625948 0.28524301 [7] 0.08116374 -0.16498333 -0.16634324 -0.44501849 Largest eigenvalues: [1] 64235361 59192184 57110478 55431953 54639039 53286536 51675227 51670450 [9] 50839331 50170692 Smallest eigenvalues: [1] 0.280525393 0.249422463 0.228567787 0.176906862 0.036208156 [6] 0.008537243 -0.009228669 -0.158428537 -0.500985944 -2.100663651 Largest eigenvalues: [1] 64627961 61042930 57961111 56809558 55350547 53855669 53369133 52684511 [9] 52553042 52266782 Smallest eigenvalues: [1] 0.4361604 0.3956956 0.3692113 0.3033934 0.2623944 0.2238133 [7] 0.1847326 0.1436362 0.0382388 -0.1312401 Largest eigenvalues: [1] 63879060 60424812 57200625 55410573 55329883 53749746 52121627 51830840 [9] 51432448 50965917 Smallest eigenvalues: [1] 0.46163234 0.43157492 0.40011987 0.33992454 0.31500426 0.28797693 [7] 0.16589392 0.05438029 -0.11109404 -2.32486400 Largest eigenvalues: [1] 64490502 59886391 57242559 56650062 54465874 52563263 52412007 51858934 [9] 51439252 50772787 Smallest eigenvalues: [1] 0.4447652 0.4376073 0.3383682 0.3038996 0.2345920 0.1971537 [7] 0.1710760 0.1480594 0.1072307 -7.7668647 Largest eigenvalues: [1] 63469948 59651569 57414414 55441716 54778946 53244337 52087971 51441766 [9] 51316261 50630420 Smallest eigenvalues: [1] 0.36754535 0.32107313 0.27980799 0.25447509 0.23266415 0.07767757 [7] 0.02722315 -0.10423419 -0.33327080 -2.83987847 Largest eigenvalues: [1] 63584550 60082602 57352709 56343256 54766013 53377536 52162298 51696595 [9] 51611748 50484382 Smallest eigenvalues: [1] 0.376242743 0.335009546 0.282948960 0.205561046 0.130162646 [6] 0.094770415 0.078240822 0.042109668 0.006704996 -0.892918355 Largest eigenvalues: [1] 65095754 59819902 56976254 56685741 54744924 53071648 52629834 52139859 [9] 52026980 51176498 Smallest eigenvalues: [1] 0.42938478 0.41198881 0.40497164 0.38030466 0.36372245 0.30553506 [7] 0.23309877 0.06698100 0.05435017 -0.53364051 Largest eigenvalues: [1] 63688782 59709442 57042996 55929155 54386294 52956519 51787536 51727538 [9] 51263209 50666235 Smallest eigenvalues: [1] 0.534394160 0.516405416 0.380551189 0.338181827 0.318908256 [6] 0.308456714 0.207898544 -0.009723578 -0.079089033 -1.295718728 Largest eigenvalues: [1] 64718979 59980378 57306269 55227918 54865041 53327516 52410385 51557769 [9] 51512587 51392588 Smallest eigenvalues: [1] 0.41474771 0.38422039 0.37773948 0.32338191 0.30560072 0.21064246 [7] 0.16969864 0.16770283 0.09400382 -0.34636825 Largest eigenvalues: [1] 64166244 60252959 56793012 56111754 54642611 52883319 52124968 52002316 [9] 51523922 51034564 Smallest eigenvalues: [1] 0.39896429 0.33249402 0.31035185 0.25004980 0.20849593 0.09166945 [7] 0.07698422 -0.16171684 -0.18755093 -0.38099873 Largest eigenvalues: [1] 63205095 60179044 57342956 55083383 55030675 53395412 52126634 52055328 [9] 51390228 51136442 Smallest eigenvalues: [1] 0.199524667 0.198956359 0.107469790 0.035149325 -0.008544322 [6] -0.248373492 -0.342425641 -0.434322374 -0.477978919 -5.574439878 Largest eigenvalues: [1] 62831870 59415961 56810063 55152822 54895667 53120709 51363481 51282138 [9] 51207718 50341227 Smallest eigenvalues: [1] 0.492768178 0.489489532 0.342775765 0.337879982 0.237183970 [6] 0.156307548 0.126677538 0.057773629 0.055365682 -0.002867192 Largest eigenvalues: [1] 64119002 60346902 57078446 55758313 55231461 53501354 52445300 51930354 [9] 51888121 51442768 Smallest eigenvalues: [1] 0.37031347 0.35822274 0.32945791 0.29700730 0.24262529 0.19415295 [7] 0.11728352 0.06967865 -0.09578262 -0.35947702 Largest eigenvalues: [1] 63429221 59438151 56438282 55132397 54868233 52773621 52126172 51420110 [9] 51320070 50764285 Smallest eigenvalues: [1] 0.40892337 0.38620366 0.36398714 0.21508130 0.10915918 0.01543246 [7] -0.06695919 -0.06935118 -0.17342179 -0.56954462 Largest eigenvalues: [1] 65908594 59837633 57322594 56285004 54346088 52598391 52375925 51721267 [9] 51352141 50880765 Smallest eigenvalues: [1] 0.37312103 0.36926382 0.35059090 0.29775826 0.28878935 0.23913253 [7] 0.21841198 0.16399680 0.06506278 -0.12079797 Largest eigenvalues: [1] 64651512 59904345 56986965 55953025 54817845 53350910 51957141 51486585 [9] 51206939 49976101 Smallest eigenvalues: [1] 0.4845686 0.4628490 0.4247119 0.3903149 0.3576087 0.3417928 [7] 0.3283418 0.3024886 0.2993924 -1.6324833 Largest eigenvalues: [1] 63081148 59974171 56969033 55197042 54928467 53375996 51559258 51530143 [9] 51124067 50623377 Smallest eigenvalues: [1] 0.40314414 0.39994863 0.38166553 0.32279453 0.25520310 0.18422688 [7] 0.11820144 0.08111155 0.01046393 -0.05450520 Largest eigenvalues: [1] 62240468 59675357 56646137 55395774 54488987 53466295 51925381 51490426 [9] 50662493 50481243 Smallest eigenvalues: [1] 0.5136513 0.4779015 0.4628519 0.4294315 0.2141643 0.2003939 [7] 0.1446269 0.1199344 0.1074424 -0.4250706 Largest eigenvalues: [1] 61995704 59819447 56422681 55071260 54882567 53175748 52217901 51613534 [9] 50861880 50738777 Smallest eigenvalues: [1] 0.42776228 0.40484304 0.39926866 0.28902663 0.23347426 0.21957151 [7] 0.18620175 0.04740884 -0.01363339 -3.25296052 Largest eigenvalues: [1] 65164658 59269651 56364924 56145355 54433225 52631690 52258202 51274561 [9] 51068785 50319909 Smallest eigenvalues: [1] 0.49070551 0.46827063 0.42385440 0.41981484 0.40253580 0.40003505 [7] 0.31313067 0.22382779 0.06227231 -0.13859479 Largest eigenvalues: [1] 65464808 59535191 57072455 56639084 54366558 52656421 52641336 51668349 [9] 51536385 50836801 Smallest eigenvalues: [1] 0.3699698 0.3557506 0.3232749 0.2523010 0.1577299 0.1465086 [7] -0.2610783 -0.6345601 -1.1700548 -1.4296391 Largest eigenvalues: [1] 65128269 60497678 57119561 56951426 55325458 53518821 53103623 52752657 [9] 52140477 51575346 Smallest eigenvalues: [1] 0.34232953 0.33262702 0.30512283 0.24292146 0.21515361 0.16818948 [7] 0.15009903 0.09289172 -0.03311363 -0.69528299 Largest eigenvalues: [1] 65241872 59904600 56674642 56253206 54916682 53207414 52358692 52159373 [9] 51848139 51196547 Smallest eigenvalues: [1] 0.3823116 0.3755541 0.3217533 0.3019909 0.3016130 0.1485883 [7] 0.1124787 0.0714449 -0.2078827 -0.3906785 Largest eigenvalues: [1] 63939503 59125152 56275464 55306338 54007616 52478829 51435756 51323875 [9] 51186785 50361919 Smallest eigenvalues: [1] 0.50882689 0.50075317 0.48144842 0.44519441 0.42594167 0.33753583 [7] 0.27869258 0.25456696 -0.06069958 -0.06535618 Largest eigenvalues: [1] 63854675 59703959 56572040 55585389 54537211 52669914 51658262 51433524 [9] 50815700 50015836 Smallest eigenvalues: [1] 0.45649287 0.41412221 0.37667398 0.35182485 0.32954510 0.32636299 [7] 0.29448418 0.27915808 0.19058528 -0.02391875 Largest eigenvalues: [1] 63808570 59670117 56915312 56116770 54461710 52804472 52178820 51686886 [9] 51106699 50588447 Smallest eigenvalues: [1] 0.220724914 0.181054654 0.121851653 0.075105997 0.014370919 [6] 0.003954583 -0.068102525 -0.117293554 -0.270865423 -0.598483811 Largest eigenvalues: [1] 65179290 60040329 57626844 56214835 55025747 53791653 52418467 52321234 [9] 51646798 50898794 Smallest eigenvalues: [1] 0.3477265 0.3382494 0.2864824 0.2788496 0.2288106 0.2053901 [7] 0.1158699 0.1123578 -0.1736892 -2.2765180 Largest eigenvalues: [1] 62516799 60576083 57220393 55263765 55214019 53796931 52263598 52047624 [9] 51273721 51056053 Smallest eigenvalues: [1] 0.304863670 0.280426175 0.269769894 0.261061491 0.259985276 [6] 0.190197306 0.008451877 -0.017938571 -0.515318793 -2.022076797 Largest eigenvalues: [1] 64614596 59906279 56820091 55943537 54836449 53144701 51973884 51807784 [9] 51606833 50637371 Smallest eigenvalues: [1] 0.37998711 0.28192784 0.27723401 0.26139988 0.23183547 0.18427750 [7] 0.16469401 0.14824012 0.06731416 -5.12656472 Largest eigenvalues: [1] 65314815 60387067 57638136 56210152 55045487 53474856 52451586 51889012 [9] 51739090 50963747 Smallest eigenvalues: [1] 0.38020275 0.34922766 0.28844905 0.25673680 0.22629373 0.21778674 [7] 0.18830183 0.14889710 0.03192554 -0.03693272 Largest eigenvalues: [1] 63693108 59171143 56713225 55495852 54662422 52979472 52127056 51536485 [9] 51386932 50847659 Smallest eigenvalues: [1] 0.56942348 0.47956819 0.47432258 0.46612022 0.45594268 0.41610416 [7] 0.26361871 0.08286752 -0.04269034 -0.17091968 Largest eigenvalues: [1] 64096855 60086363 56675723 55765869 54851525 53141721 51804636 51789820 [9] 51301106 50391147 Smallest eigenvalues: [1] 0.4340350 0.4024907 0.3888212 0.3581736 0.3032138 0.2707824 [7] 0.2470293 0.1834053 -0.3641796 -2.7561827 Largest eigenvalues: [1] 64464764 60129902 57460781 56067361 55387508 53883150 52046812 52004648 [9] 51905391 50825009 Smallest eigenvalues: [1] 0.43369943 0.41951322 0.37719865 0.31316405 0.29335078 0.20834640 [7] 0.20475525 0.09493602 -0.18010660 -0.66490814 Largest eigenvalues: [1] 63806335 59907766 56864545 55966184 54665014 52981852 52198139 52017662 [9] 51102728 50711855 Smallest eigenvalues: [1] 0.50064484 0.42639591 0.38077752 0.35239346 0.30284503 0.29561547 [7] 0.28893717 0.13885856 0.02390817 -0.05246068 Largest eigenvalues: [1] 63973422 60374186 57137324 55824788 55228202 53516670 52507648 51944496 [9] 51830404 51185042 Smallest eigenvalues: [1] 0.49950708 0.49100664 0.45904088 0.44496387 0.37752922 0.31594269 [7] 0.20897183 0.18017701 0.16348505 -0.07820728 Largest eigenvalues: [1] 64705591 60594599 57230747 56233877 55330313 53719943 52314337 52205351 [9] 51984186 51227376 Smallest eigenvalues: [1] 0.4613428 0.3986235 0.3563802 0.3221114 0.3209026 0.2802571 [7] 0.2450980 0.2176601 -0.3305451 -1.5069816 Largest eigenvalues: [1] 65246208 60759944 57569629 56405666 55600683 53894562 52570849 52499804 [9] 52431337 51417580 Smallest eigenvalues: [1] 0.48950277 0.42835856 0.40392864 0.28254733 0.26561703 0.23598338 [7] 0.23279718 0.19785960 -0.05522623 -0.05696261 Largest eigenvalues: [1] 64852783 60617888 57702054 56371880 55571485 53894456 52618612 52477220 [9] 52161761 51462191 Smallest eigenvalues: [1] 0.38212052 0.35174725 0.29528500 0.27939766 0.20196418 0.07794977 [7] -0.03871463 -0.05635074 -0.19285943 -0.51522753 Largest eigenvalues: [1] 64691927 60554210 57526722 55881709 55194237 53746334 52406788 52078161 [9] 51725391 50890734 Smallest eigenvalues: [1] 0.42094983 0.40035735 0.39629503 0.33488797 0.32065761 0.31621719 [7] 0.06825558 -0.11076073 -0.65539756 -0.87563403 Largest eigenvalues: [1] 64429779 60451116 56747914 56670787 54867924 52937451 52377013 52093379 [9] 51557568 50609782 Smallest eigenvalues: [1] 0.5317492 0.5202339 0.4558578 0.4418403 0.4375726 0.4259148 [7] 0.3322293 0.2072673 0.1764485 -0.0496080 Largest eigenvalues: [1] 64050908 60634957 57265849 56115769 55102682 53152151 52505481 52166370 [9] 51563940 51078031 Smallest eigenvalues: [1] 0.294209991 0.292330954 0.276242530 0.252170137 0.235196059 [6] 0.112033404 0.059416381 0.016941972 -0.007679314 -0.599304713 Largest eigenvalues: [1] 62244391 60110364 57361500 55319892 55135051 53752747 52393298 51878541 [9] 51256527 51097344 Smallest eigenvalues: [1] 0.5529925 0.5007083 0.4856654 0.4268885 0.3535266 0.3483023 [7] 0.2474378 0.1294687 -0.0660236 -0.3445050 Largest eigenvalues: [1] 63851328 60630562 56920193 55900352 55440496 53696604 52397252 52121257 [9] 51760574 50977081 Smallest eigenvalues: [1] 0.4631743 0.4062614 0.3764578 0.3439337 0.2456474 0.2172864 [7] 0.1375874 0.1151171 0.1064158 -0.4026055 Largest eigenvalues: [1] 66046082 60051299 57370045 57070409 54527651 53067612 52985447 51801438 [9] 51522632 51077707 Smallest eigenvalues: [1] 0.40851832 0.31176804 0.30685172 0.29311884 0.28822228 0.24267490 [7] 0.22840652 0.18635389 0.15495509 -0.03761303 Largest eigenvalues: [1] 65794694 60112379 57648243 57407047 54379094 53225263 52782900 52335047 [9] 51588838 51501845 Smallest eigenvalues: [1] 0.50038327 0.49819707 0.49508231 0.45654407 0.37995865 0.37448820 [7] 0.26296750 0.25297191 0.18827253 -0.04836541 Largest eigenvalues: [1] 63598554 60285943 57021770 55901587 55066847 53351813 52069165 51833540 [9] 51442387 50808918 Smallest eigenvalues: [1] 0.47729340 0.46810693 0.45222123 0.44119277 0.38592354 0.27908271 [7] 0.18593310 0.05595294 -0.20137736 -0.24072081 Largest eigenvalues: [1] 64564122 60510889 57519256 56626031 55086099 53122789 52518509 52201380 [9] 52066684 51220293 Smallest eigenvalues: [1] 0.31260264 0.30041979 0.25099713 0.21121671 0.20899542 0.17953973 [7] 0.17330198 -0.06270073 -0.07479795 -0.48259157 Largest eigenvalues: [1] 63314190 59237743 56816773 55734408 54420744 52891623 51687334 51464597 [9] 50977761 50220009 Smallest eigenvalues: [1] 0.4957815 0.4795986 0.4753241 0.3948453 0.3395536 0.3115004 [7] 0.2884822 0.2474319 0.1079045 -0.0887370 Largest eigenvalues: [1] 63438133 59564410 56664560 55324030 54333513 52850595 51456978 51386354 [9] 51375945 50537189 Smallest eigenvalues: [1] 0.4633509 0.4445126 0.4412881 0.4122093 0.3917410 0.3652278 [7] 0.3366746 0.2389127 0.1048716 -0.2694398 Largest eigenvalues: [1] 64033161 59678940 56629527 55948074 54366138 52877022 51943062 51552260 [9] 51236344 50390062 Smallest eigenvalues: [1] 0.35394668 0.28631417 0.25581224 0.24583801 0.23292979 0.20598352 [7] 0.13047551 0.09912355 -1.00590826 -1.38320515 Largest eigenvalues: [1] 64374489 59693340 57297582 56977487 54467650 52851328 52691341 52420035 [9] 51778876 51040013 Smallest eigenvalues: [1] 0.44106608 0.40134040 0.33587903 0.27944389 0.27379946 0.24821555 [7] 0.14185147 0.11705653 0.08756123 -0.04054477 Largest eigenvalues: [1] 64863547 60618870 57752143 56599667 54748520 53394360 52694306 52124310 [9] 51863780 51276195 Smallest eigenvalues: [1] 0.36408603 0.32962644 0.31988793 0.27237173 0.25490129 0.20409077 [7] 0.17844088 0.12175815 -0.09523532 -0.36860257 Largest eigenvalues: [1] 64622641 58959299 56694585 55359260 54151218 52917551 51434798 51418116 [9] 51307143 50736781 Smallest eigenvalues: [1] 0.51595807 0.48387446 0.44453058 0.39112117 0.31122284 0.27453355 [7] 0.23527914 0.17078696 0.07306644 -0.11596416 Largest eigenvalues: [1] 65959074 60750900 57844802 56604327 55054734 53369771 52846290 52777213 [9] 51980374 51839210 Smallest eigenvalues: [1] 0.4717270 0.4619197 0.4492732 0.3876351 0.2778257 0.2219278 [7] 0.1663721 0.1292486 0.1001942 -0.5059503 Largest eigenvalues: [1] 65543615 60676412 57495507 56957477 55051492 53347799 53035588 52191254 [9] 51804116 50863386 Smallest eigenvalues: [1] 0.322364538 0.319415501 0.284282692 0.234698264 0.221925329 [6] 0.206847339 0.134694006 0.121866050 -0.007448306 -0.047132048 Largest eigenvalues: [1] 62402494 59599538 56973013 54864892 54452469 53198741 51637902 51377556 [9] 50689237 50533438 Smallest eigenvalues: [1] 0.42972070 0.35759064 0.31985157 0.30513731 0.30014486 0.18214671 [7] 0.17132069 -0.06005723 -0.50149860 -0.66058149 Largest eigenvalues: [1] 63535603 60575743 57195175 55878468 55413652 54228227 52416290 52320219 [9] 51471640 51382763 Smallest eigenvalues: [1] 0.4730594 0.4723298 0.3875682 0.3636253 0.3084050 0.2921532 [7] 0.2883358 0.2839556 0.2566918 -1.5453906 Largest eigenvalues: [1] 64487831 60219380 57025283 56051735 55135554 53280492 52232604 51883890 [9] 51866596 50857787 Smallest eigenvalues: [1] 0.4923777 0.4276504 0.4261334 0.3695037 0.3281602 0.2684967 [7] 0.2340769 -0.0222209 -0.3504534 -0.3717939 Largest eigenvalues: [1] 61947844 59529735 55951716 54729097 54579152 52785993 51529579 50852895 [9] 50414549 49885903 Smallest eigenvalues: [1] 0.45371213 0.38330189 0.37402194 0.35301727 0.31285717 0.15689945 [7] 0.08411424 -0.12633500 -0.13436219 -1.97514557 Largest eigenvalues: [1] 63748909 60776223 57492472 56407362 55224990 53296355 52725199 52223794 [9] 52023805 51341911 Smallest eigenvalues: [1] 0.5568921 0.5059484 0.4857746 0.4213832 0.3725788 0.3629504 [7] 0.3123681 0.2489832 -0.1864722 -0.7249718 Largest eigenvalues: [1] 63523906 60026876 56453536 55408456 55292547 53557662 51862772 51709792 [9] 51363418 50484367 Smallest eigenvalues: [1] 0.25872611 0.22385998 0.18992172 0.08852940 0.05421065 -0.26298729 [7] -0.29247447 -0.33589173 -1.08957848 -2.30670822 Largest eigenvalues: [1] 62651502 59184391 56037805 55193004 54219086 52743950 51956099 51178018 [9] 50959584 50410758 Smallest eigenvalues: [1] 0.39581122 0.38604809 0.35553013 0.35164822 0.35058575 0.31245521 [7] 0.24660694 0.22503179 0.11628918 -0.03972061 Largest eigenvalues: [1] 63614140 59747250 57063923 55395705 54699561 52939569 51701444 51617349 [9] 51402437 50762495 Smallest eigenvalues: [1] 0.40082217 0.38534420 0.32855951 0.27519062 0.25700268 0.17681739 [7] 0.14350263 0.08445469 0.01886748 -0.11080579 Largest eigenvalues: [1] 64801888 59882907 57416602 56865422 54268813 53046832 52599210 52203628 [9] 51539387 51373566 Smallest eigenvalues: [1] 0.4451139 0.3707244 0.3628837 0.3242300 0.3212832 0.2605088 [7] 0.2602818 0.2534940 0.0933153 -0.4194682 Largest eigenvalues: [1] 64586921 60232214 57325084 56804853 54651113 52870518 52693745 51701106 [9] 51682407 50609113 Smallest eigenvalues: [1] 0.2773769457 0.2466841660 0.1524207671 0.1100507705 0.0002145748 [6] -0.0064816387 -0.0115964540 -0.2729710510 -2.3236728171 -2.4096397131 Largest eigenvalues: [1] 64932344 59967095 56477193 56423892 54875608 53071056 52373851 52138874 [9] 51895539 50948653 Smallest eigenvalues: [1] 0.43891113 0.43832794 0.33146422 0.27594118 0.26724295 0.24046931 [7] 0.17155929 0.06486833 0.06062705 -0.50427221 Largest eigenvalues: [1] 64244579 60375632 57450183 55822722 55800982 54246862 52868183 52344301 [9] 51852977 51499258 Smallest eigenvalues: [1] 0.44490175 0.42732571 0.37549910 0.37041748 0.29964370 0.17053014 [7] 0.15161033 0.09095674 -0.02519998 -0.25556530 Largest eigenvalues: [1] 61480744 59480948 56700459 54966493 54148092 53134158 52088275 51270395 [9] 50802329 50291877 Smallest eigenvalues: [1] 0.32603648 0.23016485 0.20202962 0.17249560 0.14478631 0.12305024 [7] 0.09516992 -0.04390640 -0.09717173 -0.11822092 Largest eigenvalues: [1] 66520084 60342715 58119381 57627007 54349701 53799534 52840737 52087247 [9] 51333497 51140675 Smallest eigenvalues: [1] 0.26433176 0.25963595 0.22714342 0.18307801 0.11048732 0.09315866 [7] -0.01542112 -0.19597882 -0.55328859 -1.55760018 Largest eigenvalues: [1] 64442765 60279945 57518453 56335313 55351739 53916937 52372324 52286943 [9] 51972740 51052697 Smallest eigenvalues: [1] 0.3935927 0.3632513 0.3155366 0.3056787 0.2989560 0.2075036 [7] 0.1792987 0.1058581 0.1011199 -0.2692723 Largest eigenvalues: [1] 63609665 60345560 57057754 55715710 55117751 53231003 51992807 51773928 [9] 51601203 50889416 Smallest eigenvalues: [1] 0.41314827 0.40292175 0.36772344 0.27771785 0.18290842 0.15014140 [7] 0.12939764 0.05872944 0.05575680 -0.16431440 Largest eigenvalues: [1] 63395269 60620655 57672706 56215761 54938609 54557485 52964852 52421742 [9] 51611522 51161601 Smallest eigenvalues: [1] 0.48951589 0.47653992 0.47204199 0.43040406 0.39677860 0.39196331 [7] 0.37851048 0.26780086 0.20230774 -0.01708545 Largest eigenvalues: [1] 64370650 59392463 57038013 55922031 54400195 52705268 51984636 51629093 [9] 51157895 50555465 Smallest eigenvalues: [1] 0.5576762 0.4256872 0.3558410 0.3376075 0.3219118 0.3133606 [7] 0.2933233 0.2650482 0.1978047 -4.3005222 Largest eigenvalues: [1] 65056478 60080402 57738824 55843326 54906169 53203319 52082865 52019591 [9] 51940266 51331020 Smallest eigenvalues: [1] 0.4235342 0.3891179 0.3317569 0.3236358 0.3018352 0.2954184 [7] 0.2920747 0.1576114 0.0838847 -0.1329351 Largest eigenvalues: [1] 63203963 59980444 56583331 55423797 54943226 53047239 52006140 51452873 [9] 51303284 50541442 Smallest eigenvalues: [1] 0.4050876 0.3624469 0.2798633 0.2679924 0.2435277 0.2413218 [7] 0.2215689 0.2203864 0.1954278 -0.4585967 Largest eigenvalues: [1] 64198624 59813463 57115264 55863741 54816674 52540609 52305276 51966151 [9] 51198161 51171881 Smallest eigenvalues: [1] 0.5409602 0.4896571 0.4542637 0.4467150 0.3401741 0.3149995 [7] 0.2900210 0.2478140 0.2408017 -0.4522807 Largest eigenvalues: [1] 64723394 60080808 56836151 56575522 54238570 52518110 52418623 51542299 [9] 51345115 50753420 Smallest eigenvalues: [1] 0.41541482 0.39159716 0.31991593 0.25163735 0.22166079 0.17612604 [7] 0.14000807 0.13832142 -0.04133121 -0.08987305 Largest eigenvalues: [1] 63330289 60423889 57440436 55437813 55374415 53843860 52506838 52108934 [9] 51515899 51175301 Smallest eigenvalues: [1] 0.5522211 0.5143494 0.5006699 0.4490609 0.4264392 0.3741724 [7] 0.3491604 0.2839451 0.1711908 -0.8154333 Largest eigenvalues: [1] 64537279 60544596 57149150 56243049 55397666 53416625 52873906 52281691 [9] 51737125 51523865 Smallest eigenvalues: [1] 0.4365364 0.4240506 0.3880275 0.3797212 0.3523477 0.3335104 [7] 0.3298973 0.2569515 0.1833409 -0.2126094 Largest eigenvalues: [1] 64539378 59931672 57202722 55624605 54209567 52792670 51942334 51728573 [9] 51180882 51096091 Smallest eigenvalues: [1] 0.53734204 0.53421694 0.47891289 0.46447700 0.44463593 0.39498166 [7] 0.36024749 0.08392692 -0.36473080 -0.45188977 Largest eigenvalues: [1] 63497211 59741086 56457751 55472272 54588654 52714377 51471080 51419748 [9] 51266083 50343097 Smallest eigenvalues: [1] 0.455879155 0.431250995 0.403890545 0.291130857 0.264666562 [6] 0.256026095 0.243279912 0.196337352 0.002324291 -4.291024385 Largest eigenvalues: [1] 64727395 59730632 56680760 56045738 54515943 52673836 52126816 51684678 [9] 51586234 50956544 Smallest eigenvalues: [1] 0.45172103 0.44937817 0.42916564 0.40353396 0.33316969 0.30067627 [7] 0.21539090 0.00869245 -0.11960191 -0.27441437 Largest eigenvalues: [1] 63129611 60080379 56531005 55738000 54654023 52949026 51914329 51556125 [9] 51315527 50526067 Smallest eigenvalues: [1] 0.40793568 0.35362448 0.29991313 0.28271367 0.24527347 0.22715089 [7] 0.11398558 0.05128599 -0.21137692 -0.57406391 Largest eigenvalues: [1] 64364083 59629359 56856694 56626747 54222221 52888910 52481750 51529016 [9] 51408446 50634832 Smallest eigenvalues: [1] 0.4831740 0.4266035 0.4149914 0.4080387 0.3812790 0.3322192 [7] 0.2152770 0.1731276 -0.1424544 -0.7218193 Largest eigenvalues: [1] 64226474 60361275 57226824 55961587 54960020 53417411 52247232 52067095 [9] 51989561 51233428 Smallest eigenvalues: [1] 0.37490704 0.33041294 0.31739777 0.27703350 0.24685853 0.22841607 [7] 0.16970585 0.15677786 -0.06554758 -0.18122120 Largest eigenvalues: [1] 63903510 60647159 58199739 55963358 55485044 54508171 52797062 52672777 [9] 51858170 51597173 Smallest eigenvalues: [1] 0.4279425 0.4228308 0.4195979 0.3874378 0.3423814 0.3200809 [7] 0.2627291 0.2485164 0.2138260 -0.1986564 Largest eigenvalues: [1] 65469788 60465411 57512828 56619930 54518265 52715243 52660222 51946620 [9] 51261617 51192516 Smallest eigenvalues: [1] 0.5796327 0.5122445 0.4957780 0.4823543 0.4115190 0.3703398 [7] 0.2632388 0.2431749 0.2416874 -0.0313019 Largest eigenvalues: [1] 63408431 60008307 56592589 55356582 55035046 53159374 51717234 51621763 [9] 51468049 50567924 Smallest eigenvalues: [1] 0.4842995 0.4790832 0.4593683 0.4590637 0.4055636 0.3859144 [7] 0.2801304 0.1912505 0.1405093 -0.5958165 Largest eigenvalues: [1] 64380246 60764756 57290992 55911807 55623290 54129129 52377148 51945671 [9] 51900558 50992775 Smallest eigenvalues: [1] 0.4916623 0.4790996 0.4693066 0.4012584 0.4006772 0.3954213 [7] 0.3906656 0.3725708 0.3486859 -1.9300247 Largest eigenvalues: [1] 64702295 59820296 57335457 56191358 55004838 53241282 52323635 52172893 [9] 51566821 51092873 Smallest eigenvalues: [1] 0.47990139 0.45238224 0.40259296 0.38256312 0.30227513 0.26535360 [7] 0.24292439 0.13868423 -0.06141004 -0.21891877 Largest eigenvalues: [1] 63946157 60140374 56663768 55704405 54885120 52933251 51809082 51759477 [9] 51647852 50698286 Smallest eigenvalues: [1] 0.51157235 0.49522121 0.46731462 0.33745805 0.30334810 0.30140608 [7] 0.22643429 0.13796497 0.08756840 -0.06544513 Largest eigenvalues: [1] 64710870 59857441 56751433 56019946 54751169 53122990 52010800 51971413 [9] 51423895 50903149 Smallest eigenvalues: [1] 0.39949087 0.37235502 0.30856421 0.22903655 0.21925367 0.15862647 [7] 0.14623276 -0.02565325 -0.04445784 -0.27550225 Largest eigenvalues: [1] 63415089 60009727 56889798 55295528 54840613 53276551 52285753 51551078 [9] 51491608 51372653 Smallest eigenvalues: [1] 0.359829483 0.331258276 0.303209906 0.299162247 0.256095785 [6] 0.252738631 0.188437860 0.157476675 0.001085834 -0.579429972 Largest eigenvalues: [1] 65001954 60241882 57449551 56570135 55203748 53494362 52521684 52271228 [9] 51994277 51241550 Smallest eigenvalues: [1] 0.37676805 0.36729280 0.34050572 0.30216720 0.28579262 0.26278719 [7] 0.11360760 0.07049062 -0.05468144 -0.18554301 Largest eigenvalues: [1] 63544284 59593588 56683525 55480151 54766561 53089252 51922600 51494918 [9] 51215943 50400754 Smallest eigenvalues: [1] 0.39184921 0.30040396 0.29393589 0.28115497 0.27231923 0.24368198 [7] 0.16124018 0.09885927 -0.06887028 -1.69150468 Largest eigenvalues: [1] 63088719 59321166 56728169 55434641 54537993 52702113 51473535 51351258 [9] 51119368 50069754 Smallest eigenvalues: [1] 0.4553332 0.3971022 0.2933993 0.2720232 0.2656623 0.2252195 [7] 0.1037370 -0.2840356 -0.4677035 -1.5076144 Largest eigenvalues: [1] 65795423 60244141 57655530 56558759 54526442 52821614 52631452 51932744 [9] 51692279 51259193 Smallest eigenvalues: [1] 0.53513915 0.51730906 0.41651519 0.41455471 0.39496722 0.39406956 [7] 0.32016504 0.26737337 0.22457298 -0.05265831 Largest eigenvalues: [1] 65488487 60272135 57388174 56976371 54927802 53415494 53030421 51860383 [9] 51832425 50784738 Smallest eigenvalues: [1] 0.35224357 0.34422440 0.31197112 0.30782255 0.29258321 0.17575419 [7] 0.16322178 -0.01798261 -0.26720890 -0.72588366 Largest eigenvalues: [1] 65272261 60743599 57368458 57266427 54841104 53282623 53004851 52068704 [9] 51706089 50602336 Smallest eigenvalues: [1] 0.35759596 0.31716139 0.29613703 0.26070347 0.21753092 0.20600154 [7] 0.13654233 0.09757256 -0.22408220 -0.34184706 Largest eigenvalues: [1] 63308571 58903990 56657513 55239267 54244798 52713841 51286837 51235296 [9] 50998925 50031864 Smallest eigenvalues: [1] 0.4075897 0.3894776 0.3545177 0.3155203 0.3123807 0.2864491 [7] 0.2572327 0.1990279 -0.1027109 -0.2176474 Largest eigenvalues: [1] 65475929 60299338 57604392 56918074 54445914 53268217 52532546 51918874 [9] 51472021 50887152 Smallest eigenvalues: [1] 0.417262373 0.370415172 0.318272783 0.298750854 0.260924276 [6] 0.235796585 0.212527031 0.109641262 0.018504889 -0.009456925 Largest eigenvalues: [1] 64232646 59833300 57141033 55547940 54994029 53595169 52421594 51695527 [9] 51569081 51000073 Smallest eigenvalues: [1] 0.46129383 0.45564494 0.45311222 0.42202348 0.40970332 0.33243629 [7] 0.31537362 0.20116386 0.11811596 -0.01583709 Largest eigenvalues: [1] 65264468 60252003 57210923 56639838 54519328 53085982 52557245 52098320 [9] 51766660 51391227 Smallest eigenvalues: [1] 0.5596549 0.5408345 0.5291771 0.4029025 0.3659956 0.3277107 [7] 0.3147081 0.2236991 0.2153930 -0.4273122 Largest eigenvalues: [1] 63493791 60264180 56534822 55601952 55186272 53402944 52323426 51577385 [9] 51520428 51024610 Smallest eigenvalues: [1] 0.53273152 0.52131649 0.50268057 0.47818130 0.47777905 0.38559107 [7] 0.38175112 0.32922218 0.07503022 -0.02680991 Largest eigenvalues: [1] 63530336 59917992 57334925 55060569 54752303 53452412 51722245 51375344 [9] 51316142 50572724 Smallest eigenvalues: [1] 0.3916677 0.3309254 0.2970611 0.2724763 0.2476844 0.2261488 [7] 0.1857745 0.1826592 0.1298817 -0.3144904 Largest eigenvalues: [1] 64584752 59583116 57189172 56006554 54817252 53497694 52134606 51771477 [9] 51449029 50532788 Smallest eigenvalues: [1] 0.29512525 0.23333020 0.22457436 0.21964919 0.17558932 0.16705179 [7] 0.15335058 0.09649002 -0.11227937 -0.38290823 Largest eigenvalues: [1] 64859590 60396723 57411961 57316175 55201171 53461962 53026159 52991053 [9] 51875831 51737098 Smallest eigenvalues: [1] 0.40319651 0.38871163 0.36230782 0.32975262 0.31450860 0.23242065 [7] 0.16751442 0.01600815 -0.19571888 -1.54780793 Largest eigenvalues: [1] 64310420 60724044 56858840 56566576 55525964 53634657 52464549 52350785 [9] 51382783 50757362 Smallest eigenvalues: [1] 0.42645423 0.39457535 0.39052401 0.37274862 0.35373979 0.32300083 [7] 0.28534645 0.07733687 0.02175007 -0.10766890 Largest eigenvalues: [1] 64250624 59357636 56502570 55500244 54328037 52605530 51597715 51185999 [9] 51170640 50375457 Smallest eigenvalues: [1] 0.4940081 0.4512550 0.4480651 0.3450871 0.3081547 0.2801896 [7] 0.2209954 0.1930185 0.1417486 -2.4633483 Largest eigenvalues: [1] 64473988 60201569 57484231 56087414 55009464 53502326 52109001 52105646 [9] 51991123 51036796 Smallest eigenvalues: [1] 0.34094894 0.30247352 0.29784051 0.22030799 0.20937260 0.18245877 [7] 0.13034914 0.11024254 0.05144119 -0.10024005 Largest eigenvalues: [1] 63604271 59757937 56929159 56077979 54338481 53058201 51882309 51307312 [9] 51096078 50179560 Smallest eigenvalues: [1] 0.4365313 0.3545631 0.3024808 0.2439440 0.2417295 0.2346421 [7] 0.2000289 0.1833187 0.1436633 -0.1930913 Largest eigenvalues: [1] 66323308 59696128 57210281 56948276 54319203 53108030 52997645 51673164 [9] 51583620 50908623 Smallest eigenvalues: [1] 0.36944669 0.30323915 0.29815414 0.28669323 0.28087647 0.20646380 [7] 0.19130047 0.09419390 -0.02681965 -0.27967117 Largest eigenvalues: [1] 64070969 59333893 56834971 55775071 54723354 53337260 51844360 51793372 [9] 51525385 50499832 Smallest eigenvalues: [1] 0.35656785 0.34963449 0.34894534 0.32420575 0.30647333 0.28473943 [7] 0.18946273 -0.02356753 -0.04769855 -0.58674645 Largest eigenvalues: [1] 62203021 59169540 56333433 54764608 54477282 53108377 51681541 51310681 [9] 50450407 50099064 Smallest eigenvalues: [1] 0.5325449 0.4831067 0.4282271 0.4122233 0.3171908 0.2517061 [7] 0.2103692 0.1131749 -0.1703525 -0.2257619 Largest eigenvalues: [1] 62279427 59686807 56649691 54982989 54802630 53386692 52092308 51349748 [9] 50773898 50365945 Smallest eigenvalues: [1] 0.44211832 0.40863511 0.34859993 0.24051583 0.23440299 0.13783851 [7] 0.10078551 -0.02014391 -0.25833555 -1.63120835 Largest eigenvalues: [1] 63798169 59627777 57067799 55704278 54884957 52773462 52585041 51661808 [9] 51546183 51142853 Smallest eigenvalues: [1] 0.39176050 0.36830837 0.35747625 0.27621652 0.23309476 0.20905463 [7] 0.15521606 0.14552030 0.11963724 -0.04574377 Largest eigenvalues: [1] 64162241 60200539 57470088 55426386 55416852 53962289 52139995 52055183 [9] 51650950 50854422 Smallest eigenvalues: [1] 0.5133241 0.4682534 0.4410342 0.3521795 0.3230714 0.2765439 [7] 0.2744915 0.2442786 -0.1708914 -4.2609585 Largest eigenvalues: [1] 65302313 60850035 57578047 57223528 55392549 53387620 53287285 52844640 [9] 51668311 51217112 Smallest eigenvalues: [1] 0.4532789 0.4330580 0.4226647 0.3164623 0.2903435 0.2696899 [7] 0.2389523 0.2116961 0.1760464 -0.3022617 Largest eigenvalues: [1] 65397717 59995175 57439600 56629345 54959946 52939278 52824757 52408738 [9] 51442629 51115656 Smallest eigenvalues: [1] 0.31748105 0.26053256 0.25016996 0.20884109 0.19721868 0.17607537 [7] 0.10524407 0.00560777 -0.02931751 -0.64303134 Largest eigenvalues: [1] 65497215 59730601 57105664 56801009 54388392 52983851 52892659 51533260 [9] 51141710 50486499 Smallest eigenvalues: [1] 0.41720201 0.39661915 0.35727929 0.35456673 0.28845945 0.27680765 [7] 0.18218221 0.05004232 -0.01128930 -0.12347167 Largest eigenvalues: [1] 65356931 60522465 57507781 56627338 55620113 54105904 52672460 52629708 [9] 52218538 51318308 Smallest eigenvalues: [1] 0.36205589 0.34871849 0.28273238 0.22418022 0.20875546 0.17437463 [7] 0.16567923 -0.04916439 -0.26702663 -3.18829811 Largest eigenvalues: [1] 62209697 59452920 56069235 55084966 54606492 53297058 51617332 51198385 [9] 50566128 50256301 Smallest eigenvalues: [1] 0.40457757 0.37105234 0.34206980 0.33927739 0.15868956 -0.02547031 [7] -0.07879285 -0.43813273 -1.14065626 -1.17479422 Largest eigenvalues: [1] 65432187 60870258 58019615 55968546 55479928 53833269 52701600 52351659 [9] 52130279 51692544 Smallest eigenvalues: [1] 0.34341878 0.30212456 0.29010952 0.28025838 0.27375064 0.27019492 [7] 0.16770015 0.09688249 0.07176449 -0.24946901 Largest eigenvalues: [1] 62711165 59656769 57379756 55073601 54723046 53294179 51954264 51603531 [9] 51115351 50906062 Smallest eigenvalues: [1] 0.54474061 0.50659142 0.46336812 0.42630154 0.33749079 0.33244587 [7] 0.28352365 0.14666376 0.07919596 -0.06035519 Largest eigenvalues: [1] 63805937 59164911 56530360 55624688 54218193 52554919 51560218 51339992 [9] 51314967 50360362 Smallest eigenvalues: [1] 0.30101602 0.28826169 0.27843258 0.25444936 0.22981135 0.22476269 [7] 0.15038949 0.05483666 -0.16478223 -0.19878346 Largest eigenvalues: [1] 64047387 60445556 58050191 55737252 55293267 53975380 52530610 52200607 [9] 51928691 51519915 Smallest eigenvalues: [1] 0.20294527 0.20005520 0.16803595 0.03827905 -0.16311319 -0.33929826 [7] -0.38956689 -1.07044696 -1.37095910 -1.38460793 Largest eigenvalues: [1] 63932747 60135675 56932395 56290436 55127858 53340011 52155455 51666176 [9] 51444684 50595903 Smallest eigenvalues: [1] 0.492724720 0.481167581 0.426896712 0.405638200 0.393113643 [6] 0.357733413 0.265071693 0.235734511 -0.008893704 -2.288256463 Largest eigenvalues: [1] 64697231 60364936 56868480 56120573 55122591 53428250 52140123 52108474 [9] 51889065 51187687 Smallest eigenvalues: [1] 0.52633209 0.51642719 0.49476744 0.38630909 0.32661979 0.26909337 [7] 0.23463650 0.18014555 0.08618074 -0.10813541 Largest eigenvalues: [1] 64330205 60470271 57279212 56333215 55347612 53512567 52402168 52346187 [9] 52109575 51169935 Smallest eigenvalues: [1] 0.4930265 0.4871813 0.4809229 0.4053347 0.3108328 0.3063834 [7] 0.2436045 0.1817364 0.1237841 -0.2755930 Largest eigenvalues: [1] 65716885 59705953 56986734 56550361 53870348 52945000 52268727 51484461 [9] 50731342 50412256 Smallest eigenvalues: [1] 0.44994614 0.42942450 0.35324007 0.33329498 0.30203708 0.29279263 [7] 0.23324230 0.15109102 -0.09354433 -0.35239474 Largest eigenvalues: [1] 65744021 60041569 57747700 57038537 54784736 53050326 53018727 52797879 [9] 51919454 51816021 Smallest eigenvalues: [1] 0.4915165 0.4872079 0.4370600 0.3214289 0.2785962 0.2576738 [7] 0.2525378 0.1907475 0.1704417 -0.1586498 Largest eigenvalues: [1] 65727945 60759489 57711568 57705463 54880238 53525622 52450331 52388966 [9] 51291747 51035598
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9909572 | 0.5825788 | 15.19244 | 0.215 | 2.768191 | 1.895482 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + steps + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
steps = steps_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_steps_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
steps = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 18. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Warning message in `^.fd`((outcome - yhatfd), 2): "The maximum error exceeds the tolerance level." Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 494 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.11759975 0.11519453 0.05519783 0.02168391 -0.04459219 [6] -0.09989738 -1.05867264 -1.47554572 -11.60490337 -13.53925404 Largest eigenvalues: [1] 59245918 56629705 53475221 52475840 51757610 50512526 49485579 48628830 [9] 48218405 47962559 Smallest eigenvalues: [1] 0.2968488 0.2902908 0.2559251 0.1743317 0.1023142 -0.2114283 [7] -0.8582463 -1.0708047 -1.1728633 -5.7160740 Largest eigenvalues: [1] 57335614 55646417 53634531 51594638 50710648 50208133 48894550 48682473 [9] 47749715 47297030 Smallest eigenvalues: [1] 0.46646169 0.43266819 0.40268675 0.34542728 0.33899549 0.27604763 [7] 0.21518843 -0.04439961 -0.08697455 -0.10675487 Largest eigenvalues: [1] 61891445 56833394 54174126 53124009 52035557 50227685 49511141 49117547 [9] 48753677 48086907 Smallest eigenvalues: [1] 0.29240381 0.25898917 0.16912645 0.09819217 0.08802493 [6] -0.19444433 -1.01707435 -11.44428156 -13.99880807 -42.19122326 Largest eigenvalues: [1] 61693579 57109248 54324750 52873440 52594541 51243848 49695208 49374592 [9] 49181295 48454970 Smallest eigenvalues: [1] 0.3290388 0.3046865 0.1934457 0.1716797 0.1638666 0.1561956 [7] 0.1255125 -0.2168174 -0.2202073 -1.6885551 Largest eigenvalues: [1] 60775416 55947781 53303029 52021440 51501452 49876116 48674032 48384849 [9] 48329665 47793670 Smallest eigenvalues: [1] 0.35693130 0.35556831 0.29404053 0.26534479 0.23321912 0.23250682 [7] 0.20574500 -0.03224006 -0.90437380 -5.19732786 Largest eigenvalues: [1] 62864191 57828059 55246663 54568444 52453687 50897463 50631186 50154481 [9] 49299434 48973227 Smallest eigenvalues: [1] 0.55228671 0.52477481 0.50700061 0.46892508 0.42574676 0.35019430 [7] 0.34164607 0.28353283 0.23420201 -0.09955738 Largest eigenvalues: [1] 59749237 56959547 53668197 52594403 52017224 50788609 49017217 48761961 [9] 48391576 47687237 Smallest eigenvalues: [1] 0.34691679 0.30183280 0.21546352 0.18962791 0.11094857 [6] 0.05107483 0.01350571 -4.33859106 -6.87438138 -10.93928184 Largest eigenvalues: [1] 61814410 56408173 54134546 53708707 51795569 50161435 49810957 49726725 [9] 48944852 48843286 Smallest eigenvalues: [1] 0.4479376 0.4420109 0.4150566 0.3618554 0.3291921 0.2802027 [7] 0.2724389 0.2164615 0.2148165 -0.8769721 Largest eigenvalues: [1] 61112611 57309352 54400590 53302545 52513984 51012538 49860963 49634059 [9] 49308484 48695084 Smallest eigenvalues: [1] 0.36765701 0.27709309 0.24644595 0.21760698 0.20000906 0.07727509 [7] 0.05621599 -0.46268686 -0.67529846 -3.04380053 Largest eigenvalues: [1] 58499610 56591831 54457543 52769628 51170826 51070651 49436369 48831489 [9] 48013527 47987099 Smallest eigenvalues: [1] 0.54331783 0.46039474 0.35717020 0.34185921 0.34055743 0.30891443 [7] 0.25758706 0.10036070 0.07583772 -0.02015530 Largest eigenvalues: [1] 61056489 57482029 54531451 53524846 52419883 50654515 49816701 49771907 [9] 49247928 48748222 Smallest eigenvalues: [1] 0.42712189 0.36935038 0.33173277 0.26881560 0.15675431 [6] 0.08015566 0.00677776 -0.11457602 -0.68594026 -15.44410703 Largest eigenvalues: [1] 60197362 56625966 54049204 52607662 52127553 51045418 49729883 49373652 [9] 48550413 48444360 Smallest eigenvalues: [1] 0.37240511 0.34305442 0.31520964 0.29327685 0.22128216 0.09462863 [7] -0.08661080 -0.50111993 -0.98650489 -5.63090737 Largest eigenvalues: [1] 62254350 56400819 53909758 53682415 51618808 50157738 49962612 48554508 [9] 48444314 47701039 Smallest eigenvalues: [1] 0.3863344 0.3813188 0.3012086 0.2897377 0.2519886 0.2326829 [7] 0.2099434 -0.1670564 -0.2601984 -0.8751103 Largest eigenvalues: [1] 60100246 56911689 54086487 52407588 52367403 50788343 50090434 48853006 [9] 48781638 48566371 Smallest eigenvalues: [1] -0.2731970 -0.4286934 -0.8271097 -1.1930917 -2.0237089 -2.0915327 [7] -2.3495205 -11.5548913 -12.0930681 -69.8219340 Largest eigenvalues: [1] 59375038 57712448 54297011 53246840 52938850 51605419 49806368 49748626 [9] 49014867 48612300 Smallest eigenvalues: [1] 0.4611782 0.4279020 0.4050982 0.2933056 0.2739197 0.2696547 [7] 0.1832078 0.1753487 -0.1893700 -0.6278470 Largest eigenvalues: [1] 60425330 56734544 54477260 52943308 52069613 50950880 49347148 49153974 [9] 49074688 48461820 Smallest eigenvalues: [1] 0.33737855 0.31209078 0.27228518 0.24297865 0.17020246 0.04907851 [7] -0.29359870 -0.37106095 -0.97303966 -2.48997571 Largest eigenvalues: [1] 62930916 56840134 53972054 53782999 51666865 50145720 49733692 49476632 [9] 48758477 48707332 Smallest eigenvalues: [1] 0.44592438 0.42762621 0.41546562 0.35814751 0.33036455 0.28248199 [7] 0.03454255 -0.14562384 -0.35093582 -1.59169841 Largest eigenvalues: [1] 61579943 56653299 54001202 53404481 51883928 49999807 49648605 49288175 [9] 48856094 48358405 Smallest eigenvalues: [1] 0.45363288 0.35412169 0.34089316 0.32415592 0.30423113 0.26846921 [7] 0.23922576 0.03197619 -0.08439322 -0.46382878 Largest eigenvalues: [1] 60728630 56320359 53806531 52960559 51507639 50066450 49458109 49182146 [9] 48893742 48284364 Smallest eigenvalues: [1] 0.23418695 0.21495560 0.18868886 0.18093427 0.11169582 [6] 0.03139363 -0.17483405 -1.82412015 -10.74849169 -22.07613889 Largest eigenvalues: [1] 60720412 56915818 54803061 53104835 51901310 50713366 50020050 49293391 [9] 49194108 49044345 Smallest eigenvalues: [1] 0.4791541 0.3776639 0.3062627 0.3002259 0.2444965 0.2004157 [7] -0.3939639 -0.6318045 -1.4427837 -3.3612877 Largest eigenvalues: [1] 61161939 56879840 54232730 53100902 52329578 50507937 49799715 49424589 [9] 49252267 48757219 Smallest eigenvalues: [1] 0.3236475 0.2880414 0.2326896 0.2230478 0.1632813 0.1424908 [7] 0.1251832 0.1068714 -1.9343528 -9.7313114 Largest eigenvalues: [1] 62155928 57747025 54689623 54266140 52733209 50887048 50538968 50010091 [9] 49671569 48917473 Smallest eigenvalues: [1] 0.4872420 0.4487984 0.4271718 0.4192335 0.4017726 0.3225788 [7] 0.1729355 0.1591491 -0.2141052 -0.8487638 Largest eigenvalues: [1] 60504797 57239842 54175451 52539333 52444032 50726191 50443102 48908511 [9] 48728045 48683492 Smallest eigenvalues: [1] 0.53461271 0.48547053 0.47406165 0.39456752 0.32932617 0.32184410 [7] 0.29093931 0.28071698 0.18775976 -0.07469584 Largest eigenvalues: [1] 60073449 57040056 54248758 52667126 52603923 51047712 49768308 49426886 [9] 48931052 48570327 Smallest eigenvalues: [1] 0.44119098 0.41827476 0.39213393 0.34028222 0.25456716 0.16724314 [7] 0.10696716 0.04529755 -0.06778547 -0.36721073 Largest eigenvalues: [1] 61457079 56621538 54340759 52857037 51636916 50182194 49232907 48666262 [9] 48594763 48136801 Smallest eigenvalues: [1] 0.2594248 0.2516792 0.2480985 0.1578670 0.1519393 0.1081103 [7] -0.1278886 -0.5668698 -1.6745653 -10.0845201 Largest eigenvalues: [1] 61314579 56684920 53893412 53561468 51942446 50368371 49859886 49695803 [9] 49383547 48777180 Smallest eigenvalues: [1] 0.22798913 0.21909386 0.16941158 0.05328828 -0.09062188 [6] -0.86903849 -1.26128342 -3.07959504 -10.95140912 -29.20921916 Largest eigenvalues: [1] 62962353 56386879 53853135 53815449 51603355 50163768 50035777 48931640 [9] 48787791 48168370 Smallest eigenvalues: [1] 0.4188670 0.3932071 0.1894995 0.1368815 0.1012176 -0.1680160 [7] -0.2088754 -1.0543885 -8.4287623 -11.4399237 Largest eigenvalues: [1] 60679256 56937760 54121591 52664065 51967571 50636571 49281409 48997111 [9] 48837546 48252386 Smallest eigenvalues: [1] 0.5221675 0.3894817 0.3861179 0.3683855 0.2644577 0.1943920 [7] 0.1692925 0.1275275 -0.0937813 -0.5795524 Largest eigenvalues: [1] 63008211 57009017 54208604 54070344 51666105 50386115 50114857 49485544 [9] 48574724 48542878 Smallest eigenvalues: [1] 0.4145045 0.4004049 0.3528923 0.3325280 0.3027909 0.2276010 [7] 0.1843536 -0.1353789 -0.3149606 -7.9084575 Largest eigenvalues: [1] 60235442 56507991 53940088 51935999 51925229 50535442 49266401 49192223 [9] 48546096 48220159 Smallest eigenvalues: [1] 0.54718904 0.45704070 0.44215172 0.37311816 0.31923690 0.28381915 [7] 0.23811836 0.22528975 0.20187192 -0.02876468 Largest eigenvalues: [1] 62013844 57437373 55188980 53925129 52026848 50680396 50280096 49839331 [9] 49197142 48960719 Smallest eigenvalues: [1] 0.4764141 0.4610814 0.4021038 0.3001321 0.2733321 0.2050224 [7] 0.1822829 0.1470086 -0.2307073 -0.5491573 Largest eigenvalues: [1] 61318845 57163105 54560978 53143360 52114501 50817331 49467576 49458077 [9] 49076698 48213066 Smallest eigenvalues: [1] 0.3391626 0.3055882 0.2921771 0.2559696 0.2400783 0.1816054 [7] 0.1794299 0.1246618 -0.8123703 -15.5866890 Largest eigenvalues: [1] 62064495 56931142 53938643 53925033 51708935 50153576 49985154 49254215 [9] 48975858 48145325 Smallest eigenvalues: [1] 0.4146259 0.4100722 0.3598118 0.3239598 0.2661714 0.1991941 [7] -0.1440754 -0.1987744 -0.3481176 -4.1354358 Largest eigenvalues: [1] 60056153 56326656 54107198 52343688 51643112 50229536 48925766 48711834 [9] 48644806 48013559 Smallest eigenvalues: [1] 0.5114456 0.5110935 0.4277844 0.3714690 0.3198004 0.3138220 [7] 0.2850153 0.2095667 0.1482962 -29.0201435 Largest eigenvalues: [1] 60851866 56728473 54098955 52715965 52136091 50514027 49100554 48993319 [9] 48970296 48290553 Smallest eigenvalues: [1] 0.3944503 0.3516754 0.3143969 0.3047692 0.2429552 0.2102555 [7] 0.1502172 -0.3353203 -1.2060121 -3.1789042 Largest eigenvalues: [1] 61070546 57394393 54315127 53480998 52162167 50340978 49867109 49708462 [9] 49244724 48857077 Smallest eigenvalues: [1] 0.113088231 0.094316288 0.075390459 0.036136766 0.002208176 [6] -0.006923469 -2.984921289 -9.321882566 -12.690959167 -15.554148219 Largest eigenvalues: [1] 63490961 57049906 54923155 53913797 51910793 50243260 50146537 50070822 [9] 49223306 48676352 Smallest eigenvalues: [1] 0.4183586 0.3950555 0.3725973 0.3288589 0.3176722 0.3142408 [7] 0.3025289 0.2595539 0.1312363 -0.1145698 Largest eigenvalues: [1] 59744426 57442701 54790866 52463562 52447190 50858899 49539838 49442668 [9] 48882692 48442816 Smallest eigenvalues: [1] 0.48956398 0.42135454 0.37455086 0.29762072 0.24342317 0.19116131 [7] 0.03167908 -0.08248460 -0.96648072 -2.47144597 Largest eigenvalues: [1] 61759559 56761289 54534142 52995044 52191875 50653175 49461866 49392142 [9] 49285025 48580510 Smallest eigenvalues: [1] 0.4238634 0.3818149 0.3597098 0.2911985 0.2626952 0.1885168 [7] 0.1605276 -0.4311474 -0.5174386 -10.2106185 Largest eigenvalues: [1] 61179995 56396167 54087079 53098194 51861298 50522799 49441731 49251275 [9] 49070439 48609179 Smallest eigenvalues: [1] 0.4147044 0.4015553 0.3394930 0.3121006 0.2667017 0.2616047 [7] 0.2528266 0.1812171 0.1657170 -1.7011160 Largest eigenvalues: [1] 61157518 56521960 54365071 53442703 51823245 50411063 49669646 49153948 [9] 48835764 48329098 Smallest eigenvalues: [1] 0.18942804 0.14448785 0.13239920 0.05528852 -0.27432728 [6] -0.30785054 -0.31640422 -0.36618001 -6.34829127 -22.13692338 Largest eigenvalues: [1] 58635530 55438487 53012841 51771735 50907036 49148899 48882610 48075347 [9] 47881398 47110458 Smallest eigenvalues: [1] 0.249695769 0.211028418 0.202322279 0.169881178 0.122353370 [6] 0.008093507 -0.161168349 -0.932892518 -6.524469994 -10.180626411 Largest eigenvalues: [1] 61962853 57838443 54984396 53987142 53495190 52378410 50263005 50144084 [9] 49734618 49407434 Smallest eigenvalues: [1] 0.361174024 0.330285475 0.258207747 0.195258201 0.183085791 [6] 0.001193101 -0.705694625 -3.681444560 -5.112545924 -9.283382626 Largest eigenvalues: [1] 60413866 57641720 54872685 52966248 52286935 50973801 49471675 49355282 [9] 49256283 48274166 Smallest eigenvalues: [1] 0.6166202 0.4695622 0.3833293 0.3734358 0.3288334 0.2833482 [7] 0.2628883 0.1881330 -0.1394222 -1.4746451 Largest eigenvalues: [1] 59726850 56940808 54267439 52532132 52407333 50778447 49584830 49035800 [9] 48775019 48276421 Smallest eigenvalues: [1] 0.43779533 0.36497834 0.36094199 0.29900326 0.28646825 0.24572136 [7] 0.23743605 0.17479466 -0.06053218 -0.08321880 Largest eigenvalues: [1] 59942459 57176870 54388728 52768363 51714161 50301213 49189077 49001275 [9] 48613944 47952766 Smallest eigenvalues: [1] 0.50769080 0.50138379 0.48418870 0.46307965 0.43256934 0.33604290 [7] 0.32475068 0.05034399 0.03016553 -3.52485595 Largest eigenvalues: [1] 61472170 57305477 54491434 53249254 52491182 50721421 49635856 49456923 [9] 49088985 48414204 Smallest eigenvalues: [1] 0.4131480 0.3989692 0.3425488 0.3156007 0.2979224 0.2150130 [7] 0.1968052 0.1802540 -1.3699372 -2.1946783 Largest eigenvalues: [1] 60309041 56449268 53882962 53386097 52003840 50401483 49431240 49393710 [9] 49339898 48046268 Smallest eigenvalues: [1] 0.454983217 0.447439925 0.415389735 0.336387445 0.271972727 [6] 0.221753311 0.186994865 0.007259486 -0.153224177 -0.520963187 Largest eigenvalues: [1] 60111228 56733244 54218667 52489072 52083331 50524250 49455240 49239889 [9] 48811009 48504413 Smallest eigenvalues: [1] 0.35546959 0.24179450 0.21292127 0.20954633 -0.03963395 [6] -0.26582023 -1.14257157 -2.42615706 -11.40986207 -15.78527904 Largest eigenvalues: [1] 62298669 56637372 54096249 53545406 51799385 50061752 49712836 49471073 [9] 48898662 48566474 Smallest eigenvalues: [1] 0.2836360 0.2369638 0.2292395 0.2147618 0.2067926 0.1418923 [7] 0.1319408 -0.1273847 -2.2732207 -13.4753350 Largest eigenvalues: [1] 62440982 56411608 54562908 53736822 51432623 50099069 49890788 48694702 [9] 48652586 48123596 Smallest eigenvalues: [1] 0.51912687 0.50254954 0.45571812 0.44412072 0.35295712 0.30750587 [7] 0.26695784 0.11186332 0.09387339 -0.61540948 Largest eigenvalues: [1] 60591727 56626455 54070547 52735474 51572975 50134909 49031375 49013942 [9] 48920168 48202195 Smallest eigenvalues: [1] 0.5307333 0.4908078 0.4671842 0.4239771 0.3775175 0.3350041 [7] 0.3130766 0.2655266 0.1010292 -0.2088797 Largest eigenvalues: [1] 60300559 57573436 54105856 53031227 52870246 51056802 50095453 49275359 [9] 49201315 48887680 Smallest eigenvalues: [1] 0.3973149 0.3556538 0.3340458 0.3114995 0.2456433 0.1992295 [7] 0.1964905 0.1137582 -0.3499786 -2.4821498 Largest eigenvalues: [1] 61325200 57390753 54660974 53222116 52402501 50961781 49797175 49540658 [9] 49505228 48866784 Smallest eigenvalues: [1] 0.35802820 0.34471978 0.32447953 0.28311807 0.12905468 0.09609255 [7] -0.17173486 -0.81161470 -1.49030615 -8.01710727 Largest eigenvalues: [1] 61105056 57600613 54252543 52846901 52746143 51178089 49955702 49401403 [9] 49054536 48925471 Smallest eigenvalues: [1] 0.43390788 0.37073338 0.36964699 0.35097726 0.29428743 [6] 0.28881210 0.26866382 0.23325600 0.04592056 -11.75393737 Largest eigenvalues: [1] 61016677 56412659 53930387 52725276 52052943 50438193 49097018 49000895 [9] 48883758 48055595 Smallest eigenvalues: [1] 0.4111781 0.3725650 0.3368662 0.2958664 0.2206949 0.2140575 [7] 0.1535194 -0.2664744 -1.3362325 -11.0143638 Largest eigenvalues: [1] 59599315 57114738 53600852 52393269 52067428 50648499 49057992 48984109 [9] 48384993 48122583 Smallest eigenvalues: [1] 0.3581320 0.2834164 0.2573484 0.2416377 0.1712044 0.1697558 [7] 0.1219815 -0.4340061 -0.5299346 -0.6310965 Largest eigenvalues: [1] 60694692 56190538 53771517 53017580 51315582 50191127 49258926 49008045 [9] 48771213 48227428 Smallest eigenvalues: [1] -0.06957346 -0.69990562 -0.91569788 -3.87719687 -7.24516399 [6] -9.99605959 -12.17572032 -32.59852715 -77.44131140 -142.68799897 Largest eigenvalues: [1] 60926567 56669758 54270644 52934279 51757160 50086238 49290057 49030890 [9] 48539484 47856430 Smallest eigenvalues: [1] 0.44679968 0.41970681 0.38915842 0.38427637 0.37684401 0.28202215 [7] 0.23731764 0.08698706 -0.10962923 -0.18634335 Largest eigenvalues: [1] 61183873 57811999 54796575 53229648 52923125 51169044 50545780 49613827 [9] 49608897 49159634 Smallest eigenvalues: [1] 0.4973586 0.4885806 0.4161627 0.4074907 0.3329852 0.2052987 [7] 0.1725354 0.1279403 -0.2014513 -4.0684164 Largest eigenvalues: [1] 60557047 56582110 53711961 52599003 52142463 50456394 49254656 48991196 [9] 48761541 48038835 Smallest eigenvalues: [1] 0.4206073 0.4119398 0.3644903 0.3559738 0.3550427 0.1870505 [7] 0.1499121 0.1292920 -0.4167845 -4.4295726 Largest eigenvalues: [1] 61477673 56866303 54329184 53066082 52453835 50883401 49741483 49568486 [9] 49310784 48834912 Smallest eigenvalues: [1] 0.4456224 0.4168914 0.4087419 0.3977425 0.3261181 0.2809803 [7] 0.2306873 0.2027823 0.1898369 -1.0165076 Largest eigenvalues: [1] 61172848 57042612 54016712 53647687 52008150 50555613 49786323 49371571 [9] 49229520 48526436 Smallest eigenvalues: [1] 0.3731567 0.3267541 0.3154992 0.2682366 0.2471300 0.2036301 [7] 0.1528135 -1.2046827 -1.4145005 -5.3339228 Largest eigenvalues: [1] 59857068 56182176 53494297 52266129 52252567 50493172 49088951 48560899 [9] 48401003 47804132 Smallest eigenvalues: [1] 0.42126079 0.37101802 0.25585390 0.24573844 0.22444463 0.09371462 [7] -0.39882779 -0.43058873 -1.56692294 -3.56178020 Largest eigenvalues: [1] 61081531 56030956 53920676 52651019 51311079 50000893 48925123 48606546 [9] 48496508 47713954 Smallest eigenvalues: [1] 0.49432625 0.44908377 0.41304375 0.39721556 0.27296106 [6] 0.21336588 0.08215902 0.06022717 0.04705052 -13.97191738 Largest eigenvalues: [1] 59269030 56279917 53747922 52145189 51331423 50578244 48986019 48848520 [9] 47981560 47698970 Smallest eigenvalues: [1] 0.4295923 0.4140698 0.4068561 0.3687875 0.3117716 0.2848645 [7] 0.2307433 0.1739668 -0.2250700 -0.5682320 Largest eigenvalues: [1] 58437369 56598188 53572341 52148164 51591648 50412770 49331875 49180125 [9] 48251262 47891608 Smallest eigenvalues: [1] 0.3989619 0.3247437 0.2543453 0.2067893 0.0680325 -0.1619079 [7] -0.1753853 -0.5725849 -1.7198096 -3.9826874 Largest eigenvalues: [1] 60555950 55718039 53242434 52062238 51672767 49991698 48591294 48459830 [9] 48372495 47610866 Smallest eigenvalues: [1] 0.4416527 0.4242140 0.3336121 0.2590310 0.2322976 0.1830904 [7] 0.1564058 0.1431793 0.0863002 -0.1187603 Largest eigenvalues: [1] 60342299 57835459 54374215 53187720 52552721 50994644 49725055 49646410 [9] 49458075 48710997 Smallest eigenvalues: [1] 0.5261730 0.5088191 0.4159429 0.3292228 0.2934735 0.2896869 [7] 0.2499551 -0.1812845 -0.4459341 -0.5181454 Largest eigenvalues: [1] 61262176 56608542 54414812 52811980 51951915 50777890 49236254 49189165 [9] 49122921 48461773 Smallest eigenvalues: [1] 0.306810571 0.236969787 0.185972633 0.153230686 0.004056011 [6] -0.066945430 -0.997909603 -1.801615016 -6.788588521 -10.613827741 Largest eigenvalues: [1] 63697119 57601193 55451158 54906184 52344810 51167320 50836596 50222501 [9] 49753105 49596851 Smallest eigenvalues: [1] 0.43087060 0.42819020 0.37351278 0.34727754 0.25345057 0.21872589 [7] 0.20082096 0.08937241 -0.06069351 -1.09444289 Largest eigenvalues: [1] 61338026 56809605 54086211 53246091 52102294 50360118 49419697 48989028 [9] 48961458 47936963 Smallest eigenvalues: [1] 0.4785558 0.4545345 0.4355433 0.3834228 0.3795366 0.2817536 [7] 0.2795443 0.2356011 0.1524734 -0.4032405 Largest eigenvalues: [1] 59641447 57278318 54118455 52686964 52301256 50937531 49413421 48827461 [9] 48616556 47989657 Smallest eigenvalues: [1] 0.3547494 0.3340287 0.3149641 0.3004229 0.2511517 0.2173563 [7] 0.1908252 -0.1218631 -0.2195041 -6.8143711 Largest eigenvalues: [1] 62522106 57373142 54621037 54071964 51838623 50428058 50188222 49520846 [9] 49027912 48795444 Smallest eigenvalues: [1] 0.25413821 0.22440340 0.19354317 0.18093980 0.16034082 0.06936268 [7] 0.05456476 -0.15390239 -0.78322330 -3.96930435 Largest eigenvalues: [1] 62267157 57384473 54311082 53286428 52311041 50776157 49695586 49495533 [9] 49270716 48825298 Smallest eigenvalues: [1] 0.403415460 0.372922764 0.339053058 0.308029621 0.296865242 [6] 0.257756560 0.211835773 0.006137938 -0.039944218 -0.091656262 Largest eigenvalues: [1] 62005980 57669417 54862619 53372524 52728561 51079601 50723890 49881147 [9] 49521612 49286148 Smallest eigenvalues: [1] 0.48421445 0.42266337 0.41061960 0.37540273 0.35247323 0.31382722 [7] 0.10349166 0.06073065 0.04195059 -4.97035155 Largest eigenvalues: [1] 61108550 57018537 54354470 53153835 51677289 50253458 49456921 49062800 [9] 48984406 48415007 Smallest eigenvalues: [1] 0.4597145 0.3911165 0.3713723 0.3047817 0.2637179 0.2540702 [7] 0.2459730 0.2313930 -0.4791964 -6.3026274 Largest eigenvalues: [1] 61306977 57334890 54582804 53793788 52392278 50984607 50100755 49872235 [9] 49510908 49029129 Smallest eigenvalues: [1] 0.4897942 0.4739730 0.4319149 0.3257935 0.2791753 0.2598534 [7] 0.2526025 0.2086651 0.1217125 -0.3170514 Largest eigenvalues: [1] 60485843 56521823 53884756 52759899 52065255 50292977 49146549 49073745 [9] 48698429 48135526 Smallest eigenvalues: [1] 0.48148525 0.47626800 0.46879729 0.39841969 0.39055755 0.37036864 [7] 0.30480696 0.29716127 0.09492443 -0.04393594 Largest eigenvalues: [1] 61086914 56652700 54365087 53124494 51840947 50383637 49431866 49089863 [9] 48646044 48145694 Smallest eigenvalues: [1] 0.26611074 0.25478846 0.23320243 0.22843295 0.21715994 0.17639351 [7] -0.01506566 -0.41094364 -2.71405257 -3.49042894 Largest eigenvalues: [1] 61215433 57051291 54076384 53546532 51973888 50601201 49845991 49775417 [9] 49103010 48800738 Smallest eigenvalues: [1] 0.447222948 0.396876004 0.311891116 0.275035248 0.240900106 [6] 0.150489201 0.086193432 0.006348429 -1.201057540 -5.934954429 Largest eigenvalues: [1] 61794747 56796461 53656606 53090329 52016389 50216736 49412447 49216863 [9] 48949739 48057932 Smallest eigenvalues: [1] 0.4169468 0.4169186 0.3431241 0.3123001 0.2875054 0.2140677 [7] 0.1974103 0.1139702 0.0975766 -0.1464623 Largest eigenvalues: [1] 60524750 56542780 54161682 52268750 51900306 50212497 48939315 48666610 [9] 48394236 47714533 Smallest eigenvalues: [1] 0.33377520 0.29669175 0.25779849 0.19924455 0.15468778 0.14136234 [7] 0.06924209 0.01030865 -0.83360067 -8.31590613 Largest eigenvalues: [1] 62050605 56879991 54525441 53493738 52258673 50492890 49906021 49615972 [9] 48977404 48828274 Smallest eigenvalues: [1] 0.50058824 0.39455557 0.35382297 0.34451543 0.22634708 [6] 0.18915167 0.03251033 -6.37260431 -13.26185894 -17.67832275 Largest eigenvalues: [1] 60572361 58024267 54600930 53503349 52983186 51861155 50027642 49522153 [9] 49314065 48637627 Smallest eigenvalues: [1] 0.41945312 0.38515364 0.34761576 0.27592034 0.27075476 [6] 0.17238199 -0.08076965 -5.78931843 -19.62834862 -20.10019192 Largest eigenvalues: [1] 60196312 56652116 53977135 52185610 52182334 50751620 49244330 48723249 [9] 48487178 48186290 Smallest eigenvalues: [1] 0.408462003 0.380986416 0.378335412 0.322107615 0.311387884 [6] 0.307542467 0.265929143 -0.005566618 -0.265109312 -0.409352524 Largest eigenvalues: [1] 59587111 57182708 53826952 52441984 52037795 50569805 49189556 48761287 [9] 48347380 48043992 Smallest eigenvalues: [1] 0.3932513 0.3331562 0.3227514 0.2262686 0.1743011 -0.1437699 [7] -1.7674359 -12.6282563 -18.2846170 -20.2854838 Largest eigenvalues: [1] 60391028 56085431 53849415 52415926 51822335 50401537 49470672 49012327 [9] 48598764 48182975 Smallest eigenvalues: [1] 0.4585123 0.4461084 0.4249138 0.2899170 0.2285372 0.2049880 [7] 0.1622307 0.1256476 -0.3369741 -0.3867203 Largest eigenvalues: [1] 61269712 57390183 54975354 53205469 52783058 51392109 50252786 49922589 [9] 49549337 49242031 Smallest eigenvalues: [1] 0.45219267 0.43940677 0.42820670 0.37751718 0.37465681 0.17953060 [7] 0.14428141 0.09077744 0.01352761 -0.80323463 Largest eigenvalues: [1] 59999976 56566075 53701652 52051650 51729929 50021719 48928094 48672877 [9] 48406386 48098398 Smallest eigenvalues: [1] 0.49965674 0.48492225 0.46107986 0.38251331 0.28348803 0.25407320 [7] 0.19090658 0.13405570 0.01850294 -2.61042749 Largest eigenvalues: [1] 60238845 56672888 53875686 52380399 52059900 50433273 49015866 48863855 [9] 48728360 47946459 Smallest eigenvalues: [1] 0.61565611 0.52233607 0.47578075 0.39249330 0.37199130 0.33022113 [7] 0.32125124 0.27509777 -0.02030376 -0.05628125 Largest eigenvalues: [1] 60286176 56856941 53860023 52812890 51856791 50005682 49230675 49133814 [9] 48444190 47939792 Smallest eigenvalues: [1] 0.28164146 0.23851359 0.18457693 0.12258670 0.11383483 0.09470023 [7] 0.06534050 -1.44717167 -1.60317122 -9.28455724 Largest eigenvalues: [1] 62150861 57151954 54729817 53831207 51976395 50889562 49958038 49759145 [9] 49481168 48884867 Smallest eigenvalues: [1] 0.2993253 0.2821829 0.2598497 0.2368275 0.2041751 0.1596735 [7] 0.1095080 -1.4313192 -3.1491655 -5.5037315 Largest eigenvalues: [1] 61018699 56340256 53368652 53132473 52030079 50437178 49757096 49239209 [9] 49124996 48372487 Smallest eigenvalues: [1] 0.4516830 0.4360128 0.4112397 0.3552742 0.3454499 0.2918701 [7] 0.2885161 0.2324237 0.2250454 -0.1474921 Largest eigenvalues: [1] 61690822 56916206 54439533 53782931 52181547 50798969 49883515 49111756 [9] 48944308 48114081 Smallest eigenvalues: [1] 0.28538274 0.28202882 0.23848967 0.18042887 0.12495418 0.03194275 [7] -0.22312054 -0.32481396 -0.39048135 -4.58400882 Largest eigenvalues: [1] 61825049 57079564 54225154 53042584 51508847 50012325 49356596 48860871 [9] 48558914 48387418 Smallest eigenvalues: [1] 0.28357656 0.21813584 0.17968909 0.17494122 0.15614628 0.14061061 [7] 0.03631024 -0.03953230 -0.25040715 -1.52006269 Largest eigenvalues: [1] 59164882 57838843 54478613 52617481 52459788 51151450 49980419 49455649 [9] 48742913 48522301 Smallest eigenvalues: [1] 0.3624519 0.3207424 0.3172560 0.3113898 0.2914644 0.2641308 [7] 0.1717547 -0.5380479 -1.0863691 -2.0025998 Largest eigenvalues: [1] 61755019 56590527 54282711 53327268 51638264 50442226 49622802 49100932 [9] 49039210 48419945 Smallest eigenvalues: [1] 0.43946763 0.33247870 0.31606122 0.31490379 0.23805887 0.21511067 [7] 0.14832635 0.09288727 0.08143682 -1.30062209 Largest eigenvalues: [1] 60620452 57134791 53938702 52770365 52266613 50738889 49553374 49292226 [9] 49083803 48648888 Smallest eigenvalues: [1] 0.39322027 0.33423365 0.31371202 0.30882274 0.24341675 0.08990376 [7] -0.05676246 -0.09629991 -1.03522009 -4.82005734 Largest eigenvalues: [1] 62185374 57275931 55023556 53532910 52403124 51019629 49962576 49826114 [9] 49232766 48577439 Smallest eigenvalues: [1] 0.36732900 0.36029602 0.30194448 0.25616272 0.23158903 0.22158520 [7] 0.09939661 0.05015184 -0.63015971 -5.26621088 Largest eigenvalues: [1] 59002037 55741746 53269409 52261739 51529384 49810198 48992140 48978161 [9] 48311860 47777005 Smallest eigenvalues: [1] 0.4918751 0.4818147 0.4359612 0.4082334 0.3729911 0.2993039 [7] 0.2710861 0.2103083 0.1652060 -0.2060750 Largest eigenvalues: [1] 60465603 57068268 54279561 52978452 52123235 50329800 49669936 49280694 [9] 48998277 48486508 Smallest eigenvalues: [1] 0.3742797 0.3518233 0.2982323 0.2850500 0.2735075 0.2697046 [7] 0.1588766 -0.5200624 -0.5337557 -2.1151559 Largest eigenvalues: [1] 61419550 57598873 55079997 53557571 52766210 51559348 50521184 50042266 [9] 49805927 49491838 Smallest eigenvalues: [1] 0.41925081 0.39552453 0.35476501 0.29666376 0.24516182 0.22831872 [7] 0.17512874 0.04962938 -1.48088563 -1.50109603 Largest eigenvalues: [1] 61966505 56921398 54077921 53457072 51486025 49946881 49743238 49029868 [9] 48348249 48275735 Smallest eigenvalues: [1] 0.34750070 0.34392474 0.31983349 0.24479434 0.19355093 [6] 0.16902388 0.06062803 -0.43001296 -4.57618396 -67.61167732 Largest eigenvalues: [1] 59890647 56753342 53980393 52767092 52662107 50992010 49436140 49169291 [9] 48930821 48158614 Smallest eigenvalues: [1] 0.42976168 0.42867276 0.41702242 0.39540675 0.34286921 0.33325330 [7] 0.27704931 0.24961441 0.10811142 -0.06421055 Largest eigenvalues: [1] 60208890 56174969 53748667 52598145 52008989 50302445 48805470 48544888 [9] 48416265 47448496 Smallest eigenvalues: [1] 0.49609546 0.41397837 0.40428179 0.39174439 0.29675067 0.21328185 [7] 0.14918387 0.12184916 0.08974958 -0.30092874 Largest eigenvalues: [1] 58828755 56369016 53138310 51975999 51881947 50106312 49172607 48445260 [9] 48018967 47533019 Smallest eigenvalues: [1] 0.27677352 0.20726174 0.17413171 0.14882560 0.13487215 [6] -0.08843992 -2.05902642 -3.75043712 -21.58718655 -22.43561207 Largest eigenvalues: [1] 61832370 56588091 54263195 53103169 52436414 50918757 49407490 49218035 [9] 48510981 47801855 Smallest eigenvalues: [1] 0.38981231 0.32775102 0.32558476 0.29948230 0.17919565 0.16901748 [7] -0.01251332 -0.07140321 -1.25485213 -4.63885013 Largest eigenvalues: [1] 59869351 56398776 53834176 52282723 52045708 50600043 49360865 49217364 [9] 48563768 48472017 Smallest eigenvalues: [1] 0.33017882 0.30439988 0.25462496 0.14442313 0.08664877 -0.10384253 [7] -0.38191603 -0.76665602 -1.02315666 -2.35168057 Largest eigenvalues: [1] 60659072 57300087 54802718 53135060 52313831 50969051 49852052 49624595 [9] 49228522 48956059 Smallest eigenvalues: [1] 0.38678808 0.33526306 0.25149170 0.22455124 0.20537057 0.18122629 [7] 0.16304496 0.15331019 -0.01762924 -0.63827793 Largest eigenvalues: [1] 58650368 56081763 53885697 52084119 51838137 50309065 49100318 48646062 [9] 48206745 47629981 Smallest eigenvalues: [1] 0.4192507 0.4077064 0.3410043 0.2778001 0.2420358 0.1973463 [7] 0.1821753 -0.2229754 -0.2744616 -0.3177189 Largest eigenvalues: [1] 61295454 57380062 54827144 53551655 52053652 50370018 49821364 49495813 [9] 49242921 48759885 Smallest eigenvalues: [1] 0.5406579 0.5003668 0.4597957 0.3588029 0.3325741 0.2955678 [7] 0.2885041 0.1619238 0.1482223 -0.5074862 Largest eigenvalues: [1] 60648032 56391887 54156534 52793418 51839235 50258124 49055121 49007539 [9] 48820880 48108566 Smallest eigenvalues: [1] 0.39419785 0.38617724 0.35403919 0.32741738 0.27403111 0.14424427 [7] 0.05499041 -0.03401287 -0.29777416 -1.10073036 Largest eigenvalues: [1] 60434190 56346286 54118193 52494278 51492292 50169993 49270240 48798722 [9] 48647031 48152355 Smallest eigenvalues: [1] 0.38417510 0.25461163 0.15015650 0.11758328 0.02145941 -0.15609713 [7] -0.18551911 -0.22016006 -0.24563160 -1.23551217 Largest eigenvalues: [1] 58207034 56804866 53781407 52206470 51645930 50808063 49681354 49334507 [9] 48109531 47896795 Smallest eigenvalues: [1] 0.45020860 0.42148541 0.39601853 0.39064089 0.28288552 0.23227884 [7] 0.15824238 0.07447579 -3.45277610 -5.36635851 Largest eigenvalues: [1] 60470924 56931249 54290099 52522916 52275227 50989538 49158590 48917650 [9] 48659855 48006792 Smallest eigenvalues: [1] 0.4493032 0.4367285 0.2364430 0.2357436 0.1747338 0.1639817 [7] -0.1398297 -0.4956277 -2.2292221 -31.6300210 Largest eigenvalues: [1] 59271412 55618053 52939937 51837217 50974396 49415680 48393000 48187862 [9] 47931640 47348080 Smallest eigenvalues: [1] 0.45520751 0.44566280 0.36639149 0.33807235 0.28932723 0.28607987 [7] 0.21986350 0.07265161 -0.12066180 -0.43917277 Largest eigenvalues: [1] 62076583 57348636 54810443 53495467 52413427 50972769 50250282 49846613 [9] 49161942 49111304 Smallest eigenvalues: [1] 0.3116315 0.2985958 0.2871249 0.2391888 0.2326053 0.2211436 [7] -0.1189162 -2.1527048 -10.2022640 -15.7198921 Largest eigenvalues: [1] 60593942 56992457 54224791 53125538 51979463 50501563 50069517 49366892 [9] 48930593 48831956 Smallest eigenvalues: [1] 0.4637383 0.3875362 0.3301318 0.2892344 0.2820832 0.2593836 [7] 0.2095194 0.1601700 -0.2305081 -0.4285403 Largest eigenvalues: [1] 62408624 56984729 54590720 53932155 51960671 50212923 50102465 49810097 [9] 48814719 48749993 Smallest eigenvalues: [1] 0.31122110 0.28234665 0.23652225 0.23010392 0.17719528 0.14485532 [7] 0.06963547 0.03707936 -1.55130328 -4.38862773 Largest eigenvalues: [1] 61294421 57763937 54278776 53411392 53007977 51060737 50456862 49703703 [9] 49090437 49070834 Smallest eigenvalues: [1] 0.31366395 0.28779193 0.27916411 0.24767994 0.22439651 0.21275749 [7] 0.15779675 0.08882063 -1.10278569 -1.14502976 Largest eigenvalues: [1] 61540134 56823891 54110758 53551240 52145753 50563925 49898067 49203197 [9] 49176370 48357032 Smallest eigenvalues: [1] 0.4239849 0.3787170 0.3426921 0.3340188 0.3292710 0.2816513 [7] 0.1806327 0.1670743 0.1197871 -0.3233019 Largest eigenvalues: [1] 59294884 57280967 53962863 52768297 52422402 50688091 49636928 49368825 [9] 48854023 48719733 Smallest eigenvalues: [1] 0.53632004 0.46766716 0.32272287 0.29422753 0.26218855 0.18913284 [7] 0.12784040 0.03740815 -0.11563543 -0.15722049 Largest eigenvalues: [1] 63588265 57286165 55147282 54505526 52110461 50832131 50384325 49853217 [9] 49189206 49093302 Smallest eigenvalues: [1] 0.35841713 0.33638821 0.20826792 0.19129876 0.16507549 0.09396055 [7] 0.07613675 -0.11048022 -0.18615755 -4.83928957 Largest eigenvalues: [1] 61516881 57581489 54263179 53087709 52536261 50816299 50240767 49403849 [9] 49221385 48935756 Smallest eigenvalues: [1] 0.34046528 0.33256557 0.31434083 0.22799051 0.22051705 [6] 0.09986872 0.02859728 -0.20648966 -5.30970348 -18.88088698 Largest eigenvalues: [1] 61782066 57001518 54513637 53373497 52257559 50727866 49774420 49369805 [9] 49126714 48242476 Smallest eigenvalues: [1] 0.131836792 0.114257089 0.112506727 0.088245789 0.007450638 [6] -0.065298361 -0.079313230 -0.303015051 -0.662625046 -45.443338720 Largest eigenvalues: [1] 59777862 57230779 54286339 52482457 52385233 50805631 49781313 49119615 [9] 48788159 48309467 Smallest eigenvalues: [1] 0.38120530 0.36685662 0.23840016 0.20976964 0.01806366 -0.09285273 [7] -0.16190265 -0.46711971 -3.26255291 -4.09162112 Largest eigenvalues: [1] 60262404 56386364 53664445 52634765 51387077 49639793 48727195 48675675 [9] 48549349 47737914 Smallest eigenvalues: [1] 0.42006515 0.36833810 0.33483251 0.24318105 0.19474352 0.11196651 [7] 0.09266439 -0.02891082 -0.24740555 -4.33810300 Largest eigenvalues: [1] 61866681 56369224 53871255 52974701 51612440 50223763 49265588 49070255 [9] 48805484 48308821 Smallest eigenvalues: [1] 0.299382605 0.217246401 0.145785694 0.073617206 0.040811053 [6] 0.008976005 -0.231941334 -0.932579108 -5.780782534 -6.075570333 Largest eigenvalues: [1] 62270949 57024164 54580720 53973783 52193056 50776080 50211366 49566862 [9] 49345149 48727551 Smallest eigenvalues: [1] 0.52510958 0.46386520 0.43481311 0.40614587 0.40539473 0.26241105 [7] 0.19934583 0.13273229 -0.09821225 -1.01697121 Largest eigenvalues: [1] 61677524 57558413 54460142 53911845 52499116 50906807 50024470 49984054 [9] 49663677 48918989 Smallest eigenvalues: [1] 0.4470429 0.4406437 0.3791411 0.3089484 0.2675828 0.2110227 [7] 0.1948143 -0.2029869 -0.6959014 -5.2934709 Largest eigenvalues: [1] 60741843 56743899 53977441 52665908 52016223 50466602 49292414 49085745 [9] 48941822 48330784 Smallest eigenvalues: [1] 0.5962806 0.5433250 0.5403848 0.4712882 0.4210564 0.3237574 [7] 0.3231302 0.2507061 0.2016491 -0.1337087 Largest eigenvalues: [1] 59196366 57238096 54414183 52277223 52083932 50751619 49429863 49249267 [9] 48560001 48367544 Smallest eigenvalues: [1] 0.527343213 0.481449902 0.423630479 0.324562346 0.262447993 [6] 0.206552456 0.196993330 0.060195356 -0.009826601 -0.136721059 Largest eigenvalues: [1] 61957631 57471215 54939933 53535837 52456145 51057611 50020727 49683250 [9] 49498419 48875414 Smallest eigenvalues: [1] 0.391163738 0.382259313 0.343626069 0.287187744 0.275968097 [6] 0.180612419 0.107215566 0.001730944 -0.556919588 -1.131280687 Largest eigenvalues: [1] 61726541 57586045 54679741 53656176 52770492 51261118 50260220 49835977 [9] 49674111 49086230 Smallest eigenvalues: [1] 0.4751794 0.4338979 0.4164889 0.3890979 0.2893370 0.2746776 [7] 0.2686471 0.1301998 0.1110316 -0.4758231 Largest eigenvalues: [1] 61150740 57743222 54043375 53499419 52462492 50582257 50109155 49664654 [9] 49145916 48999559 Smallest eigenvalues: [1] 0.49659695 0.44345113 0.40898821 0.40401861 0.32115636 0.24469731 [7] 0.23460340 -0.09529336 -0.20894937 -0.73934099 Largest eigenvalues: [1] 61233436 57696352 55401904 53233292 52387413 51253901 49716474 49627250 [9] 49584811 48976749 Smallest eigenvalues: [1] 0.37830869 0.31966236 0.30634410 0.27922753 0.25206800 0.21332421 [7] 0.20623868 0.03177369 -0.93030296 -2.13165514 Largest eigenvalues: [1] 60131929 57123889 53869652 52792703 52313405 50558798 49934771 49016179 [9] 48800604 48519326 Smallest eigenvalues: [1] 0.5779883 0.5686235 0.5313749 0.4413090 0.3697106 0.3662736 [7] 0.2101569 0.1770587 -0.2119506 -0.4446801 Largest eigenvalues: [1] 61064834 56439896 54259904 52653783 51742894 50269188 49078852 49014789 [9] 48715133 48031810 Smallest eigenvalues: [1] 0.4675412 0.4595034 0.4328221 0.4230367 0.3068548 0.2733584 [7] 0.2115269 0.1533303 -0.5148192 -2.9466759 Largest eigenvalues: [1] 61579485 56737883 53661362 52720961 51882712 50159515 49280457 49016488 [9] 48996516 48595741 Smallest eigenvalues: [1] 0.52616720 0.50713439 0.45627493 0.42524232 0.40009670 0.38532158 [7] 0.32059081 0.18087486 -0.01600144 -1.32009883 Largest eigenvalues: [1] 61265775 57302480 54302502 53455540 52715597 51086075 49822837 49747269 [9] 49160030 48570112 Smallest eigenvalues: [1] 0.3163779 0.2987390 0.2489280 0.2009231 0.1518982 0.1413334 [7] -0.2353368 -0.8320955 -1.0596978 -9.5906019 Largest eigenvalues: [1] 61810896 56957060 54080754 53295011 51751553 50360668 49617946 49189582 [9] 49149829 48380777 Smallest eigenvalues: [1] 0.417872184 0.403019014 0.364067618 0.337982843 0.290507968 [6] 0.279985342 0.236833596 -0.004323992 -0.133306996 -0.369669761 Largest eigenvalues: [1] 60447917 56681275 54724851 52614048 51798426 50386741 49074974 48875089 [9] 48756814 48094715 Smallest eigenvalues: [1] 0.37349604 0.36088349 0.23645661 0.22665584 0.22509863 0.05008246 [7] -0.36080667 -0.41968590 -0.54381151 -8.92759856 Largest eigenvalues: [1] 61983406 56656327 54488032 52511666 51746071 50598475 49336981 49157373 [9] 48984410 48689319 Smallest eigenvalues: [1] 0.4926747 0.4342801 0.4030166 0.2890331 0.2013994 0.1692464 [7] 0.0922654 -0.0961822 -0.2861295 -52.7433798 Largest eigenvalues: [1] 59997502 57076895 53725770 52590533 52534512 50544623 49605270 49176419 [9] 48766401 48246012 Smallest eigenvalues: [1] 0.4846577 0.4776786 0.3926871 0.3765648 0.3363943 0.2955917 [7] 0.2859804 0.2493600 0.1338946 -1.6125203 Largest eigenvalues: [1] 60844613 57006572 53867081 53086884 52633446 50888256 49784471 49409578 [9] 49321366 48582918 Smallest eigenvalues: [1] 0.52063058 0.49071241 0.43844052 0.31826751 0.31201550 0.27687431 [7] 0.25807263 0.08091928 -0.08009682 -0.17197054 Largest eigenvalues: [1] 61761887 56697977 53585685 53217948 51660392 49978722 49515666 48884065 [9] 48699347 48099059 Smallest eigenvalues: [1] 0.43143328 0.42081522 0.38255488 0.37397894 0.21358025 0.17653139 [7] 0.12875449 0.09876649 0.06042186 -0.16757353 Largest eigenvalues: [1] 60142246 57028270 54040533 52541064 52069059 50862415 49578240 49307527 [9] 48538281 48317690 Smallest eigenvalues: [1] 0.53236544 0.52229172 0.46827748 0.45091960 0.44155349 0.25063813 [7] 0.22134283 0.16196824 0.02279001 -1.39751865 Largest eigenvalues: [1] 61795617 57682652 54353487 53569345 52828995 51019963 49920253 49793590 [9] 49288927 48723896 Smallest eigenvalues: [1] 0.33459310 0.30177519 0.28950235 0.18515476 0.16697755 0.12515452 [7] 0.07882004 0.04177229 -1.07230525 -2.16296592 Largest eigenvalues: [1] 63009171 57270557 54374982 54318009 52111760 50660720 50545413 49775390 [9] 49659164 49025458 Smallest eigenvalues: [1] 0.3766376 0.3342775 0.2827166 0.2507207 0.2166431 0.1833937 [7] 0.1232313 -0.2659694 -0.9294953 -2.9583220 Largest eigenvalues: [1] 61446362 56257324 54274426 52862441 51720310 50529734 49246249 49147229 [9] 49038530 48479967 Smallest eigenvalues: [1] 0.3940590 0.3460800 0.3145156 0.2921522 0.2898588 0.2738630 [7] 0.2231340 0.2111581 -0.4894491 -0.5228936 Largest eigenvalues: [1] 61440268 56787905 54767623 53117186 52333125 51120774 49397788 49212010 [9] 48967295 48156013 Smallest eigenvalues: [1] -0.3163597 -0.6939889 -0.7659704 -0.7754386 -0.8826546 -0.9936103 [7] -1.1966426 -1.5837540 -1.9660663 -19.7337128 Largest eigenvalues: [1] 59412987 57479798 54417275 53557253 52350330 51591238 49525984 49255752 [9] 48637686 48093344 Smallest eigenvalues: [1] 0.32228367 0.30971945 0.26693085 0.23240276 0.15581570 0.13989633 [7] 0.02781956 -0.10424959 -0.56899945 -9.05945639 Largest eigenvalues: [1] 58960537 55965503 53058445 51654979 51611142 49955888 48543266 48133884 [9] 47862213 47391663 Smallest eigenvalues: [1] 0.3772123 0.3471470 0.3191515 0.2843143 0.2758321 0.2657427 [7] 0.2196151 0.1244580 -0.1827859 -0.1829246 Largest eigenvalues: [1] 61852968 57208998 55069446 53296113 52169107 50732193 49821493 49775096 [9] 49270942 49136606 Smallest eigenvalues: [1] 0.31785035 0.31085821 0.30367631 0.21060792 0.18652539 0.15123288 [7] 0.06660781 -0.13874761 -0.24155226 -2.07494894 Largest eigenvalues: [1] 62231200 56783743 54414742 53546615 51801063 50427583 49903020 49108168 [9] 48831898 48186435 Smallest eigenvalues: [1] 0.40166168 0.27431137 0.26692210 0.24752077 0.18908565 0.12970148 [7] 0.07432295 0.06915576 -0.83508196 -2.35804652 Largest eigenvalues: [1] 62350627 56766381 54232385 53729722 51792384 50211696 50067820 49561446 [9] 48946111 48680879 Smallest eigenvalues: [1] 0.48478048 0.45058904 0.42070936 0.31416544 0.28338867 0.20771669 [7] 0.10266092 0.03606486 -0.07390494 -3.77561209 Largest eigenvalues: [1] 62175800 57023364 54241390 53422437 51789982 50164244 49724218 49138137 [9] 48758167 48258077 Smallest eigenvalues: [1] 0.28823548 0.13120189 0.05069389 0.00408220 -0.32397746 [6] -0.34911872 -1.22364367 -8.95925401 -12.45242650 -47.71906666 Largest eigenvalues: [1] 59238381 55374048 52696385 51248966 51188979 49415805 48335904 47878619 [9] 47544906 47215742 Smallest eigenvalues: [1] 0.43537886 0.42626241 0.42558254 0.38778306 0.32259139 0.30761260 [7] 0.28655907 0.02376902 -0.00350010 -4.17533949 Largest eigenvalues: [1] 61693631 56388556 53624361 53598524 51415772 49815492 49721569 48807710 [9] 48598894 48022968 Smallest eigenvalues: [1] 0.528402876 0.504690579 0.483229260 0.437236375 0.331888613 [6] 0.271730618 0.212058671 0.198478455 -0.004638645 -3.014639638 Largest eigenvalues: [1] 63044161 57587430 54951859 53988999 52632465 50585442 50421876 50063718 [9] 49374428 49283781 Smallest eigenvalues: [1] 0.5429344 0.5400139 0.4455596 0.3792661 0.3225131 0.2837928 [7] 0.2724103 0.2358099 0.1790095 -31.2524015 Largest eigenvalues: [1] 60305527 57326450 54258940 52758191 52621490 51164619 49502746 49291942 [9] 48858767 48630233 Smallest eigenvalues: [1] 0.41592808 0.37538020 0.28915192 0.27235868 0.16884168 [6] 0.08135910 -0.03725051 -0.07324944 -0.15500263 -24.97457371 Largest eigenvalues: [1] 61025066 56289089 54098951 53004421 51561830 50032786 49357652 48882956 [9] 48813166 47796571 Smallest eigenvalues: [1] 0.4800195 0.3453841 0.3337500 0.2895167 0.2734345 0.2709365 [7] 0.2561887 0.1324717 -0.2744279 -2.4728586 Largest eigenvalues: [1] 60952975 57415870 53805027 53783453 52201526 50603387 49860958 49329266 [9] 49168398 48153359 Smallest eigenvalues: [1] 0.40921446 0.40397521 0.27914442 0.12461639 -0.02411838 [6] -0.18149470 -0.84962043 -1.96712799 -3.27651210 -16.03066299 Largest eigenvalues: [1] 60591084 56640958 53805669 52724716 51816426 50481682 49012521 48907727 [9] 48851078 47920877 Smallest eigenvalues: [1] 0.4851435 0.4172960 0.4037480 0.3575174 0.3405694 0.3084201 [7] 0.2842711 0.1924449 0.1661641 -11.0310101 Largest eigenvalues: [1] 60882537 57100704 54178649 53206124 52162797 50696490 49374607 49264912 [9] 49134633 48327263 Smallest eigenvalues: [1] 0.3449633 0.2689929 0.2674617 0.2532790 0.1776660 0.1523659 [7] -0.2797336 -0.3920454 -0.8037189 -12.2217481 Largest eigenvalues: [1] 62412328 56863309 54430964 53348900 52215404 50907064 49666601 49456788 [9] 49326453 48992279 Smallest eigenvalues: [1] 0.5546884 0.5304329 0.4600697 0.4453827 0.4184473 0.2976896 [7] 0.2439453 0.2091047 0.1222638 -0.9256579 Largest eigenvalues: [1] 61373557 57508826 54132224 53580008 52449120 50704965 49780165 49528277 [9] 49394693 48416793 Smallest eigenvalues: [1] 0.3289948 0.3113222 0.2808730 0.2697081 0.2452006 0.2312575 [7] 0.1598467 -0.7246084 -1.5851729 -2.8434746 Largest eigenvalues: [1] 62005266 56656775 53867168 53685584 51963274 50470540 49986043 49073156 [9] 49051945 48283946 Smallest eigenvalues: [1] 0.41752964 0.37106945 0.34187507 0.18355867 0.12485874 [6] 0.07246263 -0.31926985 -0.44166161 -1.88560506 -23.47400888 Largest eigenvalues: [1] 62279555 57133149 54331339 53736978 52161907 50544436 49920653 49726454 [9] 49170419 48957030 Smallest eigenvalues: [1] 0.25783768 0.22892593 0.11862846 0.07350162 -0.08815636 [6] -0.16910272 -1.87276111 -2.82019062 -7.89382940 -16.13772410 Largest eigenvalues: [1] 61358524 56939037 53929578 53656457 51878887 50561444 49739572 48995935 [9] 48986162 47974483 Smallest eigenvalues: [1] 0.3979987 0.3897463 0.3386844 0.2668677 0.2152867 0.1308378 [7] 0.1151779 -0.2860246 -0.5770757 -1.9045157 Largest eigenvalues: [1] 62714832 57274377 54911869 54351494 52246432 50679153 50629560 50216029 [9] 49261716 49166051 Smallest eigenvalues: [1] 0.3981241 0.3946529 0.3399019 0.2819012 0.2321022 0.2229595 [7] 0.2087211 0.1320222 0.1046734 -0.3699108 Largest eigenvalues: [1] 59591231 57485727 54561632 53029139 52468101 51217426 49983685 49487861 [9] 48738127 48491944 Smallest eigenvalues: [1] 0.5382623 0.4622930 0.3846954 0.3065558 0.2956224 0.2714992 [7] 0.2713373 0.1914231 -0.1185494 -0.4422132 Largest eigenvalues: [1] 61568879 56897333 54721006 53744201 51875400 50347067 49960426 49463599 [9] 48877622 48525676 Smallest eigenvalues: [1] 0.43224575 0.43049092 0.39011711 0.38555291 0.35974162 0.22007268 [7] 0.08723876 -0.22985422 -0.70185850 -0.77115855 Largest eigenvalues: [1] 61021389 57021717 54164000 52991550 52013998 50392699 49310606 49300105 [9] 49257627 48506422 Smallest eigenvalues: [1] 0.53123464 0.45400270 0.38853981 0.34032142 0.28921702 0.22092215 [7] 0.19417337 0.18182406 0.05407943 -0.27718053 Largest eigenvalues: [1] 60535856 56772481 54264677 52799728 52262534 50813447 49410257 49107292 [9] 49006730 48295221 Smallest eigenvalues: [1] 0.3251987 0.3240275 0.2435386 0.1884451 0.1285746 0.0297709 [7] -0.3280108 -0.4136464 -0.7648452 -6.6254925 Largest eigenvalues: [1] 61309277 56879541 54438797 52933980 52395909 50981418 49906869 49342329 [9] 49128068 48991347 Smallest eigenvalues: [1] 0.40744323 0.38594542 0.37049259 0.33299996 0.25690749 [6] 0.23174785 0.21793333 0.01873293 -0.22821150 -15.87033079 Largest eigenvalues: [1] 61282060 56946330 54536333 52962157 52355819 50871982 49462342 49396166 [9] 49361133 48549042 Smallest eigenvalues: [1] 0.3327716 0.3172897 0.3092849 0.2179291 0.1811371 0.1765268 [7] 0.1705095 0.1663353 -6.5427572 -13.3171176 Largest eigenvalues: [1] 60831360 57582799 54238753 53256687 52436851 50583648 49897262 49550533 [9] 48894170 48745150 Smallest eigenvalues: [1] 0.25498578 0.23364338 0.13061187 -0.02730126 -0.04535112 [6] -0.13105671 -2.10816812 -2.88635458 -9.57463125 -11.82811023 Largest eigenvalues: [1] 61955807 57459405 54190115 53258930 52676653 51177849 49813211 49565304 [9] 49389243 48942024 Smallest eigenvalues: [1] 0.38546920 0.30569562 0.30030786 0.26002536 0.21383642 0.19672300 [7] 0.14461593 0.13388213 -0.01131249 -1.19477367 Largest eigenvalues: [1] 60252027 56813001 54075367 52698201 52328171 50688661 49089982 49037739 [9] 48936679 48113873 Smallest eigenvalues: [1] 0.45367019 0.43445248 0.42952376 0.41406225 0.38693280 0.38419472 [7] 0.21247798 0.17721839 0.16056121 -0.08294111 Largest eigenvalues: [1] 59339938 57213532 54058812 52690104 52190405 51094308 49779580 49317891 [9] 48546323 48361160 Smallest eigenvalues: [1] 0.38933909 0.33158133 0.31827045 0.28651238 0.22930725 0.20056563 [7] 0.15686031 -0.08093246 -0.38597245 -1.60641760 Largest eigenvalues: [1] 58959123 57150030 54529056 53057044 51362061 51322568 49483293 49236092 [9] 48120370 48097236 Smallest eigenvalues: [1] 0.47190154 0.43160214 0.36294626 0.32577114 0.28373129 [6] 0.22782944 0.08724500 0.02268298 -0.17287610 -14.33659303 Largest eigenvalues: [1] 60283899 56899936 54201877 52455388 52133001 51041042 49559396 49425902 [9] 48607089 48455280 Smallest eigenvalues: [1] 0.52793212 0.48299634 0.42974987 0.41490155 0.40683390 0.29647934 [7] 0.22853794 0.20801019 0.06818744 -0.56743580 Largest eigenvalues: [1] 61779020 57655715 54685028 53684488 52959879 51374148 50221128 50020364 [9] 49372916 48610143 Smallest eigenvalues: [1] 0.4730599 0.4717637 0.3615370 0.3419566 0.3260494 0.3083615 [7] 0.3048087 0.2761801 0.1620163 -0.6846015 Largest eigenvalues: [1] 61052588 57156497 54003069 53070905 52503631 50772913 49447274 49244168 [9] 49224751 48206476 Smallest eigenvalues: [1] 0.2432103 0.2042841 0.1903342 0.1882352 0.1730858 0.1585371 [7] 0.1117303 -0.2387666 -1.9121208 -10.7276031 Largest eigenvalues: [1] 60839558 56841852 54091943 52879792 51691711 50492207 49269888 49132674 [9] 48801021 48437122 Smallest eigenvalues: [1] -0.2696201 -0.3727248 -0.3788205 -0.4570900 -0.6134132 -0.6791791 [7] -0.7341080 -0.7653298 -1.0638922 -4.5525826 Largest eigenvalues: [1] 61249629 57373168 54754658 53738211 52289608 50855535 50082869 49791995 [9] 49748500 49080676 Smallest eigenvalues: [1] 0.3480784 0.3447809 0.3313652 0.1913536 0.1560704 0.1549315 [7] 0.1533832 0.0837505 -0.7286488 -4.5450232 Largest eigenvalues: [1] 58561301 56768384 54097729 53174506 51522943 51342637 50011980 48628074 [9] 48123200 47842270 Smallest eigenvalues: [1] 0.5071886 0.5015757 0.4135469 0.3983790 0.3665902 0.3568987 [7] 0.2124301 0.2057271 0.1084625 -1.1570186 Largest eigenvalues: [1] 62247415 57058741 54476567 53931551 52134275 50358685 50204042 49912211 [9] 48855532 48795747 Smallest eigenvalues: [1] 0.42785338 0.40991571 0.31931309 0.21454428 0.20518782 0.18802414 [7] 0.15642693 0.12044481 0.04126479 -0.42067914 Largest eigenvalues: [1] 60388500 57064767 54108616 53020923 52463295 50968304 49728652 49221389 [9] 49004809 48275749 Smallest eigenvalues: [1] 0.41330351 0.40559825 0.40473311 0.34158786 0.25602342 [6] 0.15615590 0.08797451 -0.01980880 -0.12654621 -13.30518877 Largest eigenvalues: [1] 61366525 56288727 53940964 52746219 51694424 50334335 49227619 48935295 [9] 48627800 48473263 Smallest eigenvalues: [1] 0.3959002 0.3204508 0.3110198 0.2999301 0.2348817 0.2235670 [7] 0.1817805 0.1618775 -0.4135727 -4.3768149 Largest eigenvalues: [1] 62658909 56957554 54603616 53736673 51792794 50558848 50115207 49336673 [9] 48899175 48475231 Smallest eigenvalues: [1] 0.379457665 0.372975888 0.348872313 0.304811643 0.219146347 [6] 0.209685033 0.150282101 0.130195426 0.001570124 -0.565892613 Largest eigenvalues: [1] 61620522 56725366 54687385 53331012 51877531 50704748 49518229 49425580 [9] 49261703 48876598 Smallest eigenvalues: [1] 0.36935093 0.31771957 0.23440516 0.19006310 0.13045937 [6] 0.11594599 -0.01740653 -0.15036296 -0.23063087 -16.71050452 Largest eigenvalues: [1] 62255940 57259544 55156386 53809178 52156098 50474094 50064938 49760301 [9] 49558586 49118973 Smallest eigenvalues: [1] 0.4592252 0.3960161 0.3907904 0.2754517 0.2725689 0.2012916 [7] 0.1589252 -0.8958183 -3.1459340 -6.3225859 Largest eigenvalues: [1] 60969701 57858837 54547430 53445002 53055612 51647798 50136085 49634044 [9] 49617119 49065534 Smallest eigenvalues: [1] 0.44399706 0.37413541 0.32789273 0.28192023 0.13027950 [6] 0.02438023 -0.14169085 -1.00391922 -2.25966768 -21.68333434 Largest eigenvalues: [1] 59760738 56290745 53424249 51747287 51581109 50003698 48890451 48383647 [9] 48073702 47869110 Smallest eigenvalues: [1] 0.46364936 0.43245097 0.42137884 0.36380742 0.32807721 0.27976022 [7] 0.17171699 0.02672438 -0.14106341 -0.29644418 Largest eigenvalues: [1] 60302527 56887940 53706597 52505492 52006556 50110546 49135126 48950790 [9] 48738630 48425788 Smallest eigenvalues: [1] 0.47885996 0.40594506 0.37135664 0.35409861 0.28420595 0.21555298 [7] 0.15433303 0.01568441 -0.07605173 -0.23954093 Largest eigenvalues: [1] 61589138 57129127 54621903 53042185 52109356 50606057 49530142 49392942 [9] 49301839 48645402 Smallest eigenvalues: [1] 0.45289183 0.33440655 0.29009562 0.24337142 0.21230066 0.12913549 [7] 0.12111591 0.08851302 -0.12093250 -0.33073563 Largest eigenvalues: [1] 63158916 56725744 54661894 53996640 51466756 50485073 50034376 49040198 [9] 48521533 48311398 Smallest eigenvalues: [1] 0.49212726 0.48062993 0.40814546 0.36575238 0.35853317 0.19818619 [7] 0.08774666 0.05650257 0.04859625 -0.70186176 Largest eigenvalues: [1] 58983405 56300006 53965883 52038112 51626391 50595374 49361194 48711540 [9] 48007252 47836242 Smallest eigenvalues: [1] 0.47667699 0.41938755 0.40378262 0.38983456 0.37903303 0.34624521 [7] 0.22082671 0.11190574 0.07797660 -0.01977828 Largest eigenvalues: [1] 61550357 56989421 54450523 53467352 51847246 50437230 49796454 49066163 [9] 48979601 48167486 Smallest eigenvalues: [1] 0.4885390 0.4846938 0.4571574 0.4312058 0.4024464 0.2792770 [7] 0.2688315 0.1947389 0.1497939 -3.4510884 Largest eigenvalues: [1] 62205630 57056923 54607655 53999425 51758137 50314188 50062747 49331340 [9] 48677501 48485298 Smallest eigenvalues: [1] 0.36462231 0.35327929 0.28350234 0.24705952 0.19057182 0.18695790 [7] 0.06751266 -0.02855174 -0.78793673 -0.92900799 Largest eigenvalues: [1] 60144317 57284923 54437308 52542849 52220423 50981973 49483403 48930381 [9] 48786875 48005571 Smallest eigenvalues: [1] 0.509699566 0.499210893 0.493274718 0.313215092 0.308651687 [6] 0.269909674 0.219491072 0.121951435 -0.001762749 -0.557237561 Largest eigenvalues: [1] 60443609 56612325 53755304 52999593 51916863 50170434 49485113 49094541 [9] 49061023 48208853 Smallest eigenvalues: [1] 0.35147446 0.29824333 0.28052950 0.22664488 0.14067093 [6] 0.11483106 0.09997084 -1.41880538 -10.02786331 -16.44646890 Largest eigenvalues: [1] 62191545 57044858 54548043 53477790 52437264 51048699 49823587 49739679 [9] 49223746 48561789 Smallest eigenvalues: [1] 0.3279844 0.2991115 0.2698473 0.2378653 0.2251274 0.1667304 [7] 0.1622551 0.1189911 -1.1584352 -2.4698089 Largest eigenvalues: [1] 62239701 57127395 54138015 54040755 51911031 50406159 50256535 50164845 [9] 49312946 49075471 Smallest eigenvalues: [1] 0.3659295 0.3421568 0.2951490 0.2925708 0.2535854 0.1406956 [7] -0.3748997 -2.6932590 -4.3399124 -5.7460369 Largest eigenvalues: [1] 60277942 57082654 54376451 52959072 52366349 50936439 49401047 49381065 [9] 49216547 48463521 Smallest eigenvalues: [1] 0.399893373 0.353066423 0.338472467 0.258965240 0.167474525 [6] 0.147212355 0.120959737 0.002822353 -0.869214549 -32.777625035 Largest eigenvalues: [1] 59605894 57585507 54733801 53154730 52434702 51539808 50281980 49465738 [9] 48702462 48612311 Smallest eigenvalues: [1] 0.54906439 0.53156309 0.33387275 0.32732769 0.23542289 0.13170213 [7] 0.07899525 0.06431167 -2.94163934 -6.91226047 Largest eigenvalues: [1] 61877072 56688735 53743941 53629148 51822700 50132489 49847353 49105202 [9] 49043280 48112413 Smallest eigenvalues: [1] 0.4208114 0.3616818 0.3394315 0.3288885 0.2170461 0.1611744 [7] 0.1574711 0.1501619 -0.2156835 -2.1166502 Largest eigenvalues: [1] 60763529 57079062 54329312 52774700 52107272 50608086 49266020 49123501 [9] 48845401 48446712 Smallest eigenvalues: [1] 0.48840637 0.48073097 0.35830665 0.31868349 0.29251419 0.25716255 [7] 0.23017513 -0.01698269 -1.13667987 -3.97184048 Largest eigenvalues: [1] 61703796 56739081 54272210 53413440 51847579 50622004 49681663 49505028 [9] 48878280 48626037 Smallest eigenvalues: [1] 0.5400668 0.4987775 0.4686579 0.4039596 0.3551848 0.3360950 [7] 0.3229468 0.3211843 0.3027462 -11.0153712 Largest eigenvalues: [1] 59863314 56809338 54115721 52542099 52051026 50359947 49079458 48870127 [9] 48757291 47912532 Smallest eigenvalues: [1] 0.37521739 0.30393826 0.30054082 0.26336103 0.24939871 0.24933361 [7] -0.02240462 -0.42562209 -0.42902856 -6.82831809 Largest eigenvalues: [1] 59532698 56919266 53701565 52410448 51576889 50148486 49222111 49086122 [9] 48609733 48190065 Smallest eigenvalues: [1] 0.45414194 0.45199362 0.31376597 0.31229278 0.28865897 0.25861197 [7] 0.18071507 0.09284467 -0.55858617 -0.73468635 Largest eigenvalues: [1] 60452815 57563361 54470302 52959108 52226397 50811989 49710658 49695853 [9] 49285855 48833670 Smallest eigenvalues: [1] 0.56146567 0.55036863 0.40428437 0.37013852 0.35820852 0.33638605 [7] 0.30441905 0.03823034 -0.26899933 -0.33000762 Largest eigenvalues: [1] 60326108 56806088 54196788 52571399 52127741 50668999 49281899 49218269 [9] 48894051 48237014 Smallest eigenvalues: [1] 0.57941655 0.48703107 0.46775732 0.39251795 0.38746004 0.31962709 [7] 0.30162716 0.11235960 0.08714428 -0.20076717 Largest eigenvalues: [1] 61811355 57514874 54415628 53278997 52748178 51148507 49678991 49587016 [9] 49338970 48431143 Smallest eigenvalues: [1] 0.32608451 0.30830041 0.26864895 0.19430569 0.11891875 0.09719704 [7] -0.96127199 -1.79953920 -4.32634773 -5.05157534 Largest eigenvalues: [1] 59884673 56301374 53975555 52421083 51478565 50508127 49355445 49159692 [9] 48592923 48428867 Smallest eigenvalues: [1] 0.48844241 0.43597832 0.38618662 0.32674637 0.26653503 0.22191069 [7] 0.17814152 0.11152074 0.02005887 -2.94665620 Largest eigenvalues: [1] 60804714 57540239 54805088 53188095 52875449 51321678 49722599 49703147 [9] 49448897 48511838 Smallest eigenvalues: [1] 0.4386887 0.4053393 0.3588944 0.2880324 0.2868159 0.2693010 [7] 0.1667450 0.1383977 -0.5005862 -8.0270663 Largest eigenvalues: [1] 59818272 56336863 53878643 51973226 51846216 50318762 49173017 48578878 [9] 48192085 47906586 Smallest eigenvalues: [1] 0.40926731 0.30920097 0.30316277 0.27090417 0.25586102 0.20864753 [7] 0.08453194 0.06568759 -0.54045309 -2.78669978 Largest eigenvalues: [1] 59565900 55900474 53740271 52011794 51576491 50190542 48912567 48740052 [9] 48311396 47688261 Smallest eigenvalues: [1] 0.59845895 0.52519853 0.44738907 0.37773856 0.32485333 0.31060168 [7] 0.27368305 0.10865708 0.04605266 -0.35481314 Largest eigenvalues: [1] 62157653 57470764 54671850 53968258 52533768 50702156 50253415 49769042 [9] 49270694 48643134 Smallest eigenvalues: [1] 0.48769512 0.48183869 0.45220765 0.30329599 0.24960013 0.24710339 [7] 0.20352193 -0.07782453 -0.20082527 -0.95011384 Largest eigenvalues: [1] 61152685 57130845 54563595 53185029 52457838 50730424 49786354 49528412 [9] 49421951 48750696 Smallest eigenvalues: [1] 0.45516370 0.39900609 0.32624053 0.31239373 0.28330105 0.27626319 [7] 0.17141732 0.15069993 -0.07127875 -0.39237906 Largest eigenvalues: [1] 60005810 57580883 54322838 53009894 52752272 51281597 50485985 49673654 [9] 49113713 48890834 Smallest eigenvalues: [1] -0.3192497 -0.3641236 -0.4968987 -0.8589310 -1.0168099 -1.6923999 [7] -1.9993637 -4.5486783 -5.7714185 -10.0224569 Largest eigenvalues: [1] 62495286 57852974 54195462 53751984 53187535 51301262 50355306 50029893 [9] 49254273 49238548 Smallest eigenvalues: [1] 0.4256595 0.4249179 0.3292673 0.3150990 0.2659408 0.2630464 [7] 0.2552083 0.2297464 -0.1943231 -0.2452156 Largest eigenvalues: [1] 60293924 57268540 54682456 53154643 52840129 51220434 50228679 49418340 [9] 49384070 48803976 Smallest eigenvalues: [1] 0.22011203 0.18798333 0.15779337 0.15514424 0.15281943 0.05838464 [7] 0.01548702 -0.04863282 -0.96672203 -5.86800189 Largest eigenvalues: [1] 60516965 56887730 54064219 52410118 52038234 50935653 49745473 49457403 [9] 48850775 48510924 Smallest eigenvalues: [1] 0.4076317 0.3723512 0.3203764 0.2399224 0.2284312 0.2201157 [7] 0.2116526 0.1723039 -0.0704165 -0.1743759 Largest eigenvalues: [1] 61538541 56888785 54443621 53587385 51549521 50457291 49865581 48995861 [9] 48747354 48169791 Smallest eigenvalues: [1] 0.41360861 0.36553079 0.36282850 0.35830358 0.29282790 0.28285776 [7] 0.27078392 0.12435801 -0.01842499 -0.07970028 Largest eigenvalues: [1] 59026314 56788655 54055834 52284969 51658931 50932441 49670126 48725607 [9] 48105610 47883918 Smallest eigenvalues: [1] 0.223536041 0.209044986 0.157704090 0.019773038 -0.006674767 [6] -0.145668639 -0.420577499 -1.263644141 -20.112173550 -32.659189916 Largest eigenvalues: [1] 59074398 56271541 53475535 52347983 51336692 50378005 48972234 48493258 [9] 47940532 47489942 Smallest eigenvalues: [1] 0.52754077 0.50219463 0.46807168 0.43741845 0.33066532 0.25540185 [7] 0.10614152 0.09639581 -0.06711066 -3.54062598 Largest eigenvalues: [1] 60547244 56560485 53770132 52656924 51396958 49726432 48920049 48675448 [9] 48281023 47857967 Smallest eigenvalues: [1] 0.47735944 0.41078339 0.37843947 0.35803626 0.29761180 0.20522432 [7] 0.13184251 0.12391783 0.09118706 -0.13078051 Largest eigenvalues: [1] 62425372 57401852 54395876 53685400 52213850 50694101 49918282 49518451 [9] 49457340 48832971 Smallest eigenvalues: [1] 0.38983414 0.35792073 0.34871948 0.19969289 0.19651135 0.17916727 [7] 0.11795739 -0.07157888 -0.89234300 -2.03223132 Largest eigenvalues: [1] 61260120 57133965 54435384 53682793 52511969 51121295 49899671 49829460 [9] 49753065 48811847 Smallest eigenvalues: [1] 0.39260729 0.34849456 0.30559180 0.16623647 0.14326479 0.03781588 [7] -0.15828144 -0.30750267 -0.71101095 -2.82616200 Largest eigenvalues: [1] 60832080 56750314 53956501 53698570 52137649 50438047 49996888 49675003 [9] 49527288 48546269 Smallest eigenvalues: [1] 0.33423317 0.26690670 0.22564015 0.20650699 0.20601109 0.17192209 [7] 0.16859454 0.02264137 -0.71646835 -9.78735965 Largest eigenvalues: [1] 60236409 57035158 54464520 52758290 52526787 51091224 49947556 49011971 [9] 48739854 48299666 Smallest eigenvalues: [1] 0.50608003 0.47083322 0.42990666 0.38215378 0.31678071 0.29517903 [7] 0.28292218 0.21902721 0.12034255 -0.09583888 Largest eigenvalues: [1] 59348467 56260959 53913254 52204857 51830694 50208551 48734010 48721058 [9] 48479070 47829128 Smallest eigenvalues: [1] 0.4824399 0.4334597 0.4152391 0.4010560 0.3940131 0.2397180 [7] 0.2307609 0.1763561 -0.1117882 -0.4902346 Largest eigenvalues: [1] 61019381 56854456 54156747 53220262 51798630 50159320 49405626 49283799 [9] 49085575 48501027 Smallest eigenvalues: [1] 0.5541878 0.5088885 0.4538716 0.3557807 0.3277846 0.2744693 [7] 0.2498319 0.2354386 0.1793992 -0.1429816 Largest eigenvalues: [1] 60761809 56630163 54098377 52687375 51945304 50456321 49078680 48754690 [9] 48694956 47773306 Smallest eigenvalues: [1] 0.38384570 0.33748294 0.33582867 0.22210700 0.16861759 [6] -0.05969512 -0.22860554 -0.30205247 -11.69326564 -37.12660551 Largest eigenvalues: [1] 60331005 56943597 53991377 52260707 52241744 50657442 49637865 49055659 [9] 48668251 48500366 Smallest eigenvalues: [1] 0.4771165 0.3352665 0.3167202 0.3091691 0.2261011 0.2152673 [7] 0.2035332 -0.4584838 -1.0208242 -1.2885227 Largest eigenvalues: [1] 61566724 56811436 54128848 53413875 51948826 50240380 50160702 49713132 [9] 49072941 48970454 Smallest eigenvalues: [1] 0.4773682 0.4564842 0.4076168 0.3897601 0.3219099 0.2810229 [7] 0.2171431 0.1746532 0.0824828 -0.6441086 Largest eigenvalues: [1] 60113984 57484918 54604711 52693266 52228135 51081808 49953712 49280052 [9] 48742620 48522219 Smallest eigenvalues: [1] 0.41147860 0.39156071 0.33777490 0.30948373 0.23749989 [6] 0.23474789 0.21187758 0.19680293 -0.09878452 -14.40866374 Largest eigenvalues: [1] 60192228 56138128 53851640 52381968 51438382 49828385 48786468 48689249 [9] 48290936 47640258 Smallest eigenvalues: [1] 0.54781296 0.49634563 0.43891840 0.42307954 0.40809411 0.34451431 [7] 0.30747788 0.28867788 0.01535167 -0.27393333 Largest eigenvalues: [1] 60501619 57163123 54007422 53096330 52156689 50391565 49392966 49273626 [9] 48934477 48235407 Smallest eigenvalues: [1] 0.5397361 0.5056801 0.4704349 0.4340496 0.3608806 0.3172314 [7] 0.2590753 0.2303959 0.1301523 -11.8721330 Largest eigenvalues: [1] 59441764 56635373 53636954 52070935 52010209 50364590 48840737 48509207 [9] 48322556 47643090 Smallest eigenvalues: [1] 0.39158197 0.37335006 0.33914636 0.23048811 0.22776263 0.15186533 [7] 0.08310912 -0.07700362 -0.16661063 -4.96153420 Largest eigenvalues: [1] 61476769 56831381 54287026 53029567 52311815 50572861 50151925 49365179 [9] 49117231 49017698 Smallest eigenvalues: [1] 0.38036553 0.37152004 0.35666276 0.33803615 0.20750919 [6] -0.07292445 -0.24837107 -0.69346397 -5.95487597 -22.75342217 Largest eigenvalues: [1] 61151055 56664328 53924411 53156101 51883729 50335920 49348319 49315922 [9] 49283773 48483517 Smallest eigenvalues: [1] 0.07577418 -0.21466705 -0.80276743 -1.04089999 -1.28523696 [6] -4.19222702 -6.14341317 -35.38397038 -44.10755822 -50.37978452 Largest eigenvalues: [1] 62053488 56577695 53863048 53671280 51631677 50302780 49788265 48843989 [9] 48535956 47824579 Smallest eigenvalues: [1] 0.48197926 0.45779312 0.42735592 0.39283497 0.32399117 [6] 0.14864271 0.09961016 0.09402510 -2.56466915 -17.16193423 Largest eigenvalues: [1] 59189670 57440199 53854906 52863953 52168213 51110600 49502680 49258602 [9] 48442500 48312142 Smallest eigenvalues: [1] 0.38710375 0.37450667 0.34751638 0.15844434 0.14583332 0.13750541 [7] 0.13374282 0.09455328 0.08635825 -6.86735816 Largest eigenvalues: [1] 59418875 56763049 54045013 53051160 51776665 51172946 49471493 49386918 [9] 48396710 48116334 Smallest eigenvalues: [1] 0.52220613 0.49976495 0.39012587 0.37743679 0.24325199 0.15265113 [7] 0.01739840 -0.02228364 -0.07452527 -0.37205984 Largest eigenvalues: [1] 59345634 55983428 52863386 51756343 51336084 49499447 48280924 48181841 [9] 47978973 47332216 Smallest eigenvalues: [1] 0.3929610 0.3363814 0.2984957 0.2780176 0.1736340 0.1501597 [7] 0.1298350 0.1242632 -0.3122030 -1.1081691 Largest eigenvalues: [1] 62020636 56153875 54079564 53091072 51687563 50180569 49487543 48959604 [9] 48802904 48210560 Smallest eigenvalues: [1] 0.5587650 0.5264955 0.4698078 0.4420742 0.3405764 0.3388369 [7] 0.2949213 0.2914038 0.2736783 -1.3461873 Largest eigenvalues: [1] 62290247 56902855 54371533 54094611 52052228 50592095 50295511 49466567 [9] 49361659 48542137 Smallest eigenvalues: [1] 0.4752313 0.4436238 0.4340575 0.4214729 0.3229614 0.2888121 [7] 0.1898384 -0.1613281 -0.4425740 -0.9114261 Largest eigenvalues: [1] 62206266 57442697 55069937 53629692 52575521 50894514 50509986 50033434 [9] 49741461 49377361 Smallest eigenvalues: [1] 0.3815545 0.3279717 0.2834949 0.2297587 0.1894288 0.1820309 [7] 0.1486541 0.1016408 -0.9774141 -2.3506032 Largest eigenvalues: [1] 62931338 56282551 53738838 53648638 51576647 50149474 49914005 49149828 [9] 48883186 48390438 Smallest eigenvalues: [1] 0.31348797 0.30360753 0.18797860 0.17671321 0.05684698 -0.23179085 [7] -0.38546890 -0.56174680 -1.32425900 -3.37321892 Largest eigenvalues: [1] 61646927 56729868 53689765 53252176 51317982 49854692 49437141 48861746 [9] 48770798 48134419 Smallest eigenvalues: [1] 0.4841052 0.4193218 0.3923431 0.3057651 0.2709355 0.2601504 [7] 0.2349510 0.2039716 -0.1188956 -6.7275196 Largest eigenvalues: [1] 61317034 56707393 54090274 53352835 51971258 50320290 49576067 48955930 [9] 48772378 48148988 Smallest eigenvalues: [1] 0.54228172 0.39314691 0.38089776 0.32935447 0.27219198 0.24777976 [7] 0.18488296 0.09721208 -0.20356037 -1.86484850 Largest eigenvalues: [1] 61527409 56407189 54484164 53269211 51475941 50072593 49659020 48810976 [9] 48689091 47931595 Smallest eigenvalues: [1] 0.3819995 0.3601517 0.3065941 0.2670016 0.2356865 0.1774529 [7] 0.1384545 0.1029310 -0.0569955 -3.0960319 Largest eigenvalues: [1] 62096124 57371873 55068231 53084927 52289762 51140254 49647876 49553263 [9] 49429086 48483318 Smallest eigenvalues: [1] 0.3035512 0.2846392 0.2784677 0.2495718 0.2280931 0.1592669 [7] 0.1108972 -1.6677846 -26.0709358 -29.7145504 Largest eigenvalues: [1] 61941290 56831751 53904231 53442662 52064254 50558867 49667690 49376225 [9] 49355993 48554151 Smallest eigenvalues: [1] 0.26817372 0.21613537 0.16008748 0.15473738 0.15468351 0.12539758 [7] -0.01979232 -0.17147172 -2.24627954 -6.42266699 Largest eigenvalues: [1] 61602922 56295380 53325376 53120608 51596460 50170049 49273322 49210284 [9] 48898335 48355808 Smallest eigenvalues: [1] 0.4113670 0.3558879 0.3353538 0.3324130 0.3131391 0.2607270 [7] 0.2573398 0.1865885 -21.8868949 -30.5379340 Largest eigenvalues: [1] 61600007 57223793 54583426 53559112 52451316 50977889 49834643 49476184 [9] 49241755 48474938 Smallest eigenvalues: [1] 0.3058565 0.2856233 0.1442651 0.1324406 -0.2394078 -0.5051559 [7] -0.8675156 -2.3548078 -9.0872581 -12.9552366 Largest eigenvalues: [1] 61990282 57226962 54442876 53388940 52517162 51015780 49624707 49574833 [9] 49457448 48556360 Smallest eigenvalues: [1] 0.4422177 0.4025370 0.2687712 0.2523224 0.2242800 0.1216324 [7] -0.4747098 -0.6980977 -0.7821793 -1.1210840 Largest eigenvalues: [1] 58968854 56764323 53994311 52459130 51871717 50802980 49708885 49053154 [9] 48346188 48207035 Smallest eigenvalues: [1] 0.3040017 0.3004577 0.2935229 0.2375510 0.1253672 0.1207880 [7] -0.1988924 -0.6151019 -10.0334810 -11.4427705 Largest eigenvalues: [1] 61552360 56949953 54222085 53171265 52229733 50622436 49699683 49481798 [9] 48758118 48318276 Smallest eigenvalues: [1] 0.54632893 0.43498110 0.42193335 0.40157459 0.29895170 0.28580287 [7] 0.24782916 0.13022041 0.07982283 -0.58466648 Largest eigenvalues: [1] 61852433 57602766 54342438 53857976 52655873 50926724 50033431 49942961 [9] 49437166 48849458 Smallest eigenvalues: [1] 0.37030557 0.36345061 0.34044548 0.29822409 0.29137453 0.19394862 [7] 0.11360659 0.10202595 0.03597045 -0.49789658 Largest eigenvalues: [1] 61781339 57617699 54820106 53789424 52985643 51455199 50235519 49973526 [9] 49738732 48983300 Smallest eigenvalues: [1] 0.53636312 0.46215688 0.42610568 0.40954671 0.33387113 0.31294576 [7] 0.28635439 0.23393347 0.06121316 -0.06926746 Largest eigenvalues: [1] 61139434 57852125 55508894 52916197 52806366 51543942 50255621 49794031 [9] 49443629 49209031 Smallest eigenvalues: [1] 0.48783834 0.42537067 0.41551393 0.40304681 0.33162491 0.20686126 [7] 0.16086673 0.09628232 -0.23160070 -0.74427166 Largest eigenvalues: [1] 61438458 57353553 54735099 52997283 52529005 51187004 49713390 49657580 [9] 49357598 48784493 Smallest eigenvalues: [1] 0.28306653 0.27932696 0.23600699 0.21272961 -0.02656672 [6] -0.19260834 -1.50265164 -1.60179973 -3.65170328 -14.35110598 Largest eigenvalues: [1] 61491928 56396876 53638232 52781549 51746549 50154303 49195509 48853716 [9] 48205090 47422630 Smallest eigenvalues: [1] 0.38834741 0.31839170 0.26605727 0.20116019 0.10626607 [6] 0.07590181 -0.03330955 -0.82290678 -1.73999865 -15.06702094 Largest eigenvalues: [1] 61682431 57647525 54596848 54162091 52229512 50205145 50160327 49317020 [9] 49231521 48441467 Smallest eigenvalues: [1] 0.172457000 0.148723048 0.128129017 0.103360963 0.004761457 [6] -0.066728737 -2.601409463 -3.467904983 -8.325014639 -28.689920892 Largest eigenvalues: [1] 58798269 56840296 54493930 52253399 51461909 50981691 49229165 49167213 [9] 48343378 47922761 Smallest eigenvalues: [1] 0.47385309 0.43401749 0.42805676 0.24616559 0.22671502 0.18030622 [7] -0.07844261 -0.51682237 -1.67005688 -3.03589807 Largest eigenvalues: [1] 61932204 57680368 54663648 53759726 52839868 51205075 50411408 49964241 [9] 49644135 49194110 Smallest eigenvalues: [1] 0.30259554 0.28994283 0.26862911 0.18359397 0.13819175 [6] 0.12950282 0.04996976 -0.18276856 -1.25025447 -14.12026107 Largest eigenvalues: [1] 59864097 56567945 53714984 52478983 52130039 50521713 49521373 48982791 [9] 48685565 48261501 Smallest eigenvalues: [1] 0.57065696 0.53574787 0.49979061 0.42744591 0.40950185 0.38802542 [7] 0.34914624 0.30842700 0.26156400 -0.01251103 Largest eigenvalues: [1] 60116328 57050509 54108077 53066707 52394654 50570264 49494918 49440518 [9] 49142881 48327251 Smallest eigenvalues: [1] 0.2895363 0.2563151 0.1966756 0.1881640 0.1848180 0.1554454 [7] -1.1603565 -1.2872661 -1.9470245 -5.5679466 Largest eigenvalues: [1] 60551750 56336313 54197717 53265190 51573299 50286018 49418518 48920567 [9] 48819324 48043436 Smallest eigenvalues: [1] 0.56508567 0.56207102 0.48860797 0.37273905 0.36083905 0.35521123 [7] 0.30850582 0.29998902 0.24122011 -0.02714331 Largest eigenvalues: [1] 60151865 56746937 53891798 52664443 51741823 50122637 48999536 48920248 [9] 48710497 48143317 Smallest eigenvalues: [1] 0.44465788 0.43987401 0.42858930 0.39992520 0.38387856 0.32356597 [7] 0.24267266 0.17422714 -0.06217521 -1.19356981 Largest eigenvalues: [1] 60953730 56368411 53853615 53410136 51967798 50391442 49489517 49251777 [9] 49189172 48271343 Smallest eigenvalues: [1] 0.44119654 0.39131675 0.38728820 0.35376936 0.27617680 [6] 0.18339429 0.07624087 -0.20614322 -0.27756319 -11.43942765 Largest eigenvalues: [1] 61875192 56747669 54502470 53314430 51820384 50387912 49672659 49299752 [9] 49043326 48381023 Smallest eigenvalues: [1] 0.22339787 0.22134696 0.15646319 0.13019136 0.10010082 0.01947175 [7] -0.34159411 -1.74831268 -6.41307044 -7.52728200 Largest eigenvalues: [1] 60016969 56695393 53578928 52688013 51563646 50130459 49107948 48909911 [9] 48900766 48312064 Smallest eigenvalues: [1] 0.4612909 0.4002415 0.3923534 0.3666081 0.3566948 0.2464878 [7] 0.2409846 0.2011406 -0.0263149 -0.1909707 Largest eigenvalues: [1] 60533083 56698441 54613439 53064588 51528422 50171593 49327114 49168701 [9] 48842945 48456318 Smallest eigenvalues: [1] 0.31737785 0.29272011 0.28897271 0.28040345 0.20116880 0.18586698 [7] 0.12955417 0.08284158 -0.54475810 -0.90491526 Largest eigenvalues: [1] 59619831 56419246 54095015 52282466 52244351 50770008 49488236 48580249 [9] 48521481 47876922 Smallest eigenvalues: [1] 0.3693455 0.3642734 0.3201752 0.3174283 0.2946600 0.2799460 [7] 0.2787288 0.2637924 0.1909357 -0.1348770 Largest eigenvalues: [1] 61558481 57205574 54628314 54008712 51847271 50563339 50178399 49596483 [9] 48905541 48631371 Smallest eigenvalues: [1] 0.5271368524 0.4741773739 0.4333002800 0.3675921899 0.2671287581 [6] 0.2649786561 0.1678971055 0.0119868750 0.0002818979 -0.0628815243 Largest eigenvalues: [1] 59144020 56499688 53738906 52250791 52133302 50445487 49422779 49063038 [9] 48453415 48144389 Smallest eigenvalues: [1] 0.36297860 0.34727825 0.24700489 0.24089456 0.09709237 [6] -0.10668919 -0.30814681 -0.41429732 -7.51970850 -20.31708983 Largest eigenvalues: [1] 61630029 56174956 53830725 52732088 51540313 50319512 48958422 48835100 [9] 48662306 48150370 Smallest eigenvalues: [1] 0.53869546 0.48056094 0.45035212 0.44573638 0.31247488 0.27269191 [7] 0.22162558 0.12995192 -0.01726772 -0.04677941 Largest eigenvalues: [1] 61937046 57439918 54585286 53715359 52289789 50602612 50131137 50058928 [9] 49209737 49128508 Smallest eigenvalues: [1] 0.44547142 0.41387134 0.29987522 0.24375112 0.23204446 0.19388214 [7] 0.19020763 0.09565894 0.03561604 -0.07021743 Largest eigenvalues: [1] 61567136 57274383 54329186 53524660 52405985 50777084 49793879 49624414 [9] 49400897 48606429 Smallest eigenvalues: [1] 0.38548747 0.30487165 0.28867506 0.27946251 0.24096028 [6] 0.02429095 -0.23250330 -2.24828979 -9.51773309 -14.71480035 Largest eigenvalues: [1] 61080790 57050739 54268924 52847648 52276760 50850797 49355132 49327305 [9] 49179867 48710827 Smallest eigenvalues: [1] 0.26647409 0.19324602 0.18885614 0.14735052 0.03939683 [6] -0.02467086 -1.03561656 -1.19542613 -2.32074277 -73.40258345 Largest eigenvalues: [1] 61141104 57256965 54246565 53324909 52870692 51303563 49823714 49783885 [9] 49370239 48993906 Smallest eigenvalues: [1] 0.46300648 0.45557774 0.42832519 0.34085195 0.31232123 0.27599119 [7] 0.26405735 0.23342092 0.20452771 -0.01802679 Largest eigenvalues: [1] 59546564 57245973 54147896 52398575 52390603 50976094 49823820 48912399 [9] 48610248 48205363 Smallest eigenvalues: [1] 0.50062859 0.48837669 0.39642986 0.35683514 0.34523069 0.27775410 [7] 0.21936403 0.08395141 -0.02366618 -0.04937289 Largest eigenvalues: [1] 62332001 56909209 54085368 53355921 52403245 50540532 49817606 49731396 [9] 48926245 48741208 Smallest eigenvalues: [1] 0.37681955 0.36493948 0.26909130 0.18361298 0.13927241 [6] 0.10381980 0.05969520 -0.03304384 -1.00761888 -17.10390106 Largest eigenvalues: [1] 60649874 56301226 52904908 52480053 51649141 49746915 48792840 48667711 [9] 48507041 47767190 Smallest eigenvalues: [1] 0.4124631 0.4098655 0.3233414 0.2964143 0.2234228 0.1953904 [7] 0.1213895 0.0520657 -0.5757630 -17.4404497 Largest eigenvalues: [1] 60885862 57374007 53953401 52936241 52884529 51338008 50044490 49412016 [9] 49101023 48641929 Smallest eigenvalues: [1] 0.43164167 0.22046006 0.09325817 0.03929236 -0.05626717 [6] -0.99473745 -1.88958691 -5.80751659 -14.64264489 -22.88452554 Largest eigenvalues: [1] 60441921 56118704 53510023 52497539 51523290 50048199 49248453 48571185 [9] 48486482 47881590 Smallest eigenvalues: [1] 0.5242968 0.4528744 0.3746077 0.3455156 0.3402478 0.3007240 [7] 0.2589339 0.2261131 0.1472645 -0.6581062 Largest eigenvalues: [1] 61382895 56709406 53667663 53050308 51898674 50250288 49396877 49294944 [9] 48760144 48456545 Smallest eigenvalues: [1] 0.4201678 0.4028160 0.3920768 0.3638857 0.3117124 0.2972377 [7] 0.2738566 0.0977866 -0.2117887 -2.5852988 Largest eigenvalues: [1] 60150716 56576310 54328097 52193411 51745869 50090661 48831211 48710835 [9] 48467786 48013986 Smallest eigenvalues: [1] 0.4372878 0.3848718 0.3637617 0.3120119 0.2936867 0.2790229 [7] 0.1821967 0.1196975 -0.3971291 -0.5749063 Largest eigenvalues: [1] 61397146 57127042 54283921 53456001 52271714 50789616 49746434 49214191 [9] 49155783 48212280 Smallest eigenvalues: [1] 0.38396514 0.35275432 0.34273141 0.29702799 0.28621115 [6] 0.18679149 0.11656280 0.11566745 -0.07280567 -23.86415052 Largest eigenvalues: [1] 58236601 56180004 53491873 51842028 50959753 49952364 48589909 48014547 [9] 47430043 47253997 Smallest eigenvalues: [1] 0.3499243 0.3401431 0.3043064 0.2784503 0.2751097 0.2715228 [7] 0.2291704 0.1625926 0.1335382 -0.1403669 Largest eigenvalues: [1] 59072660 56313172 53644513 52078899 51743484 50285819 48857162 48538227 [9] 48300442 47763889 Smallest eigenvalues: [1] 0.360613783 0.323130503 0.318246571 0.299944839 0.288143593 [6] 0.235345048 0.006906573 -0.812772341 -1.427933394 -20.591254506 Largest eigenvalues: [1] 61317990 57215128 54439692 53562591 52290323 50516522 49752892 49514081 [9] 49366966 48338894 Smallest eigenvalues: [1] 0.23082779 0.22115176 0.14329393 0.08710430 0.05316245 [6] -0.63465479 -1.55515696 -3.15623118 -3.70854008 -83.91631335 Largest eigenvalues: [1] 61586236 56815213 53571923 53454194 52034857 50330133 49597756 49381184 [9] 49161485 48316484 Smallest eigenvalues: [1] 0.56105578 0.50005169 0.43948868 0.38133509 0.37739006 0.29505879 [7] 0.14999177 0.10860312 0.07121852 -0.55846771 Largest eigenvalues: [1] 60341622 57037962 54266686 52774785 52179892 51153188 49570772 49262602 [9] 48610246 48359665 Smallest eigenvalues: [1] 0.4885337 0.4756377 0.3834402 0.3171454 0.3114576 0.2950203 [7] 0.2612420 0.2195895 0.1433516 -0.6745835 Largest eigenvalues: [1] 61028552 56764938 54638327 53018301 52599658 51153114 49717386 49377774 [9] 49264609 48669142 Smallest eigenvalues: [1] 0.297182294 0.279255894 0.251438357 0.246735560 0.146237809 [6] 0.137491756 0.120208607 0.005428975 -0.288284578 -1.759612351 Largest eigenvalues: [1] 57968528 56089613 53787178 52012557 51212653 50361814 49391920 48627944 [9] 48317579 47559226 Smallest eigenvalues: [1] 0.39839590 0.39024635 0.30199555 0.29454206 0.26859548 0.24846861 [7] 0.24023214 0.15597442 -0.09065493 -3.54881474 Largest eigenvalues: [1] 61363975 56944719 54012880 53383415 52008125 50355178 49710541 49158760 [9] 48803316 48149158 Smallest eigenvalues: [1] 0.39575540 0.38113141 0.34057457 0.31013803 0.22541344 0.20147078 [7] 0.14257764 0.08941422 0.03110219 -1.29263491 Largest eigenvalues: [1] 62314791 57060318 54599269 53887650 52306832 50997897 50223097 49317388 [9] 49202467 48245040 Smallest eigenvalues: [1] 0.3493131 0.3337269 0.2892494 0.2790288 0.1456771 0.1367938 [7] 0.1336202 0.1079044 -0.2040339 -4.9093716 Largest eigenvalues: [1] 59957923 57766656 54341010 52943339 52698578 51312901 50488776 49544527 [9] 49417220 48952436 Smallest eigenvalues: [1] 0.37031519 0.29918059 0.26861681 0.26708867 0.18239568 0.07326837 [7] -0.03395980 -0.80969851 -1.19417260 -7.33038375 Largest eigenvalues: [1] 60417828 57238649 54257278 52903385 52590871 51270691 50035910 49286354 [9] 48921411 48791047 Smallest eigenvalues: [1] 0.5724432 0.5099677 0.3935385 0.3727481 0.3646484 0.3273439 [7] 0.2934019 0.2258051 0.1920886 -0.8042753 Largest eigenvalues: [1] 60676086 56639147 54265734 52603868 52099194 50644840 49422653 49252502 [9] 48904174 48479882 Smallest eigenvalues: [1] 0.4394855 0.3930451 0.3731450 0.3277383 0.2728043 0.1536384 [7] -0.2665673 -0.6577459 -1.4074642 -1.9658887 Largest eigenvalues: [1] 61798382 57250550 54206667 53158306 52216831 50435516 50061143 49521000 [9] 49004291 48748349 Smallest eigenvalues: [1] 0.20093558 0.15460809 0.13328035 -0.07004664 -7.47491582 [6] -10.70352272 -20.09395665 -43.02253978 -44.97379173 -45.95386369 Largest eigenvalues: [1] 61547035 57134313 54835580 53100195 52471936 50441494 50020841 49418394 [9] 49317138 49138187 Smallest eigenvalues: [1] 0.4143698 0.3806197 0.3135725 0.2040917 -0.1067484 -0.1894938 [7] -0.2142496 -0.8897743 -1.9223137 -4.1271353 Largest eigenvalues: [1] 61173013 56668337 53684685 53180369 51499805 49930818 49308129 49105274 [9] 48900996 48157744 Smallest eigenvalues: [1] 0.28545951 0.19944245 0.15408568 0.12990053 0.06990041 [6] -0.02217001 -0.05417481 -1.03266822 -1.23043281 -13.97373361 Largest eigenvalues: [1] 58892516 57101321 54110963 52736352 51178775 50992355 49716348 48845087 [9] 48163084 47997955 Smallest eigenvalues: [1] 0.51832438 0.51507136 0.45420674 0.34648149 0.31458839 0.29901368 [7] 0.26688667 0.15831286 0.07129153 -1.24245670 Largest eigenvalues: [1] 60204605 56780793 54477655 52298566 52007679 50563799 49377963 48977901 [9] 48720247 48439724 Smallest eigenvalues: [1] 0.41322221 0.39338438 0.37107515 0.36334885 0.19780196 0.14254834 [7] 0.07378896 -0.11313841 -0.74888843 -6.98703687 Largest eigenvalues: [1] 60721206 56834018 54112195 52738184 51863020 50470663 49724841 48969018 [9] 48892822 48858791 Smallest eigenvalues: [1] 0.54591136 0.50654662 0.48657837 0.46342706 0.43598210 0.38736118 [7] 0.19360581 0.13999623 -0.05302026 -1.96955349 Largest eigenvalues: [1] 61199503 56741589 54024763 53137348 51763829 50024161 49401172 49059275 [9] 48825928 48223430 Smallest eigenvalues: [1] 0.3272388 0.3246140 0.3173594 0.3019645 0.2500908 0.1790376 [7] 0.1590405 -0.2673127 -2.1435318 -79.2884765 Largest eigenvalues: [1] 58794868 56647315 53235773 52022350 51882109 50143769 49312022 48572327 [9] 48076312 47773235 Smallest eigenvalues: [1] 0.4532039 0.3173140 0.2911425 0.2896573 0.2710577 0.2588845 [7] 0.2491383 0.2421482 -1.0094096 -4.5310353 Largest eigenvalues: [1] 61708217 56946595 53801549 53666780 52176716 50425284 49913675 49864820 [9] 49065139 48863600 Smallest eigenvalues: [1] 0.39679018 0.38660264 0.38023324 0.32847708 0.23307124 0.11450474 [7] -0.05277803 -0.10585854 -1.01667002 -8.74651736 Largest eigenvalues: [1] 60739205 56997130 54461853 52932866 51766857 50356992 49285656 49205664 [9] 49073906 48568607 Smallest eigenvalues: [1] 0.3120734 0.2941493 0.2534024 0.2440380 0.2180089 0.2036373 [7] 0.1805841 0.1540712 -2.2935465 -3.6227514 Largest eigenvalues: [1] 60653776 56260279 53517988 52922639 51568009 50210136 49052244 49001388 [9] 48329438 47684613 Smallest eigenvalues: [1] 0.31730278 0.25919321 0.19504488 0.18417382 0.13995289 0.13903878 [7] 0.09889956 0.03181261 -1.33762613 -3.36781480 Largest eigenvalues: [1] 60094802 57453702 54652613 52698534 52380950 50956872 50220778 49536135 [9] 49221512 48996771 Smallest eigenvalues: [1] 0.41150342 0.33247941 0.22278490 0.21309265 0.12719062 0.09354510 [7] -0.03535945 -0.09758639 -0.30314502 -0.78720884 Largest eigenvalues: [1] 60042898 57127595 54229095 52659602 52172143 51132953 49754673 49318136 [9] 48543119 48425180 Smallest eigenvalues: [1] 0.44338776 0.41362992 0.35318634 0.30466279 0.26667000 0.25482162 [7] 0.22816601 0.14097607 0.10474068 -0.05674704 Largest eigenvalues: [1] 61960536 57886505 54593802 53936775 52738638 50950323 50295944 50096029 [9] 49212570 49194850 Smallest eigenvalues: [1] 0.39121354 0.37162867 0.33972715 0.32680376 0.32138827 [6] 0.28735921 0.19829199 0.06800142 -0.73075199 -16.10605955 Largest eigenvalues: [1] 59718387 56529420 53501898 52482975 51771887 50298326 49003071 48957125 [9] 48648563 48204881 Smallest eigenvalues: [1] 0.3526066 0.3507056 0.3134071 0.2590029 0.1843413 0.1634195 [7] 0.1312385 -0.1255664 -0.3285346 -0.8120371 Largest eigenvalues: [1] 62748369 56956047 54994044 54007649 51660796 50314810 50278299 49508750 [9] 48911643 48839504 Smallest eigenvalues: [1] 0.319983374 0.300000898 0.254501530 0.119615021 0.113519606 [6] 0.059834421 -0.006232157 -0.017940569 -0.688933599 -3.888730173 Largest eigenvalues: [1] 60378308 58045797 54940966 52835474 52374078 51468403 49757373 49591505 [9] 48834942 48620984 Smallest eigenvalues: [1] 0.50245197 0.45552756 0.38713084 0.29643347 0.27147716 0.25563625 [7] 0.21358564 0.20242045 -0.05923261 -1.52209947 Largest eigenvalues: [1] 61961958 57624283 54501346 53592991 53031319 51561553 49924439 49891516 [9] 49852105 49066525 Smallest eigenvalues: [1] 0.50945474 0.45949625 0.43348907 0.41162968 0.37600245 0.35225360 [7] 0.31695458 0.22013719 0.05430134 -4.31971382 Largest eigenvalues: [1] 60396581 56802729 54316866 52870955 52490264 50915854 49439475 49151497 [9] 49089597 48257240 Smallest eigenvalues: [1] 0.5067116 0.4882665 0.4587631 0.3324501 0.2643893 0.2493352 [7] 0.2370293 0.1847793 0.1490126 -0.3964830 Largest eigenvalues: [1] 61651615 56834934 53535493 53414688 51811509 49877342 49643430 49076728 [9] 48715673 48160009 Smallest eigenvalues: [1] 0.55523608 0.51193463 0.48189558 0.47297097 0.38096002 0.33766157 [7] 0.26751359 0.18549163 0.08537344 -0.07110883 Largest eigenvalues: [1] 60587990 56885078 53941420 52469831 52155481 50832458 49377738 49142591 [9] 48598537 48375000 Smallest eigenvalues: [1] 0.352340229 0.318895494 0.310571759 0.286896633 0.278908360 [6] 0.262222897 0.145422568 -0.008028557 -0.318559858 -2.348658348 Largest eigenvalues: [1] 59423147 56443162 53866278 51603018 51499804 50117359 48857407 48570309 [9] 48247994 48025113 Smallest eigenvalues: [1] 0.40138169 0.35776456 0.35306231 0.30936662 0.27418108 0.21536110 [7] 0.21118826 -0.09033148 -0.50737412 -1.11713563 Largest eigenvalues: [1] 63139919 57762741 55678891 54354070 52541074 51234928 50755089 50180148 [9] 49860520 49284360 Smallest eigenvalues: [1] 0.4211715 0.4023504 0.3518663 0.3006542 0.2128347 0.1604205 [7] 0.1553507 -0.3554280 -4.4385515 -4.9015903 Largest eigenvalues: [1] 61463994 57169402 54130358 52936705 52116766 50384854 49843861 49356458 [9] 48920157 48626112 Smallest eigenvalues: [1] 0.570667115 0.530390643 0.446296336 0.402871329 0.369543654 [6] 0.270166149 0.246221198 0.217548477 0.031254285 -0.008525335 Largest eigenvalues: [1] 60746020 56775452 53971209 52737085 51989532 50207362 49048428 49023984 [9] 48830299 48031823 Smallest eigenvalues: [1] 0.48696248 0.46901752 0.37464827 0.36839085 0.32457018 0.31402224 [7] 0.21421051 0.18324177 0.08788199 -0.01711724 Largest eigenvalues: [1] 60826367 56567913 54073064 52451666 51991334 50397200 49265360 48812338 [9] 48593141 47865304 Smallest eigenvalues: [1] 0.3446097 0.2342628 0.2137899 0.1726198 0.1709127 0.0599499 [7] -0.1088735 -0.2380491 -0.4730524 -43.7756924 Largest eigenvalues: [1] 60765318 56377373 53856517 52982169 51681701 50026833 49269223 49221962 [9] 48570182 47788285 Smallest eigenvalues: [1] 0.389996851 0.388665667 0.380638452 0.302766248 0.295507205 [6] 0.192248361 0.169694273 0.099483633 0.078357169 -0.002984752 Largest eigenvalues: [1] 60187204 57232853 54045583 52622569 52279310 50635337 49229791 49047894 [9] 48953545 48166016 Smallest eigenvalues: [1] 0.2323943 0.1803474 0.1559938 0.1543501 0.1129005 -0.0170259 [7] -0.8926041 -2.0052744 -22.5802806 -27.2139183 Largest eigenvalues: [1] 62018768 56713334 54300650 53420467 51692689 50181949 49926220 49682450 [9] 49210217 49085559 Smallest eigenvalues: [1] 0.4191048 0.4059177 0.3613530 0.2784968 0.2550466 0.2523693 [7] 0.2048876 0.1292614 -1.2633721 -10.1475183 Largest eigenvalues: [1] 62104274 56741119 54348837 53894958 51531314 50184170 50164886 49063441 [9] 49030355 48440976 Smallest eigenvalues: [1] 0.55093988 0.45502096 0.43261036 0.38253711 0.33331661 0.26418454 [7] 0.26143995 0.18230047 0.07955738 -0.98473366 Largest eigenvalues: [1] 62003087 57400460 54568826 54094394 52385757 50700515 50348928 49611419 [9] 49381415 48527018 Smallest eigenvalues: [1] 0.4686639 0.4428894 0.4131769 0.4010316 0.3833951 0.3781866 [7] 0.2669119 0.2629616 0.1993791 -1.2637632 Largest eigenvalues: [1] 60746057 56994746 54035540 53244785 52154585 50677185 49646097 49405260 [9] 48925752 48239667 Smallest eigenvalues: [1] 0.33870225 0.23295839 0.22717611 0.22266403 0.05789483 0.04414513 [7] -0.19269129 -0.57604365 -3.73696129 -8.76516412 Largest eigenvalues: [1] 62492146 56220773 53855788 53109211 51075263 49637714 49483061 48741247 [9] 48334356 47926246 Smallest eigenvalues: [1] 0.14870438 0.08592403 0.07063419 -0.02909018 -0.45170093 [6] -1.10159584 -10.55233598 -12.70571969 -14.15854413 -22.67339065 Largest eigenvalues: [1] 60367311 56277435 54103852 52672242 51954518 50541009 49007426 48890297 [9] 48808356 47826437 Smallest eigenvalues: [1] 0.30899428 0.30178321 0.24706514 0.21582513 0.14186291 [6] -0.03332608 -0.08916350 -0.90197917 -10.79833658 -30.69525042 Largest eigenvalues: [1] 60198454 56811515 53517310 52940683 52089814 50254431 49466473 49097650 [9] 48811175 48274654 Smallest eigenvalues: [1] 0.4402253 0.3916358 0.3751367 0.3474146 0.3228600 0.2984106 [7] 0.2783365 0.2410652 0.1970938 -1.2124872 Largest eigenvalues: [1] 60979968 56859207 54166834 52659687 52358726 50957406 49745216 49100748 [9] 48970575 48473078 Smallest eigenvalues: [1] 0.5022565 0.4686686 0.4478753 0.3324490 0.2986369 0.2545173 [7] 0.2426628 0.1964309 0.1367384 -5.4439030 Largest eigenvalues: [1] 61958040 57494988 54593364 53279515 52193737 50510558 49661317 49289540 [9] 49212552 48514519 Smallest eigenvalues: [1] 0.5191223 0.4472410 0.4247659 0.4069959 0.3527973 0.3309592 [7] 0.2826756 0.2612016 -0.1483051 -0.1896565 Largest eigenvalues: [1] 59166487 57268163 54061885 52646363 52241324 50526829 49474294 49091182 [9] 48720102 48088746 Smallest eigenvalues: [1] 0.44968389 0.43432879 0.40906025 0.39239648 0.33937191 0.33800952 [7] 0.27115871 0.06571163 0.03748450 -2.54345639 Largest eigenvalues: [1] 60372076 56832892 54150163 52357135 52244339 50886593 49387341 49030093 [9] 48651890 48286813 Smallest eigenvalues: [1] 0.37939189 0.33035289 0.28030219 0.27701635 0.19823506 0.15960168 [7] 0.06599043 -1.13891870 -5.24297476 -9.68681075 Largest eigenvalues: [1] 60346221 57076310 53423067 52711666 52352463 50659526 49543529 49031844 [9] 48912666 48442002 Smallest eigenvalues: [1] 0.47169350 0.45233755 0.43849730 0.38436059 0.30823527 0.17881341 [7] 0.09078722 0.09067441 -0.10587495 -5.14037157 Largest eigenvalues: [1] 61513831 57026664 54651941 53240050 51934637 50750195 49498216 49407813 [9] 49178214 48564903 Smallest eigenvalues: [1] 0.4026326 0.3262625 0.2760441 0.2740694 0.2618078 0.2183853 [7] 0.1862497 -0.1569601 -0.9577239 -1.1340502 Largest eigenvalues: [1] 61484915 56725264 54686696 53149814 52161967 51039096 49511113 49413140 [9] 49348716 48665306 Smallest eigenvalues: [1] 0.30603775 0.30372261 0.28550123 0.26858160 0.26080426 0.10958037 [7] 0.09244892 0.08269669 -0.17257367 -1.58484947 Largest eigenvalues: [1] 59027861 56939841 53791804 52641193 51989672 50659761 49077095 48700673 [9] 48292973 47709077 Smallest eigenvalues: [1] 0.4157076 0.3363701 0.2576163 0.2502222 0.2389831 0.1891671 [7] -0.3655199 -3.1680631 -10.0106360 -25.8209726 Largest eigenvalues: [1] 60814808 57680611 54055451 53388703 52897826 51222156 49867051 49624917 [9] 48946368 48439592 Smallest eigenvalues: [1] 0.46179115 0.43091411 0.38895157 0.35488317 0.34359584 0.09974296 [7] -0.03913103 -0.29992946 -1.80821907 -9.79633723 Largest eigenvalues: [1] 61192193 56397696 54012562 52428399 51669393 50043891 48791408 48714580 [9] 48669419 47975152 Smallest eigenvalues: [1] 0.53165372 0.40274175 0.37970943 0.27570791 0.27474707 0.25022044 [7] 0.23796668 -0.09176933 -0.52908367 -5.49580617 Largest eigenvalues: [1] 60660559 56662652 53948650 52425478 52412288 50902938 49480409 49052044 [9] 48771877 48198535 Smallest eigenvalues: [1] 0.3290764 0.3056106 0.2771728 0.2441116 0.2112559 0.1934479 [7] 0.1732795 0.1391931 -0.1784300 -0.7168688 Largest eigenvalues: [1] 59811706 57156843 54205675 52937283 51932780 50742214 49136205 49115554 [9] 48998019 48101083 Smallest eigenvalues: [1] 0.3535318 0.3010332 0.2495670 0.2407851 0.2318093 0.1746198 [7] 0.1161130 -0.9635806 -1.7498247 -3.7730808 Largest eigenvalues: [1] 62457967 56585112 54173203 53981067 51696984 50458942 50281188 48971679 [9] 48898288 48292036 Smallest eigenvalues: [1] 0.389161840 0.294135147 0.276181395 0.249251539 0.248513695 [6] 0.201425852 -0.007060416 -1.223195952 -1.796170225 -1.940858347 Largest eigenvalues: [1] 61823959 56763772 54737222 53714683 51762128 50441648 49962827 49574370 [9] 48972858 48837303 Smallest eigenvalues: [1] 0.5333120 0.4943729 0.3641004 0.3394227 0.2585095 0.2451496 [7] 0.2381711 0.2263346 -1.0795920 -2.2828445 Largest eigenvalues: [1] 60207307 56552626 54044672 52538586 52203970 50875552 49407573 49219719 [9] 48741937 48290640 Smallest eigenvalues: [1] 0.54300585 0.52855008 0.46517011 0.38818401 0.29381276 0.18122202 [7] 0.09600804 0.09125548 -0.73885152 -1.40737678 Largest eigenvalues: [1] 59934450 56415927 53634732 52123061 51958120 50651059 49141220 48779745 [9] 48276692 47720549 Smallest eigenvalues: [1] 0.4622443 0.3987063 0.3268634 0.2664115 0.2073778 0.1719860 [7] 0.1390684 -0.3547308 -2.0553737 -14.2249814 Largest eigenvalues: [1] 59999368 56657248 53956445 52452366 52382571 51055864 49932155 49231752 [9] 48548217 48331561 Smallest eigenvalues: [1] 0.5670198 0.5387322 0.5113118 0.4674800 0.4201758 0.3639382 [7] 0.3160560 0.2994868 0.2619558 -0.2471928 Largest eigenvalues: [1] 59556190 56602918 54059429 52230358 52168173 50346138 49735111 48823509 [9] 48547204 48394857 Smallest eigenvalues: [1] 0.38173914 0.22578431 0.20074961 0.17087987 0.13405107 0.09380402 [7] 0.03224086 0.02125660 -1.40048360 -4.76001401 Largest eigenvalues: [1] 61030199 56458948 54280698 52348756 52149585 50662041 49188369 49023181 [9] 48785063 48180627 Smallest eigenvalues: [1] 0.41086374 0.35681446 0.30963847 0.26814350 0.26112175 0.25628568 [7] 0.10071607 0.04015024 -0.03995307 -0.28022370 Largest eigenvalues: [1] 60126168 56893231 54189104 52625688 52421343 50822456 50036258 49258788 [9] 49044573 48864545 Smallest eigenvalues: [1] 0.4289359 0.3950907 0.3783711 0.3623820 0.3018641 0.2955898 [7] 0.2551930 0.1559691 -0.6305254 -0.7333129 Largest eigenvalues: [1] 61624897 56357237 53571311 53259126 51808629 50150503 49611461 48629333 [9] 48479690 47592252 Smallest eigenvalues: [1] 0.4803209 0.4512281 0.4127469 0.3534740 0.3221978 0.2529718 [7] 0.2088123 0.1907809 0.1873931 -0.1172393 Largest eigenvalues: [1] 60690141 57087520 54299232 53266609 52177041 50790105 49449469 49244176 [9] 49093247 48448566 Smallest eigenvalues: [1] 0.4439649 0.3898715 0.2998521 0.2723315 0.2550672 0.1711473 [7] 0.1499616 0.1457232 0.1103189 -1.2177641 Largest eigenvalues: [1] 62223994 57237675 54586785 53757813 52415362 51049153 50091368 49659331 [9] 49644504 48704613 Smallest eigenvalues: [1] 0.24992155 0.19821666 0.19260588 0.18687583 0.11574283 [6] -0.03853566 -2.26150403 -15.72113414 -18.38973391 -46.48648778 Largest eigenvalues: [1] 60373788 57530577 54027671 53095311 52775686 51732321 49979533 49676520 [9] 48973736 48822051 Smallest eigenvalues: [1] 0.40785164 0.39404390 0.34082493 0.23993409 0.21004917 [6] 0.15616988 0.02025404 -0.36702657 -10.89062299 -14.50229837 Largest eigenvalues: [1] 60818780 56915523 54586793 52665118 52215509 50922098 49555519 49448950 [9] 48886226 48587448 Smallest eigenvalues: [1] 0.4913620 0.4497253 0.4466122 0.4314280 0.3721452 0.3597995 [7] 0.3243416 0.1857508 0.1837245 -0.2520058 Largest eigenvalues: [1] 59847039 56924084 54337872 52468450 52435675 50634228 50019776 48937318 [9] 48906332 48796638 Smallest eigenvalues: [1] 0.5703175 0.5303038 0.4822052 0.3749495 0.3192475 0.3177358 [7] 0.2815970 0.2529439 0.1763980 -0.1400922 Largest eigenvalues: [1] 60005139 56684094 53846553 52552444 51848262 50347014 49092614 48806902 [9] 48798014 48104824 Smallest eigenvalues: [1] 0.3732083 0.3505868 0.3315426 0.2623437 0.2133517 0.1668389 [7] -0.4053639 -1.8686760 -4.7956924 -11.8713398 Largest eigenvalues: [1] 60433290 55894671 53472007 52550915 51260404 49916482 48929245 48800799 [9] 48651553 47891150 Smallest eigenvalues: [1] 0.26101253 0.25076085 0.22821208 0.22544798 0.22407172 0.04044592 [7] -0.63766012 -1.24328673 -2.12339934 -4.60049209 Largest eigenvalues: [1] 59424317 56930881 53627549 52186769 52145530 50532870 49605107 48901926 [9] 48502486 48325570 Smallest eigenvalues: [1] 0.31564260 0.21367931 0.20749078 0.19863209 0.18929329 [6] 0.18214824 -0.09996127 -0.51840553 -6.91026109 -34.81725336 Largest eigenvalues: [1] 60853237 57461701 54399792 53620915 53038309 51470595 50053943 49731810 [9] 49547624 48977440 Smallest eigenvalues: [1] 0.4972782 0.4747164 0.4432018 0.4296695 0.3994533 0.3916961 [7] 0.2882557 0.1920210 0.1031796 -0.3680169 Largest eigenvalues: [1] 60358874 56608381 53316529 52460314 51933329 50301306 49205233 48853540 [9] 48678082 48120183 Smallest eigenvalues: [1] 0.4376309 0.4268220 0.3714861 0.3418039 0.2994845 0.2720832 [7] 0.2540180 0.1969878 0.1785853 -43.1808457 Largest eigenvalues: [1] 59845261 57351419 54428275 53186790 52374251 51614581 49837484 49004533 [9] 48660578 48207361 Smallest eigenvalues: [1] 0.4255473 0.4123912 0.3521531 0.3219596 0.2894944 0.2311587 [7] 0.2092418 -0.6280675 -1.3918889 -1.7768789 Largest eigenvalues: [1] 62565590 56789323 54106725 54043798 51660856 50365049 50083385 49749188 [9] 48658638 48561693 Smallest eigenvalues: [1] -0.1390819 -0.2170049 -0.3323154 -0.5326482 -0.6168624 -0.6742931 [7] -0.8621925 -0.8709568 -1.0180588 -1.2162951 Largest eigenvalues: [1] 59831312 56404945 53548153 52506619 52100424 50289192 49225035 49121773 [9] 48655367 48161106 Smallest eigenvalues: [1] 0.36371888 0.32185477 0.25653160 0.25411209 0.19994200 [6] 0.19687083 0.09628776 -0.54192461 -0.77546351 -17.07839671 Largest eigenvalues: [1] 62233714 57786110 54935747 54203205 52440786 50331466 50244035 50149106 [9] 49223045 49103326 Smallest eigenvalues: [1] 0.5580760 0.4939797 0.4922788 0.4126050 0.3790359 0.2819348 [7] 0.2765272 0.1390174 0.0327105 -1.2835989 Largest eigenvalues: [1] 60055542 57089761 54091674 52439503 52100195 50422442 49187750 48980912 [9] 48724080 48316289 Smallest eigenvalues: [1] 0.44012583 0.35307503 0.27568932 0.26065686 0.22184490 0.19663255 [7] 0.15724436 -0.08638441 -0.28698729 -1.21350044 Largest eigenvalues: [1] 60412182 57025739 54601193 53006969 52673138 51144169 49828632 49441164 [9] 49243910 48611841 Smallest eigenvalues: [1] 0.54945647 0.39558115 0.37765923 0.32760085 0.29121211 0.27650916 [7] 0.12815696 0.07123199 -0.02304807 -0.21196796 Largest eigenvalues: [1] 61305480 57203925 54333730 53006388 52385503 50714894 49554707 49382795 [9] 49030651 48321000 Smallest eigenvalues: [1] 0.4471790 0.4468151 0.3706218 0.3090550 0.3081898 0.2316257 [7] 0.1304340 -0.2240167 -0.7994059 -5.1780936 Largest eigenvalues: [1] 60452341 56482856 53851217 52493420 51737298 50057187 49058702 48695860 [9] 48627866 47948721 Smallest eigenvalues: [1] 0.3841541 0.3589080 0.3148786 0.2399918 0.2255127 0.2132834 [7] 0.1350854 0.1239517 -1.1252585 -4.0426740 Largest eigenvalues: [1] 60600586 57752544 54659578 53182707 53103503 51699364 50090454 49970623 [9] 49283784 48818003 Smallest eigenvalues: [1] 0.3114201 0.2796522 0.2356031 0.2103930 0.1597068 -0.2842413 [7] -0.3221553 -1.5569055 -1.8706072 -3.1528805 Largest eigenvalues: [1] 60473768 56415909 54212450 51917381 51735732 50245517 49468047 48571256 [9] 48476005 48410191 Smallest eigenvalues: [1] 0.43168236 0.42504436 0.40896166 0.38808241 0.33410139 0.31714291 [7] 0.21878530 0.06689256 -0.17149900 -0.55398932 Largest eigenvalues: [1] 61588155 57289505 54613751 53446355 52271833 50521755 49855045 49838530 [9] 48803633 48342970 Smallest eigenvalues: [1] 0.47138063 0.45650980 0.45500700 0.41787431 0.35809832 0.34194951 [7] 0.21248448 0.10051370 0.09703461 -0.04463957 Largest eigenvalues: [1] 60013585 57357053 54242350 52356724 52235184 50821791 49459613 49141697 [9] 48644061 48444619 Smallest eigenvalues: [1] 0.54671661 0.46792009 0.40153316 0.36887710 0.31562460 0.28257160 [7] 0.17169124 0.10448762 0.07140511 -0.22071932 Largest eigenvalues: [1] 61659931 56422074 53860824 52870848 51564574 50032360 49209159 48700471 [9] 48665787 48084182 Smallest eigenvalues: [1] 0.34835336 0.32663927 0.27187825 0.23542007 0.16776220 0.07968264 [7] -0.03345215 -0.77837593 -5.90228931 -9.23992327 Largest eigenvalues: [1] 60910785 56641751 53836067 53111589 52322494 50796633 49242446 49228065 [9] 49063831 48395203 Smallest eigenvalues: [1] 0.17662191 0.14701573 0.14649222 0.10347165 0.07814492 [6] 0.05710740 -0.70549348 -1.82760890 -6.34490195 -32.51025849 Largest eigenvalues: [1] 62944964 57089649 54483648 53947707 52423586 50872967 50365958 50321588 [9] 49477911 48997101 Smallest eigenvalues: [1] 0.3176975 0.2823086 0.2509452 0.2043332 0.1858994 0.1692234 [7] -0.1271624 -0.1859470 -0.5507800 -0.8548960 Largest eigenvalues: [1] 62527511 56632378 54485810 53989127 51459639 50287804 50051946 48759354 [9] 48675418 48160534 Smallest eigenvalues: [1] 0.5162945 0.4511005 0.4385022 0.4009457 0.2869997 0.2591677 [7] 0.2196847 0.1921336 -0.2971061 -2.5016950 Largest eigenvalues: [1] 61493261 56697859 54251552 53049877 51688169 49972951 49705693 49445785 [9] 48878473 48690327 Smallest eigenvalues: [1] 0.41535924 0.40812665 0.39807359 0.34445798 0.32794427 [6] 0.29240453 0.02002087 -0.02918034 -16.60262717 -36.07439184 Largest eigenvalues: [1] 60557788 56827046 54157762 52210247 52164056 50793135 49250690 49046916 [9] 48544317 48458460 Smallest eigenvalues: [1] 0.4266901 0.4055665 0.3727555 0.2985601 0.2802720 0.1518603 [7] 0.1222462 -0.1000245 -0.3731731 -0.9471946 Largest eigenvalues: [1] 59982663 56654977 54574897 52480810 52061028 51223902 49627939 49102761 [9] 48414196 48261435 Smallest eigenvalues: [1] 0.4068204 0.4009320 0.3762176 0.3381411 0.3079746 0.2763121 [7] 0.2255566 0.1730536 0.1615744 -0.4189887 Largest eigenvalues: [1] 61765482 57643524 54693149 53828687 52540377 51037725 50083958 49984245 [9] 49443775 48646642 Smallest eigenvalues: [1] 0.50735683 0.50713093 0.41962333 0.31519830 0.29439871 0.26235806 [7] 0.22445070 0.17373163 0.07618286 -0.12460078 Largest eigenvalues: [1] 60981741 57058200 54397488 53169725 52264623 50570973 50296596 49534610 [9] 48876111 48802405 Smallest eigenvalues: [1] 0.4240886 0.4165069 0.3742436 0.2854681 0.2121542 0.1946346 [7] 0.1450766 0.1419572 -0.3662326 -6.4153035 Largest eigenvalues: [1] 60649173 57171478 54716914 52864166 52592305 51339458 49872373 49812053 [9] 48918500 48735103 Smallest eigenvalues: [1] 0.3695670 0.3548248 0.3500379 0.3246229 0.2488123 0.1844365 [7] 0.1656266 0.1568008 0.1339524 -0.8944041 Largest eigenvalues: [1] 60117208 56716287 53993213 52120908 51842030 50159961 48493505 48453238 [9] 48212275 47330846 Smallest eigenvalues: [1] 0.4089921 0.4073233 0.3547962 0.3108988 0.2454954 0.2390874 [7] -1.0227305 -1.1333625 -3.9568769 -14.4350513 Largest eigenvalues: [1] 62196725 56786965 54104297 53772645 51952737 49962935 49940587 49663923 [9] 48835501 48496093 Smallest eigenvalues: [1] 0.3147089 0.2691223 0.2551160 0.2485574 0.2235012 0.2190282 [7] 0.2085586 0.2046603 -0.7633386 -11.1113128 Largest eigenvalues: [1] 60150171 56226284 53567587 52579483 51878059 50424135 49305834 48777236 [9] 48263560 47601906 Smallest eigenvalues: [1] 0.42191679 0.41483440 0.35077710 0.28367138 0.26105530 0.22739990 [7] 0.11722243 0.06569049 -0.04358547 -2.77606260 Largest eigenvalues: [1] 59750129 56056589 53323082 51819652 51535432 49878817 49100399 48236444 [9] 48169070 48049494 Smallest eigenvalues: [1] 0.499231791 0.440008579 0.418095418 0.401997353 0.311957781 [6] 0.307089010 0.231114788 0.147381575 0.137940294 -0.004165697 Largest eigenvalues: [1] 60814897 56820649 54296278 53101644 51875864 50402499 49326352 49121693 [9] 49088459 48374843 Smallest eigenvalues: [1] 0.3910972 0.3254893 0.3204014 0.2910008 0.2647446 0.2378803 [7] -0.1787452 -0.5617049 -1.1635131 -16.4891594 Largest eigenvalues: [1] 60378344 56312114 53776659 52413283 52011193 50499427 49027468 48847216 [9] 48746072 47927949 Smallest eigenvalues: [1] 0.439499735 0.396451408 0.360217018 0.340929618 0.312705953 [6] 0.200430848 0.171564137 0.083689198 -0.004879004 -0.564904759 Largest eigenvalues: [1] 61905507 57990558 54494612 53774053 52710946 51069457 50076060 49984080 [9] 49642822 49093538 Smallest eigenvalues: [1] 0.3969204 0.3510861 0.3302470 0.3083795 0.2345656 0.2248264 [7] 0.2018016 0.0804707 -1.5454891 -3.0450980 Largest eigenvalues: [1] 59589090 56493623 54125406 52834144 51759232 51087430 49640188 48569031 [9] 48102181 47844745 Smallest eigenvalues: [1] 0.4536524 0.3685705 0.3475585 0.3172027 0.2820355 0.2300680 [7] 0.2043613 -0.1605662 -0.7447793 -0.9546099 Largest eigenvalues: [1] 62732873 57582517 54991170 54402441 52407132 50711778 50701529 50210614 [9] 49333069 49031926 Smallest eigenvalues: [1] 0.5520704 0.5448518 0.4112108 0.3746011 0.3153940 0.2825629 [7] 0.2572838 0.1301782 -0.1497266 -0.5291301 Largest eigenvalues: [1] 60819202 57034914 54356302 53328852 52128264 50434897 49603230 49530212 [9] 49157756 48701862 Smallest eigenvalues: [1] 0.55300944 0.53405229 0.36639161 0.36362757 0.35401949 0.33323917 [7] 0.26615738 0.18628319 -0.05703658 -0.21817642 Largest eigenvalues: [1] 60684636 56318185 53709856 52712446 51867130 50374714 48909748 48898454 [9] 48579262 47795086 Smallest eigenvalues: [1] 0.3343917 0.2569268 0.2326976 0.2087988 0.1745439 0.1523458 [7] 0.1456388 0.1332859 -0.1943149 -18.0702373 Largest eigenvalues: [1] 59762373 56016769 53803644 52344934 51481891 49991848 48739492 48667669 [9] 48625799 48059891 Smallest eigenvalues: [1] 0.2366141 0.2085159 0.1861823 0.1588452 0.1235713 -0.6508953 [7] -2.8090842 -14.2662866 -16.4916976 -26.7953621 Largest eigenvalues: [1] 60820010 55818597 53495864 52105190 51615599 50196661 49034030 48766494 [9] 48520197 48028894 Smallest eigenvalues: [1] 0.31745225 0.30649946 0.23084139 0.16257985 0.15427284 [6] -0.02641795 -0.57626254 -1.10627634 -8.19919001 -27.84661070 Largest eigenvalues: [1] 60003448 56110090 53267627 52676044 51340431 49806059 48869123 48379053 [9] 48058181 47166258 Smallest eigenvalues: [1] 0.2970569 0.2238655 0.2010375 0.1659331 0.1605131 -0.1098398 [7] -0.4973454 -1.5010336 -14.8695651 -43.2579018 Largest eigenvalues: [1] 61738072 56675809 53699647 53255058 52045488 50490070 49460487 49432170 [9] 49156956 48646518 Smallest eigenvalues: [1] 0.4937931 0.3797228 0.3312952 0.3309922 0.2847543 0.2343620 [7] 0.1875436 -0.1631735 -0.2138261 -0.3478553 Largest eigenvalues: [1] 62130410 56699044 54527331 53724895 51707202 50028865 49911759 49451783 [9] 48965321 48765848 Smallest eigenvalues: [1] 0.4806181 0.4624442 0.4238570 0.2627189 0.2240836 0.1977554 [7] 0.1870243 0.1830931 0.1267200 -0.8954530 Largest eigenvalues: [1] 58061088 56552048 53763418 52336739 50941736 50540209 48885622 48762779 [9] 47926680 47538050 Smallest eigenvalues: [1] 0.159178732 0.009386789 -0.098827629 -0.233465977 -0.295322587 [6] -0.431743797 -0.573295139 -1.293248266 -1.545804191 -2.061804181 Largest eigenvalues: [1] 60087397 56995240 53719790 52781376 52483943 50659500 49462741 49040369 [9] 48994992 48296913 Smallest eigenvalues: [1] 0.4602684 0.4455640 0.4038406 0.3679004 0.3488780 0.2877631 [7] 0.2540486 0.1715845 -0.3514743 -7.2217864 Largest eigenvalues: [1] 60558884 56918813 54302667 52711773 52497467 51256125 49721367 49573576 [9] 48823974 48552749 Smallest eigenvalues: [1] 0.40174318 0.39038637 0.37460023 0.29341706 0.28539993 0.17156788 [7] 0.14909510 0.06605809 0.03272562 -2.19620856 Largest eigenvalues: [1] 61428556 56651872 53953030 52719585 51929654 50286100 49052974 48949175 [9] 48917280 48337116 Smallest eigenvalues: [1] 0.39200316 0.36513878 0.35120954 0.31525517 0.29361319 0.26342386 [7] 0.21066937 0.14889299 -0.02671328 -0.28138865 Largest eigenvalues: [1] 58848291 56327839 54140006 52021989 51733893 50627917 49193028 48423560 [9] 48130500 47710759 Smallest eigenvalues: [1] 0.36661718 0.35880548 0.29746880 0.26332123 0.12297637 -0.07308289 [7] -0.37239779 -1.19361192 -1.89481121 -8.60750358 Largest eigenvalues: [1] 61897164 57015226 54311511 53521909 51896503 50077519 49843360 49144885 [9] 48920826 48473019 Smallest eigenvalues: [1] 0.4705004 0.3947833 0.3364615 0.3305103 0.3187152 0.2197134 [7] -0.1535119 -0.2164121 -0.9195204 -10.6409927 Largest eigenvalues: [1] 61393207 56657195 54098691 53223888 52051359 50171540 49482777 49378477 [9] 48853519 48306208 Smallest eigenvalues: [1] 0.42588232 0.37955921 0.37568724 0.29979840 0.20818049 0.19855462 [7] -0.07359839 -0.08140830 -0.60399217 -0.66676398 Largest eigenvalues: [1] 60790173 56180495 53884491 52519517 51513187 49824244 48907293 48855882 [9] 48558386 48104679 Smallest eigenvalues: [1] 0.3875242 0.3607722 0.3542732 0.3491930 0.3373780 0.2605059 [7] 0.2056434 0.2049081 -0.1167760 -0.5538089 Largest eigenvalues: [1] 60999558 56286611 53783757 52834510 51730539 50129936 49165203 48668855 [9] 48387832 47537487 Smallest eigenvalues: [1] 0.4227196 0.3925881 0.3707511 0.2749182 0.2390396 0.1883664 [7] 0.1858637 0.1554571 0.1203926 -1.2167088 Largest eigenvalues: [1] 61802304 57154877 54672945 53999036 52125030 50843809 50230655 49170785 [9] 48788895 48050858 Smallest eigenvalues: [1] 0.5580718 0.4813434 0.4756031 0.4389980 0.4108176 0.3367040 [7] 0.2817007 0.2623414 0.1046230 -0.2389845 Largest eigenvalues: [1] 60220114 56975564 54220607 52279020 52265113 50605537 49293656 48826488 [9] 48715647 47946281 Smallest eigenvalues: [1] 0.35447580 0.34934731 0.33113164 0.25465531 0.25264764 0.24747485 [7] 0.20829666 0.08355711 -0.09107919 -0.83898856 Largest eigenvalues: [1] 61671484 56834140 54312267 53482233 52471377 50877057 49651453 49487737 [9] 48922173 48645474 Smallest eigenvalues: [1] 0.51257920 0.44957028 0.43721844 0.33349725 0.29252488 0.19255276 [7] 0.16481403 0.10570990 -0.02914557 -0.27503378 Largest eigenvalues: [1] 61391218 57242473 54265797 52960897 52143770 50711601 49436822 49310663 [9] 49173034 48655507 Smallest eigenvalues: [1] 0.41413222 0.33301498 0.32848325 0.29382472 0.27898602 [6] 0.22579549 0.19905472 0.05521943 -0.71269817 -37.85904742 Largest eigenvalues: [1] 60434609 57066515 54008978 53018985 52312753 50820888 49405612 49181116 [9] 49088032 48280753 Smallest eigenvalues: [1] 0.3248489 0.2826673 0.2597613 0.2399535 0.2010673 0.1897887 [7] 0.1243988 -2.3242182 -4.3734430 -8.5131688 Largest eigenvalues: [1] 61901139 57900738 54384919 54226329 53107283 51395179 50461277 49791579 [9] 49434558 48688952 Smallest eigenvalues: [1] 0.4136482 0.3770308 0.3576600 0.2933905 0.2543331 0.2460215 [7] 0.2165575 -0.3080185 -0.4171580 -0.5490019 Largest eigenvalues: [1] 59681303 56212059 53704806 51929347 51721745 50150165 49029644 48654891 [9] 48400692 48196375 Smallest eigenvalues: [1] 0.5232527 0.5151313 0.5075324 0.3945570 0.3913021 0.2788334 [7] 0.2784558 0.2104368 0.1613865 -0.1665843 Largest eigenvalues: [1] 61432044 57332683 54685553 52737564 52641299 50883309 49381475 49343808 [9] 49279577 48386850 Smallest eigenvalues: [1] 0.4146894 0.2931616 0.2741223 0.2701020 0.2343389 0.2297259 [7] -0.2542258 -0.2833549 -0.9194391 -15.5219621 Largest eigenvalues: [1] 60678627 56437749 53905953 52672472 51855729 50041635 49015051 48852103 [9] 48808432 48132048 Smallest eigenvalues: [1] 0.48394620 0.43965886 0.39786691 0.38425004 0.33497993 0.31980896 [7] 0.20160213 0.18608163 0.08693398 -0.65186771 Largest eigenvalues: [1] 59565798 56980428 53815465 52501342 52195091 50691688 49397047 49317538 [9] 48715760 48411507 Smallest eigenvalues: [1] 0.36203016 0.35139501 0.33360260 0.30218734 0.26849243 0.25804722 [7] 0.12708800 -0.03147284 -0.40261943 -3.04388181 Largest eigenvalues: [1] 60507507 57148441 54472354 52967071 52041069 50691881 49307167 49247603 [9] 49221163 48458873 Smallest eigenvalues: [1] 0.33941021 0.23822724 0.16821041 0.11469921 -0.04501172 -0.32298686 [7] -0.80100980 -1.50782981 -1.96247650 -4.83001963 Largest eigenvalues: [1] 61193021 57386215 54097537 54095279 52525917 50507598 50040747 50018617 [9] 49405306 48648078 Smallest eigenvalues: [1] 0.3954332 0.2639436 0.2593385 0.2372815 0.1945548 0.1805734 [7] 0.1079849 -1.1482784 -1.2031355 -67.9996430 Largest eigenvalues: [1] 59967957 55941968 53373855 52270754 51846331 50315039 49126061 48721111 [9] 48453667 48002982 Smallest eigenvalues: [1] 0.5095137 0.4679926 0.3942853 0.3122799 0.2719831 0.2697274 [7] 0.2053577 -0.1299356 -0.4848006 -2.9449581 Largest eigenvalues: [1] 61785375 56280212 53711880 53004639 51643303 49941259 49305600 48872952 [9] 48793748 47977484 Smallest eigenvalues: [1] 0.42178225 0.40868595 0.33012645 0.31262087 0.26496476 0.21882746 [7] 0.18523890 0.01204778 -1.85513784 -5.05620358 Largest eigenvalues: [1] 60269686 57243208 54731308 52743760 52003643 51317946 49412102 49378419 [9] 48517112 48359413 Smallest eigenvalues: [1] 0.36968155 0.34138465 0.27757725 0.23688959 0.20693207 0.09448451 [7] 0.06079864 0.05061530 -1.15838416 -4.96608575 Largest eigenvalues: [1] 61954665 56499096 53701703 53483094 51830502 50243642 49677164 49324153 [9] 48495623 48445700 Smallest eigenvalues: [1] 0.32309284 0.21005326 0.18017066 0.16016262 0.07738761 [6] 0.06086700 -0.06452118 -1.79371967 -10.87460485 -15.97641340 Largest eigenvalues: [1] 60107059 57017553 53939313 52597031 51989780 51027536 49718388 49659270 [9] 48794972 48431083 Smallest eigenvalues: [1] 0.55864955 0.54356446 0.41104668 0.40577362 0.39437248 0.32488028 [7] 0.30957986 0.25658556 0.18261240 -0.07195788 Largest eigenvalues: [1] 60376740 56362003 54169819 52252216 51870522 50477751 49072086 48728482 [9] 48603240 48044460 Smallest eigenvalues: [1] 0.26573334 0.22690222 0.12901061 0.07454859 -0.05466274 -0.30103262 [7] -0.46403007 -0.92394236 -1.08706770 -3.80218258 Largest eigenvalues: [1] 60276272 55703685 53301393 52718096 50944922 49533448 48837772 48360915 [9] 48323088 47389914 Smallest eigenvalues: [1] 0.431867741 0.372614473 0.267122477 0.227364940 0.182068131 [6] 0.139920660 -0.008522181 -2.132147476 -3.747067491 -23.279231912 Largest eigenvalues: [1] 60904712 56581981 53586356 52660736 52070099 50689199 49334951 49249119 [9] 48893386 48336414 Smallest eigenvalues: [1] -0.08802358 -0.09412573 -0.22002134 -0.30140960 -0.34476998 -0.42181532 [7] -0.54625285 -1.35448529 -2.90772791 -7.04167338 Largest eigenvalues: [1] 61990771 57487979 54249336 53843505 52956721 51307424 50009083 49934875 [9] 49573599 49009580 Smallest eigenvalues: [1] 0.48394273 0.45743958 0.41790292 0.31572695 0.26416957 0.20078505 [7] 0.16933878 0.16764347 0.08503126 -0.06902037 Largest eigenvalues: [1] 61632929 56981466 54360548 53476149 52212436 50558300 50080607 49733207 [9] 49335067 49087324 Smallest eigenvalues: [1] 0.356654058 0.349521877 0.341194408 0.314330352 0.303301185 [6] 0.240079953 0.201519934 0.097892396 -0.006077542 -0.174273599 Largest eigenvalues: [1] 61666707 56399899 53719762 52816827 51369343 49926122 49335619 49047406 [9] 48406112 48208360 Smallest eigenvalues: [1] 0.36019327 0.29663626 0.26120413 0.23845004 0.15468699 0.06598445 [7] -1.05582334 -1.83997886 -3.53585996 -3.66530156 Largest eigenvalues: [1] 61582605 57178036 53979749 53129124 52451416 50706384 49851493 49543538 [9] 48882829 48560221 Smallest eigenvalues: [1] 0.5044813 0.4828255 0.4419376 0.3659268 0.3548451 0.2703001 [7] 0.2696013 0.2465577 0.2251820 -0.4896558 Largest eigenvalues: [1] 60418738 56481699 54096546 52604776 51668351 50312685 49126026 48907108 [9] 48884759 48384148 Smallest eigenvalues: [1] 0.3722600 0.3184194 0.2580759 0.2331599 0.2022322 0.1429425 [7] -0.3171552 -0.8617764 -10.8614376 -20.2505700 Largest eigenvalues: [1] 60366721 56866995 54087795 52782614 52401237 51342176 49759356 49155271 [9] 48641789 48435916 Smallest eigenvalues: [1] 0.4965561 0.4044152 0.3447775 0.3285556 0.2796134 0.2449597 [7] 0.2142338 0.1501360 0.1162406 -0.3276573 Largest eigenvalues: [1] 59097536 57134438 53809783 52242966 52184861 50632559 48992897 48903971 [9] 48405743 47919183 Smallest eigenvalues: [1] 0.26118717 0.25914742 0.25063944 0.16602732 0.07823036 [6] 0.07236635 -0.27423246 -1.04475096 -4.73173522 -20.16313290 Largest eigenvalues: [1] 62797678 56904649 54990856 54323788 51790645 50673761 49909294 49813715 [9] 48863822 48644868 Smallest eigenvalues: [1] 0.48791362 0.47760226 0.46780066 0.39482623 0.35959547 0.32187561 [7] 0.26866625 0.09457191 -0.62546352 -7.61497821 Largest eigenvalues: [1] 60170017 57393001 54117725 53022143 52200098 50474729 49584718 49252941 [9] 48687534 48296292 Smallest eigenvalues: [1] 0.5215488 0.4470798 0.4151331 0.3600295 0.3449611 0.3102762 [7] 0.2349280 0.2200590 0.1834186 -0.2201999 Largest eigenvalues: [1] 60425352 56654518 54319369 52343425 52310133 50768711 49307536 49065594 [9] 48703065 48388378 Smallest eigenvalues: [1] 0.23551207 0.23258500 0.20657833 0.08828505 0.03713145 [6] -0.16128231 -0.45311228 -3.71039893 -10.23069146 -13.38582639 Largest eigenvalues: [1] 61836741 57181904 54732182 53823834 52288816 50717147 50131533 49642596 [9] 49315722 48723066 Smallest eigenvalues: [1] 0.43992125 0.42094593 0.30971952 0.29868932 0.16415782 0.13015577 [7] 0.08285453 -0.08290483 -0.11926624 -4.88819655 Largest eigenvalues: [1] 61519957 56763027 54404152 53135439 51941171 50426976 49487104 49460561 [9] 48881666 48475901 Smallest eigenvalues: [1] 0.41577326 0.39713697 0.37830078 0.19544009 0.19480598 0.08698267 [7] 0.05714332 -0.72629843 -1.24119140 -8.69483774 Largest eigenvalues: [1] 60255801 56781713 53671719 52281972 51883190 50401785 49176092 48859176 [9] 48595168 48409135 Smallest eigenvalues: [1] 0.3663924 0.3627366 0.3508961 0.3258831 0.2362026 0.1413982 [7] 0.1040180 -0.3007408 -1.2295748 -8.3170534 Largest eigenvalues: [1] 61295945 56699364 54082553 53121324 51887758 50392919 49546996 49444161 [9] 49140496 48679536 Smallest eigenvalues: [1] 0.07050201 0.05718619 -0.04248789 -0.07866189 -1.19862286 [6] -2.78179726 -5.08194630 -7.92995027 -44.76202018 -45.08175498 Largest eigenvalues: [1] 61609484 56705800 53600573 53063060 52137387 50405722 49800486 49363823 [9] 48625217 48472253 Smallest eigenvalues: [1] 0.53286784 0.44794487 0.38540445 0.34780048 0.31179227 0.29277845 [7] 0.21403901 0.12105206 0.06529864 -0.14125647 Largest eigenvalues: [1] 61711029 57990496 55041661 53592729 53096614 51715270 50181507 50092692 [9] 49870359 49156558 Smallest eigenvalues: [1] 0.5452084 0.4777621 0.4543715 0.4279139 0.3519336 0.3353493 [7] 0.2977777 0.2767443 0.1339215 -2.5822400 Largest eigenvalues: [1] 61754279 57105566 54164338 53309853 52218843 50679567 49596993 49358115 [9] 48950155 48476574 Smallest eigenvalues: [1] 0.4187649 0.3830171 0.3197251 0.3067155 0.2941940 0.1953803 [7] 0.1656330 0.1288161 -0.5412452 -11.7839864 Largest eigenvalues: [1] 59965415 56233825 53781525 52240001 52190440 50649267 49047305 48620363 [9] 48502291 47632999 Smallest eigenvalues: [1] 0.5171943 0.3932629 0.3835900 0.2943932 0.2851526 0.1931129 [7] 0.1339003 -0.0333617 -1.0402600 -7.1688060 Largest eigenvalues: [1] 61531845 57021322 54387228 52763500 52722512 51104017 49644047 49374079 [9] 49056311 48901314 Smallest eigenvalues: [1] 0.3723298 0.3474942 0.3100412 0.2710962 0.2659115 0.1807546 [7] 0.1197395 0.0674782 -0.2711414 -0.9392399 Largest eigenvalues: [1] 60701728 57262422 53810744 53298945 52103618 50529611 49437223 49061446 [9] 49053304 48327546 Smallest eigenvalues: [1] 0.4783583 0.4248015 0.3739803 0.3688025 0.3563851 0.1712337 [7] 0.0268449 -0.1548360 -0.5643596 -4.3257666 Largest eigenvalues: [1] 59825360 56295231 53970897 51922871 51707342 50565349 48965807 48583088 [9] 48127366 47859037 Smallest eigenvalues: [1] 0.11824586 0.11779102 0.09272212 -0.50310614 -0.55833461 [6] -1.75756728 -15.05611061 -23.00087490 -26.07882653 -42.94884800 Largest eigenvalues: [1] 62443147 57570500 54821995 54333135 52990771 51393081 50382605 50352961 [9] 49455795 49163795 Smallest eigenvalues: [1] 0.56233224 0.45486657 0.45283725 0.40255552 0.30229992 0.25099012 [7] 0.18845315 0.01365011 -0.10530342 -0.38169700 Largest eigenvalues: [1] 60846156 56621275 53631496 52882109 51866463 49929002 49073006 48767133 [9] 48467844 47516722 Smallest eigenvalues: [1] 0.48890983 0.46499137 0.43140000 0.38461842 0.27781239 0.20255095 [7] 0.17857041 0.06436231 -0.05042630 -2.14027136 Largest eigenvalues: [1] 60993197 57168839 54349768 53277235 51890212 50594430 49527234 49108062 [9] 48840042 47968026 Smallest eigenvalues: [1] 0.36720582 0.36618929 0.35050856 0.25330771 0.25068227 [6] 0.18522255 0.13247165 -0.03035573 -5.08119620 -14.49139855 Largest eigenvalues: [1] 60161611 56597206 54535032 52128515 52003755 50755728 49546417 48710910 [9] 48448726 48137986 Smallest eigenvalues: [1] 0.3900543 0.3876171 0.3579453 0.3352295 0.2923148 0.2685221 [7] 0.2453548 0.1630981 -0.1616682 -0.6827609 Largest eigenvalues: [1] 61801490 57375249 54379707 53489468 52757416 51054022 49997297 49879177 [9] 49283839 48739162 Smallest eigenvalues: [1] 0.44475212 0.41275753 0.39298752 0.36153024 0.32331346 0.30908240 [7] 0.27205324 0.17709786 -0.04148515 -0.27171112 Largest eigenvalues: [1] 61078556 57238729 54782249 53328502 52745365 51407756 49960847 49728965 [9] 49530043 49005638 Smallest eigenvalues: [1] 0.39985673 0.34901062 0.33594935 0.33277216 0.22183412 [6] 0.12357724 0.00794805 -0.57480741 -8.19465506 -11.90813206 Largest eigenvalues: [1] 61349118 56385395 53759997 52916261 51826942 50229325 49197898 49182063 [9] 48733925 47897788 Smallest eigenvalues: [1] 0.4823605 0.4550646 0.4122300 0.3563737 0.3211078 0.2681999 [7] 0.2043704 0.1467183 -0.2499244 -0.7559955 Largest eigenvalues: [1] 61673721 56941260 54129133 53040569 52160730 50748522 49387268 49285551 [9] 49165283 48290356 Smallest eigenvalues: [1] 0.4623288 0.4380419 0.3252336 0.3176281 0.2688846 0.2637597 [7] 0.1930479 -0.1021357 -0.4267492 -4.5724210 Largest eigenvalues: [1] 60593578 56814359 54223193 53192548 52151391 51469860 50021884 48914074 [9] 48516757 48126797 Smallest eigenvalues: [1] 0.41497254 0.34453026 0.33394633 0.32185247 0.31511965 0.22658572 [7] 0.18295444 0.15329198 0.03361928 -0.44209410 Largest eigenvalues: [1] 59637525 56033717 53739716 52259451 51607122 50612132 49210546 48714120 [9] 48048074 47836842 Smallest eigenvalues: [1] 0.25729410 0.24200477 0.21027044 0.12193439 0.05099067 [6] -0.07301389 -0.21492613 -6.33637916 -13.40809126 -15.22904798 Largest eigenvalues: [1] 62385880 56085247 53888280 53664941 51125959 49867043 49488249 49309741 [9] 48556288 48477103 Smallest eigenvalues: [1] 0.4030718 0.3686695 0.3439895 0.2843486 0.2030892 0.1288293 [7] 0.1008753 -0.1112656 -0.2212221 -4.1230713 Largest eigenvalues: [1] 61278040 56990122 54432030 52939944 52504690 50827187 49627907 49588661 [9] 49367781 48804409 Smallest eigenvalues: [1] 0.435137846 0.397301393 0.381047404 0.370238558 0.352072968 [6] 0.329283724 0.202330205 0.187266226 0.108106251 -0.007852709 Largest eigenvalues: [1] 61393191 56865161 54702324 53432474 52246819 50701281 49628665 49560001 [9] 49214880 48522921 Smallest eigenvalues: [1] 0.4902092 0.4639326 0.4167734 0.3228402 0.3099322 0.2943941 [7] 0.2312352 0.1952533 -0.1542093 -0.9407169 Largest eigenvalues: [1] 61595888 56726223 54219921 53195644 52212842 50900610 49351581 49258212 [9] 49218237 48486341 Smallest eigenvalues: [1] 0.39022089 0.33305672 0.30101112 0.28017426 0.27944535 0.25540180 [7] 0.20333862 0.14687396 0.08815677 -0.19402103 Largest eigenvalues: [1] 60605900 56959782 54216068 52667601 52554914 50680708 49035259 48952041 [9] 48829301 48257816 Smallest eigenvalues: [1] 0.39045039 0.33140119 0.30005425 0.23326185 0.09299865 [6] 0.07927156 0.07824957 0.03982120 -0.05397127 -11.65603366 Largest eigenvalues: [1] 62342596 57172371 54574527 53298354 52033727 50712343 49734315 49661818 [9] 49074305 48960146 Smallest eigenvalues: [1] 0.36755025 0.36350692 0.35912693 0.28536110 0.27257565 0.19600893 [7] 0.13662145 0.05402214 0.00227399 -7.03035510 Largest eigenvalues: [1] 59506087 57325516 53978917 52683020 52420361 50755030 49195136 49166998 [9] 48828297 48398858 Smallest eigenvalues: [1] 0.4618625 0.4277725 0.3907306 0.3109066 0.2684919 0.2575722 [7] 0.2215640 0.1513702 -0.2664108 -9.8046663 Largest eigenvalues: [1] 58828981 56061908 53441399 52011533 51411303 49731052 49032194 48268485 [9] 48249742 47654758 Smallest eigenvalues: [1] 0.331949456 0.262705755 0.223931293 0.170245022 0.144538711 [6] 0.084785249 -0.004901921 -0.059570902 -0.352946329 -9.400104338 Largest eigenvalues: [1] 60732567 57648242 54286332 53123470 53055733 51133704 50012367 49156587 [9] 49084147 49032944 Smallest eigenvalues: [1] 0.32393860 0.27415378 0.21484623 0.19364242 0.15815200 [6] 0.12804334 0.08812595 -1.15372659 -2.66378935 -22.79358021 Largest eigenvalues: [1] 60448234 56331068 54078631 52053030 52024089 50885393 49410882 49040669 [9] 48486103 48329361 Smallest eigenvalues: [1] 0.5670946 0.5146144 0.4754313 0.4627517 0.4255053 0.3882429 [7] 0.3355448 0.2812436 0.0279167 -4.9047624 Largest eigenvalues: [1] 61667034 57370159 54455166 53509807 52617057 51149867 49775055 49635520 [9] 49467332 48674709 Smallest eigenvalues: [1] 0.3946648 0.3564784 0.3338006 0.3080434 0.2917042 0.2123989 [7] 0.1851480 0.1514834 0.1402906 -0.8055767 Largest eigenvalues: [1] 60201397 57432839 54431355 52871503 52808836 51243920 49690355 49658709 [9] 48977241 48614646 Smallest eigenvalues: [1] 0.4402191 0.3759932 0.2977007 0.2889548 0.2745540 0.2358266 [7] 0.1821043 -0.0382577 -0.3797676 -5.5209038 Largest eigenvalues: [1] 60751629 56023600 53263947 52400647 51723676 50127497 48691817 48652273 [9] 48412865 47610050 Smallest eigenvalues: [1] 0.385131215 0.362520854 0.358572023 0.230147772 0.138420789 [6] 0.134132088 0.001046094 -0.939758376 -1.731910192 -6.373648675 Largest eigenvalues: [1] 59453998 56813973 53757123 52269748 52268110 50628625 49401632 49242839 [9] 48250272 47963487 Smallest eigenvalues: [1] 0.48138738 0.44785107 0.44776696 0.42427035 0.38038804 0.28411955 [7] 0.23894970 0.19963934 0.06156493 -2.73204631 Largest eigenvalues: [1] 60723551 57227318 53785752 53281473 52528144 50777641 49398592 49358501 [9] 48997651 48046187 Smallest eigenvalues: [1] 0.4652629 0.4402783 0.4357373 0.4192262 0.3423177 0.2740178 [7] 0.2135654 0.2126790 0.1955623 -0.1722335 Largest eigenvalues: [1] 60727817 56757227 54135162 52678469 52455991 50920550 49287607 49010341 [9] 48945976 48187980 Smallest eigenvalues: [1] 0.44415345 0.40975772 0.35468509 0.32914204 0.31868858 0.27592037 [7] 0.21120167 0.03306288 -0.58962323 -4.01139751 Largest eigenvalues: [1] 60381543 56831372 54570687 52557294 52185154 50685202 49948382 48964507 [9] 48941340 48763080 Smallest eigenvalues: [1] 0.29415346 0.21794766 0.17234694 0.15719172 0.09493242 0.08831225 [7] -0.42407156 -0.80273419 -2.84317298 -7.83927846 Largest eigenvalues: [1] 60741337 57447226 54906225 53363741 52577864 51391218 50079670 49883850 [9] 49421404 48877115 Smallest eigenvalues: [1] 0.41107197 0.40760010 0.40447799 0.34883482 0.29710879 0.29397087 [7] 0.27134827 0.14165099 0.08935935 -0.49468456 Largest eigenvalues: [1] 61218801 57260191 54646281 52873685 52065030 50889159 49282202 49091617 [9] 48944035 48251468 Smallest eigenvalues: [1] 0.1438057 -0.1288305 -0.1909403 -0.2716392 -1.6055091 -2.7424463 [7] -3.7736922 -5.6168819 -5.8237784 -31.1640356 Largest eigenvalues: [1] 58927179 55964225 53261539 52009211 51700068 50146396 49057688 49017326 [9] 47938924 47685416 Smallest eigenvalues: [1] 0.3554608 0.3111554 0.2814189 0.2773139 0.2154793 0.2112908 [7] 0.1895101 0.1666524 -0.5421869 -1.4298095 Largest eigenvalues: [1] 60475231 57317362 54774035 53295784 52561467 51265844 50171952 49614110 [9] 49394458 49160218 Smallest eigenvalues: [1] 0.3621322 0.3293360 0.3174574 0.3107943 0.3090577 0.2037012 [7] 0.1347536 -0.8186934 -2.6150792 -8.2109647 Largest eigenvalues: [1] 60403040 56610658 53734115 52871482 51514687 50240041 49100258 48806661 [9] 48612302 47951517 Smallest eigenvalues: [1] 0.42755345 0.36044127 0.31299401 0.29783375 0.27046879 0.20485714 [7] 0.08744774 -0.15716369 -1.76536992 -2.51658944 Largest eigenvalues: [1] 61181693 56490594 53714488 53543577 51458792 50108713 49710958 49151303 [9] 48619385 48252980 Smallest eigenvalues: [1] 0.3753757 0.3722959 0.3701148 0.2774156 0.2754704 0.2327637 [7] 0.1762103 0.1472211 -0.4350028 -0.7704539 Largest eigenvalues: [1] 61418943 56860335 53992277 53177854 52238158 50648627 49528067 49472722 [9] 49230244 48583948 Smallest eigenvalues: [1] 0.3173845 0.3047457 0.2511964 0.2210569 0.2024896 -0.1181932 [7] -0.6387505 -1.8540959 -8.1824464 -53.3303594 Largest eigenvalues: [1] 63030011 57181051 54972313 54691051 51863559 50838233 50286222 49685288 [9] 49288599 49112048 Smallest eigenvalues: [1] 0.53007287 0.42853930 0.39065401 0.38395514 0.35775705 0.28784991 [7] 0.15103535 0.10393287 0.03757311 -0.12044170 Largest eigenvalues: [1] 61935358 58027055 54734818 54089156 52961112 50841632 50383651 50281565 [9] 49643515 49304655 Smallest eigenvalues: [1] 0.6046799 0.5745960 0.4964054 0.4098630 0.3970436 0.3781611 [7] 0.3434390 0.2579412 0.1630675 -0.1363721 Largest eigenvalues: [1] 60381197 56442479 53846773 52496918 51851036 50300049 49408781 48934477 [9] 48796599 48421216 Smallest eigenvalues: [1] 0.4027470 0.3913490 0.3912340 0.3549024 0.3345217 0.2203419 [7] 0.1646664 0.1471640 -1.5741631 -17.6398554 Largest eigenvalues: [1] 60285641 56712810 53985092 52369038 52157164 50697908 48853087 48819044 [9] 48681455 48038201 Smallest eigenvalues: [1] 0.4004761 0.3869652 0.3635221 0.3356740 0.3243954 0.2000877 [7] 0.1476040 -0.1955125 -0.6150248 -4.2024429 Largest eigenvalues: [1] 59812972 57092889 54203771 52368371 52307191 50603846 49535452 48843768 [9] 48675241 48495198 Smallest eigenvalues: [1] 0.3741883 0.3529521 0.2865198 0.2237121 0.1821920 0.1820760 [7] 0.1573903 0.1555990 -0.2084509 -1.2776487 Largest eigenvalues: [1] 61180320 56600847 54224753 52760614 52020529 50594171 49424142 48972549 [9] 48900138 48659975 Smallest eigenvalues: [1] 0.30522987 0.24206191 0.20856040 0.18958943 0.17792456 [6] 0.14593476 0.12149449 0.09310473 -0.97997359 -20.22982331 Largest eigenvalues: [1] 59445581 56502242 53819902 51890979 51829167 50194952 49100885 49045086 [9] 48439754 48222412 Smallest eigenvalues: [1] 0.4330956 0.3805700 0.3575331 0.3215187 0.3122891 0.2919843 [7] 0.1638085 0.1630907 0.0970133 -0.5891288 Largest eigenvalues: [1] 61928111 56812792 54570889 53711681 51691880 50326287 49951928 49211543 [9] 48741124 48327910 Smallest eigenvalues: [1] 0.3746639 0.3261630 0.2986129 0.2855983 0.2763041 0.2308618 [7] 0.1617434 0.1291869 -1.3768379 -3.3911655 Largest eigenvalues: [1] 61536822 57328995 54375096 53350174 52605998 51207740 49927757 49634134 [9] 49504649 48528815 Smallest eigenvalues: [1] 0.37584788 0.37563116 0.30801611 0.28209525 0.24154831 0.15232508 [7] 0.08178809 0.06403454 -0.09600118 -0.61170927 Largest eigenvalues: [1] 59935746 56942657 54189239 52478243 52142814 50536525 49592028 48875859 [9] 48775114 48125252 Smallest eigenvalues: [1] 0.3286931 0.2923529 0.2466297 0.1865464 0.1274534 0.1204055 [7] -0.3336186 -1.9380959 -2.2669762 -7.7087225 Largest eigenvalues: [1] 59117134 56474754 54155245 52622907 51533530 51070816 49804218 49392423 [9] 48633976 48027668 Smallest eigenvalues: [1] 0.29346765 0.25949488 0.23008176 0.19551164 0.13151404 0.11307123 [7] -0.06695442 -0.14504181 -3.19612657 -4.10930947 Largest eigenvalues: [1] 60856879 56523720 54236215 53014689 51955050 50616992 49172279 48997313 [9] 48878267 48429473 Smallest eigenvalues: [1] 0.37163535 0.31590923 0.27117154 0.23427003 0.23409090 0.16723556 [7] 0.10481618 0.09935329 0.03574874 -5.14496972 Largest eigenvalues: [1] 60582821 57365093 54610364 53202023 52616935 51062362 49778748 49541943 [9] 49483622 48771969 Smallest eigenvalues: [1] 0.526958768 0.475773384 0.474013500 0.470767771 0.320339522 [6] 0.263306778 0.223180161 0.184423444 0.134478689 -0.009004654 Largest eigenvalues: [1] 61642439 56811724 54111425 53052201 51637509 49993573 49429580 48966249 [9] 48832820 48288986 Smallest eigenvalues: [1] 0.42795890 0.36226957 0.35845374 0.32646872 0.31025624 0.30599406 [7] 0.25427064 -0.02183352 -0.24942632 -4.59847699 Largest eigenvalues: [1] 60294124 56554801 54163593 52530563 51730989 50120401 49086579 48951448 [9] 48777579 48244995 Smallest eigenvalues: [1] 0.19873295 0.17806241 0.08600430 0.07799111 -0.06940455 -0.41468371 [7] -0.58604974 -2.41330914 -2.80019782 -7.55021174 Largest eigenvalues: [1] 62107000 57054980 54254144 53020101 52238964 50874691 49502221 49470183 [9] 48896208 47839744 Smallest eigenvalues: [1] 0.3849546 0.3391538 0.1784226 0.1453718 0.0438147 -0.1038324 [7] -0.6407237 -1.6964340 -3.6561347 -21.0935763 Largest eigenvalues: [1] 61325182 56777647 53838558 52921271 52038218 50397788 49330859 49206124 [9] 48677509 48021891 Smallest eigenvalues: [1] -0.6801403 -0.8250202 -1.8280455 -4.7721806 -8.6429795 [6] -42.0608876 -43.3148551 -45.6237067 -88.0467525 -144.4625258 Largest eigenvalues: [1] 62698414 55913107 53637902 53411140 51193627 49690310 49529330 49266034 [9] 48786510 48537575 Smallest eigenvalues: [1] 0.2262604 0.2216863 0.2053162 0.1238122 0.1109405 0.1104616 [7] -0.2601667 -0.4467474 -2.7332768 -18.5144519 Largest eigenvalues: [1] 59395684 55710352 53096211 52074596 51137468 49706707 48690229 48285013 [9] 48162105 47281996 Smallest eigenvalues: [1] 0.45958017 0.42323968 0.38100435 0.27113273 0.17136275 0.16110600 [7] 0.13825267 0.02147330 -0.04946506 -4.39292346 Largest eigenvalues: [1] 58767333 56693373 54048265 51907982 51712536 50379924 49223079 48936421 [9] 48486101 48192022 Smallest eigenvalues: [1] 0.4460233 0.3324391 0.3306288 0.2896460 0.2675674 0.2463477 [7] 0.2323300 0.1987867 -0.5104327 -0.7131444 Largest eigenvalues: [1] 59822899 57008563 54132452 52641311 52312987 50816363 49319994 49205728 [9] 48945765 48433414 Smallest eigenvalues: [1] 0.52399669 0.51852709 0.45419601 0.44204388 0.37564924 0.27643631 [7] 0.18977572 0.02305043 -0.06354444 -0.46642052 Largest eigenvalues: [1] 61620083 57477877 54842185 53167590 52225561 50797453 49642442 49538767 [9] 49339365 48850474 Smallest eigenvalues: [1] 0.46220688 0.43345056 0.41204641 0.35985893 0.28472452 0.24642175 [7] 0.19398944 0.12013317 0.06910627 -0.11376863 Largest eigenvalues: [1] 61941747 57122879 54969705 53265729 52509792 50710966 49803154 49719131 [9] 49205633 48664609 Smallest eigenvalues: [1] 0.4717943 0.4551337 0.3340419 0.3086120 0.2758056 0.2510398 [7] 0.2151098 0.2072384 0.2050866 -0.2411751 Largest eigenvalues: [1] 61597967 56706900 54559772 53267203 51687750 50466046 49657236 49078430 [9] 48777874 48382915 Smallest eigenvalues: [1] 0.2630521 0.2595272 0.2189682 0.2146682 0.2020538 -0.2935609 [7] -0.4503623 -0.8564189 -1.4259427 -7.2469401 Largest eigenvalues: [1] 61879845 57268028 54625676 54103238 52217394 50678058 50343672 50070444 [9] 48848681 48559730 Smallest eigenvalues: [1] 0.4698739 0.4416851 0.3713047 0.3238198 0.2898404 0.2850621 [7] 0.1749582 -0.2354831 -3.9899517 -32.4261345 Largest eigenvalues: [1] 60283815 56579684 53921454 52613024 52433231 50938210 49067516 48982943 [9] 48799222 48265109 Smallest eigenvalues: [1] 0.45071049 0.44306643 0.41914692 0.36654760 0.32449349 0.29723858 [7] 0.21437954 0.08412595 -0.05640778 -0.20523915 Largest eigenvalues: [1] 60993718 57192905 54537919 52682157 51998353 50624117 49392022 49182895 [9] 49037928 48619960 Smallest eigenvalues: [1] 0.4885786 0.4607187 0.3937427 0.3145667 0.2561769 0.2323242 [7] 0.2177278 0.1845565 -0.2942461 -10.5128529 Largest eigenvalues: [1] 61573701 56971220 54513295 53834944 52111309 50156357 50057324 49331684 [9] 49067827 48367919 Smallest eigenvalues: [1] 0.4021701 0.3784051 0.2922592 0.2748855 0.2096465 0.1866577 [7] 0.1498187 0.0583667 -0.1502983 -3.1108515 Largest eigenvalues: [1] 59368971 57172142 54015351 52632929 52604459 51074285 49672880 49608468 [9] 48781183 48575522 Smallest eigenvalues: [1] 0.39459183 0.36623610 0.26832882 0.26721891 0.20068006 0.07691399 [7] -0.38678943 -0.52973956 -2.91451124 -3.32011068 Largest eigenvalues: [1] 62363843 56857527 54812335 53449109 51930834 50941960 49824900 49569345 [9] 49423267 48951640 Smallest eigenvalues: [1] 0.3903445 0.3901906 0.3393929 0.3160973 0.3000504 0.2731530 [7] 0.1814825 0.1375826 -0.9476045 -3.0360224 Largest eigenvalues: [1] 62428415 57468260 54785938 53996326 52469858 50592401 50331304 49530302 [9] 49493212 48707229 Smallest eigenvalues: [1] 0.4465162 0.4355504 0.3443253 0.3088987 0.2951879 0.1100454 [7] 0.1012690 -0.3946835 -0.5110460 -13.9277431 Largest eigenvalues: [1] 61888831 56532540 53682788 52811733 51682143 50101369 49138148 49037133 [9] 48644492 48093471 Smallest eigenvalues: [1] 0.436631473 0.427000005 0.368914047 0.312638306 0.289951990 [6] 0.249490433 0.106535110 0.009602588 -0.182603810 -0.422015364 Largest eigenvalues: [1] 60552591 56622673 54502925 53188939 51598308 50244902 49525267 49367824 [9] 48802052 48725464 Smallest eigenvalues: [1] 0.55654102 0.50755541 0.46968907 0.38649047 0.38068972 0.35551759 [7] 0.33565268 0.04322577 -0.11273736 -0.18183394 Largest eigenvalues: [1] 61115955 57213539 54492847 53153258 52150857 50766730 49438822 49382438 [9] 49229822 48288623 Smallest eigenvalues: [1] 0.260533983 0.163364417 0.158795517 0.146401631 0.069356093 [6] 0.017175141 0.002324824 -0.033940530 -0.295170122 -2.055072540 Largest eigenvalues: [1] 56852266 56656292 53964208 52532893 50810819 50565899 49346267 48731173 [9] 47998609 47724181 Smallest eigenvalues: [1] 0.29118347 0.28489733 0.28026174 0.25999018 0.08777053 [6] -0.11785590 -0.70060267 -3.49331544 -13.64811248 -17.56523748 Largest eigenvalues: [1] 58976104 56720752 53939609 52043243 51642946 50375582 49123811 48879845 [9] 48363657 48273697 Smallest eigenvalues: [1] 0.48953567 0.45197409 0.42140663 0.40045530 0.39605595 0.36301187 [7] 0.32425021 0.22670188 0.08065016 -0.29537116 Largest eigenvalues: [1] 59845595 56507351 53564012 52372950 51937572 50406851 49445784 48538684 [9] 48429256 47745555 Smallest eigenvalues: [1] 0.48596488 0.46292815 0.37398289 0.32645640 0.27524587 0.26239896 [7] 0.19375040 0.07218173 -0.05151682 -0.24814098 Largest eigenvalues: [1] 61402191 56538695 54325703 52784237 51753876 50290613 49302344 48650704 [9] 48586047 47971453 Smallest eigenvalues: [1] 0.42433499 0.34175174 0.29165675 0.25529057 0.21170713 0.15614671 [7] 0.14555489 0.09361946 -1.00763621 -5.28750324 Largest eigenvalues: [1] 61347904 57101025 54869403 53008588 52416003 51169388 49722472 49443542 [9] 49299307 48917797 Smallest eigenvalues: [1] 0.36643533 0.31333113 0.26496466 0.17868642 0.16239341 [6] 0.05113204 -0.25285174 -1.04615977 -2.54992736 -29.31745335 Largest eigenvalues: [1] 61505028 56710982 54331961 52863980 52323701 50474148 49793880 49205923 [9] 49137344 48947432 Smallest eigenvalues: [1] 0.447639936 0.382680277 0.323319125 0.227768204 0.149650318 [6] 0.001436324 -0.013990639 -0.458823225 -5.382201337 -7.052337114 Largest eigenvalues: [1] 62318267 57039533 54314831 53945887 51779894 50227428 50128445 48899879 [9] 48711076 47763870 Smallest eigenvalues: [1] 0.36210018 0.35904707 0.32408736 0.18341260 -0.05317542 [6] -0.16817783 -0.24250663 -1.23932180 -2.24377750 -18.99911887 Largest eigenvalues: [1] 59100924 56062632 53765964 52065397 51670865 50619171 49030326 48639058 [9] 47932294 47576607 Smallest eigenvalues: [1] 0.14366366 0.05681732 -0.11138906 -0.18001424 -0.19484689 -0.60424350 [7] -0.64675070 -0.94448524 -1.16014157 -1.17947928 Largest eigenvalues: [1] 62148907 56530898 54308376 53775302 51509585 50270909 50004280 49283108 [9] 48849192 48536242 Smallest eigenvalues: [1] 0.4640112 0.4528071 0.3865665 0.2336814 0.1570571 0.1517641 [7] 0.1281990 -0.2479216 -1.0852059 -6.7204959 Largest eigenvalues: [1] 61332933 57424842 53955278 53464735 52700835 50780343 50032681 49500494 [9] 49296992 48500308 Smallest eigenvalues: [1] 0.339175511 0.307912971 0.307208770 0.199144661 0.156294940 [6] 0.139293495 0.130744065 -0.003598397 -0.196524446 -1.657573122 Largest eigenvalues: [1] 58027611 56981897 53981192 52718677 50905419 50725588 49342560 48417841 [9] 47780163 47688626 Smallest eigenvalues: [1] 0.2793720 0.2352363 0.1989567 0.1710637 0.1501798 -0.7099137 [7] -6.0949207 -6.3589111 -9.1482238 -39.2491201 Largest eigenvalues: [1] 59811521 56491167 53820843 52899871 51765049 50076012 49412384 49096790 [9] 48952380 48377946 Smallest eigenvalues: [1] 0.549759838 0.504900627 0.476635716 0.390003195 0.356372543 [6] 0.347380444 0.325125089 0.316424075 0.266936507 -0.006116805 Largest eigenvalues: [1] 60078706 56940455 54198162 52531248 52374660 50791948 49119881 48910229 [9] 48826398 48013635 Smallest eigenvalues: [1] 0.38784599 0.32083920 0.26631119 0.14999510 0.03100831 [6] -0.61933901 -1.79219047 -3.25251313 -11.46399409 -19.10913050 Largest eigenvalues: [1] 60285230 56358518 53753803 52551106 51980443 50499249 49518830 49193290 [9] 48699352 48320638 Smallest eigenvalues: [1] 0.4435208 0.3520587 0.2974127 0.2551893 0.2288605 0.1443867 [7] 0.0694762 -0.5085564 -1.1207016 -18.5116352 Largest eigenvalues: [1] 60400168 56877356 53892888 52929407 52184277 50512210 49908089 49115168 [9] 49044229 48802320 Smallest eigenvalues: [1] 0.5333649 0.4755432 0.4133360 0.4018409 0.3810956 0.3547434 [7] 0.2703130 0.1411500 0.1136397 -0.0358267 Largest eigenvalues: [1] 58584933 57411956 54424324 52959806 51450167 51146218 49551412 49371717 [9] 48497421 47977790 Smallest eigenvalues: [1] 0.31764977 0.25853021 0.23470100 0.22189263 0.19157742 0.17745888 [7] 0.06121566 -0.56323065 -0.81808028 -3.90698733 Largest eigenvalues: [1] 61481185 57346391 54626891 53659179 52890198 51388639 49964974 49700971 [9] 49411590 48659591 Smallest eigenvalues: [1] 0.47641663 0.35432400 0.32609368 0.28310366 0.27358396 0.27355493 [7] 0.12530882 -0.07098368 -0.12279130 -5.72540601 Largest eigenvalues: [1] 59093092 56266150 53498621 52142210 51349941 49879261 48881942 48558201 [9] 48374190 48002228 Smallest eigenvalues: [1] 0.38390521 0.27367857 0.26061777 0.16204851 0.01257977 [6] -0.62844663 -1.20956883 -3.56087148 -20.59333590 -34.16226829 Largest eigenvalues: [1] 60902431 56460794 53134343 53087743 51311845 49720924 49275072 48896458 [9] 48739715 47947326 Smallest eigenvalues: [1] 0.4097731 0.4051816 0.3785287 0.3591862 0.2946844 0.2721150 [7] 0.2589106 0.2406565 0.1819014 -1.1173823 Largest eigenvalues: [1] 60077495 56297999 53688644 52418559 51691157 50284136 48864657 48717926 [9] 48284317 47628659 Smallest eigenvalues: [1] 0.45047281 0.41015872 0.39756197 0.38943886 0.38160479 0.16588583 [7] 0.16189752 0.09771213 0.06718701 -0.12993299 Largest eigenvalues: [1] 61095825 57293261 54225411 53219838 52416428 50809656 49966312 49333671 [9] 49323751 49052566 Smallest eigenvalues: [1] 0.54850374 0.53135245 0.50275939 0.44642900 0.44155686 0.36090623 [7] 0.35871315 0.33571241 0.21521167 -0.05471739 Largest eigenvalues: [1] 60420813 57286119 54628617 52673949 52630859 50879071 49732959 49123521 [9] 49055113 48441678 Smallest eigenvalues: [1] 0.5447109 0.4878263 0.4863066 0.4268897 0.3568845 0.3309560 [7] 0.3065167 0.2010307 0.1462200 -8.8785981 Largest eigenvalues: [1] 60163228 56804659 54101596 52754821 52375271 50832973 49620835 49067479 [9] 48890030 48151958 Smallest eigenvalues: [1] 0.26790295 0.23910157 0.22179608 0.07719870 0.03627669 [6] 0.01945338 -0.90492194 -0.93704521 -0.94525045 -15.05997686 Largest eigenvalues: [1] 58957316 56405039 53386010 52300613 51791320 50228594 49268228 49112759 [9] 48278832 48103191 Smallest eigenvalues: [1] 0.3353948 0.2543446 0.2524597 0.2505750 0.2238432 0.1460797 [7] -0.1885191 -0.6325138 -5.3688326 -11.6301707 Largest eigenvalues: [1] 60061773 56497743 53343176 52433954 52073134 50476958 49187085 48635308 [9] 48386963 47721259 Smallest eigenvalues: [1] 0.48178706 0.45544995 0.40896900 0.38827427 0.29736962 0.19858588 [7] 0.16091296 0.10801610 -0.09518595 -1.11474871 Largest eigenvalues: [1] 60173019 56528922 54147633 52657320 51725081 50952280 49509551 49256941 [9] 48353770 48146081 Smallest eigenvalues: [1] 0.43163787 0.38054631 0.33210746 0.32035137 0.31477398 0.28584600 [7] 0.23353781 0.10434569 -0.05329913 -3.08974048 Largest eigenvalues: [1] 62252324 57063421 54209754 53185784 52215329 50435998 49547412 48981006 [9] 48797587 48412911 Smallest eigenvalues: [1] 0.42148238 0.40905621 0.27409166 0.26120059 0.21317944 0.20203543 [7] 0.03471340 -0.02042252 -0.64588415 -1.91713842 Largest eigenvalues: [1] 60673275 58062415 54138265 52962157 52929630 51230616 50343122 49207146 [9] 49058611 48863892 Smallest eigenvalues: [1] 0.46095383 0.44457359 0.29982216 0.25504081 0.10874690 0.10403961 [7] -0.05483162 -2.54237391 -2.73523559 -8.33702123 Largest eigenvalues: [1] 59998629 56389740 53761474 52511336 51721979 50244670 49111109 48686836 [9] 48538131 47732093 Smallest eigenvalues: [1] 0.47158431 0.45799175 0.33368068 0.30414562 0.26854217 0.24957315 [7] 0.24324980 0.09508194 0.08057482 -1.01592687 Largest eigenvalues: [1] 61781827 57089315 54482363 53956655 52401089 50941922 50175064 49782786 [9] 49170977 48579451 Smallest eigenvalues: [1] 0.5098786 0.4465045 0.3879235 0.3078002 0.2615741 0.2552321 [7] 0.2409576 0.1077741 -0.4290085 -1.4614653 Largest eigenvalues: [1] 61925021 56411071 53542487 53396024 51439195 49716816 49614202 48849052 [9] 48651802 48054131 Smallest eigenvalues: [1] 0.39622642 0.34405737 0.33027956 0.27819052 0.20873570 [6] 0.07909117 -0.01269290 -1.02854220 -15.61452221 -19.39787167 Largest eigenvalues: [1] 63061551 56864627 54809677 53896933 51631080 50248701 49790132 49552380 [9] 48973727 48595372 Smallest eigenvalues: [1] 0.5423656 0.4910305 0.3444046 0.3069521 0.2680991 0.2579143 [7] 0.2365904 0.2308456 0.1825648 -0.2020273 Largest eigenvalues: [1] 62285603 56842489 54656757 53616303 52233999 50817500 50044193 49268544 [9] 49118765 48343122 Smallest eigenvalues: [1] 0.56142911 0.53773567 0.52086709 0.49501931 0.42443595 0.30871022 [7] 0.29925135 0.09509862 0.02037768 -0.32438306 Largest eigenvalues: [1] 59509079 56572930 53618587 51829487 51728805 50057614 49029657 48471805 [9] 48192120 47922658 Smallest eigenvalues: [1] 0.33949217 0.33803577 0.20666739 0.18366437 0.06969104 [6] -0.13261974 -0.40391647 -8.39635927 -16.78613768 -27.70082206 Largest eigenvalues: [1] 60592441 56358036 53918962 52865285 51481458 50198923 49216932 49034845 [9] 48785509 48315967 Smallest eigenvalues: [1] 0.5252320 0.4068926 0.3678924 0.2888089 0.2776018 0.2107020 [7] 0.2004570 -0.2433275 -0.2588334 -0.4191841 Largest eigenvalues: [1] 62757182 57525160 55160255 54666312 52396290 50883688 50766379 50096961 [9] 49608110 49125633 Smallest eigenvalues: [1] 0.34200906 0.29045965 0.25533998 0.23016847 0.17769350 0.06670765 [7] -0.01802079 -0.10795047 -1.09399591 -6.00853886 Largest eigenvalues: [1] 60809287 56408096 53917298 52676513 51865352 50502337 49198363 48874516 [9] 48798061 48242631 Smallest eigenvalues: [1] 0.2971786 0.2794462 0.2578279 0.2487571 0.1793941 -0.2017744 [7] -0.8718174 -1.6391411 -4.9906278 -11.6318728 Largest eigenvalues: [1] 60985286 57102378 54525156 52964539 52720729 51316453 49969974 49646572 [9] 49292600 48902220 Smallest eigenvalues: [1] 0.50971424 0.46053441 0.33399340 0.30219284 0.28981686 0.27723250 [7] 0.24858656 -0.01027211 -0.32022824 -0.67075791 Largest eigenvalues: [1] 60704998 57030454 54377220 52904816 52179012 50768238 49389217 49372898 [9] 49226104 48435867 Smallest eigenvalues: [1] 0.4402515 0.4049418 0.3474676 0.2887192 0.2820669 0.2164072 [7] 0.1234106 0.1167003 -0.4638426 -1.5059732 Largest eigenvalues: [1] 59857237 57311806 54367127 52655927 52068086 50667817 49735715 49183565 [9] 48969577 48828793 Smallest eigenvalues: [1] 0.314030622 0.285601403 0.259711788 0.239102235 0.161113736 [6] 0.009876714 -0.605135381 -5.271492951 -6.617853614 -19.113927369 Largest eigenvalues: [1] 61243047 56982822 54174588 52932402 52612589 50686177 49345786 49244404 [9] 49207540 48460126 Smallest eigenvalues: [1] 0.31511518 0.24385121 0.23850909 0.20758819 0.18241314 0.15758979 [7] 0.07120119 -0.46825107 -0.62621139 -3.16036797 Largest eigenvalues: [1] 59349775 56280840 53975617 51986685 51807131 50408657 48898540 48694432 [9] 48324891 48070235 Smallest eigenvalues: [1] 0.4508281 0.4423478 0.4225551 0.4146955 0.4090791 0.3148231 [7] 0.3146502 0.2606874 0.2296801 -0.2237024 Largest eigenvalues: [1] 60941272 56468751 53539636 52865900 51893150 50281783 49173924 48828301 [9] 48637290 47919746 Smallest eigenvalues: [1] 0.4347725 0.3627567 0.3291757 0.3134036 0.3115428 0.2749950 [7] 0.2477781 0.2199183 0.1421373 -0.2857909 Largest eigenvalues: [1] 61271813 56815048 53730287 52875327 52038043 50337037 49246212 49037824 [9] 48876943 48218396 Smallest eigenvalues: [1] 0.4910655 0.4890154 0.4360432 0.3191403 0.2616882 0.2271939 [7] 0.2191214 0.1988822 0.1396233 -0.5111051 Largest eigenvalues: [1] 60800877 57771715 54261069 53386073 52964523 51212364 50423100 49603599 [9] 49378913 48774721 Smallest eigenvalues: [1] 0.56772685 0.53136156 0.48970770 0.36706839 0.32119377 0.28510216 [7] 0.25532904 0.19250793 0.05833616 -0.14891229 Largest eigenvalues: [1] 60343529 56827662 54024625 52544327 52150922 50289480 49491577 48943118 [9] 48831098 48152604 Smallest eigenvalues: [1] 0.20834974 0.18960037 0.13656326 0.11928204 0.01317776 [6] -0.03442447 -1.30962481 -4.15751099 -26.22441190 -33.70775313 Largest eigenvalues: [1] 60314777 57038021 54011562 52318541 51684195 50727284 49161274 48889373 [9] 48664044 48015788 Smallest eigenvalues: [1] 0.41824215 0.38153962 0.31328214 0.25768773 0.16123829 [6] 0.01464603 -0.26533252 -0.40173305 -0.51126494 -20.63714505 Largest eigenvalues: [1] 63311846 57073473 54437712 53727916 51812577 50197060 50062158 49427953 [9] 49100895 48927738 Smallest eigenvalues: [1] 0.30232228 0.26997100 0.26240753 0.23583639 0.23050949 0.21737139 [7] 0.06163849 -0.32711451 -1.94496454 -7.87675623 Largest eigenvalues: [1] 61675428 55956342 54015043 53329432 51169866 49693470 49598128 48877129 [9] 48632746 48044227 Smallest eigenvalues: [1] 0.38916819 0.38684856 0.30577739 0.17589424 0.10741200 [6] 0.08766567 0.04284418 -2.47324938 -9.63713136 -24.21626619 Largest eigenvalues: [1] 59899175 57355085 54281021 52972183 51832365 51315424 49905177 49111614 [9] 48574248 48382498 Smallest eigenvalues: [1] 0.348059043 0.301915751 0.300416857 0.270096223 0.112456101 [6] 0.001729192 -0.539484795 -4.512547760 -51.909515872 -52.961187649 Largest eigenvalues: [1] 60600196 56700310 54494119 53178318 52210746 50618606 49529498 49304286 [9] 49229472 48636373 Smallest eigenvalues: [1] 0.3182713 0.3025223 0.2713749 0.2322011 0.2196419 0.1975188 [7] 0.1891580 -0.7996352 -6.6101499 -9.0374399 Largest eigenvalues: [1] 60563900 56957752 54282467 53076469 52388597 51463878 50076769 49232548 [9] 48682014 48518212 Smallest eigenvalues: [1] 4.689397e-01 4.682354e-01 4.388693e-01 3.655827e-01 3.496670e-01 [6] 2.934439e-01 8.185994e-02 -7.043162e-04 -7.767521e-01 -1.520887e+01 Largest eigenvalues: [1] 60896387 56987225 53702324 52796052 52384080 50812435 49276830 49163470 [9] 48970573 48409355 Smallest eigenvalues: [1] 0.40632874 0.40126512 0.29345013 0.22006015 0.16052347 0.06023394 [7] -0.05025302 -0.21568122 -0.25433145 -2.88296807 Largest eigenvalues: [1] 59378654 56147099 53547902 52031358 51495051 50205615 48842588 48823149 [9] 48009829 47871754 Smallest eigenvalues: [1] 0.355797393 0.280437357 0.223174516 0.162479591 0.138431972 [6] 0.007023788 -0.746266959 -1.523684331 -4.681798899 -34.868754382 Largest eigenvalues: [1] 62585711 57130987 54848305 53964617 52260428 50449782 50322939 50267455 [9] 49027184 48873772 Smallest eigenvalues: [1] 0.16607192 0.14306791 0.06301988 0.01136553 -0.02101099 -0.07411093 [7] -0.93007851 -1.50250834 -4.21593645 -7.19805001 Largest eigenvalues: [1] 61677328 56415181 53991103 52346626 51588008 50112759 48820152 48558262 [9] 48382751 47950519 Smallest eigenvalues: [1] 0.4347337 0.3949646 0.3911517 0.3799328 0.3620830 0.3164204 [7] 0.2842868 0.1541302 0.1387818 -0.2894760 Largest eigenvalues: [1] 60013886 57072989 54464831 52281232 51953373 50776904 49274807 49122951 [9] 48491688 48365570 Smallest eigenvalues: [1] 0.33410650 0.25496856 0.22934880 0.10244216 0.04663886 [6] -0.12400820 -0.38103637 -3.68947051 -9.56906650 -14.27356981 Largest eigenvalues: [1] 61331244 55971884 53377388 53075800 51226343 49816550 49218873 49008289 [9] 48884827 47991241 Smallest eigenvalues: [1] 0.4324697 0.4058812 0.3484058 0.3326332 0.3158235 0.2315195 [7] 0.2125285 0.1788258 0.1565272 -3.4889222 Largest eigenvalues: [1] 61479838 56841967 54310852 53269393 51996114 50515089 49602465 49256943 [9] 49058740 48351937 Smallest eigenvalues: [1] 0.40652559 0.35255020 0.28946028 0.26758903 0.19425038 0.18984491 [7] 0.17046889 0.14286037 -0.07237851 -0.93400345 Largest eigenvalues: [1] 58816222 56240981 53505957 51957971 51552587 50241008 48691149 48223308 [9] 47891293 47551007 Smallest eigenvalues: [1] 0.47522129 0.43065724 0.36815529 0.22724140 0.22029721 0.09921582 [7] 0.05796817 -0.80382553 -1.17622260 -5.26424778 Largest eigenvalues: [1] 62508304 57392133 54573662 53786971 52297792 50630489 50034398 49791413 [9] 49655409 48938738 Smallest eigenvalues: [1] 0.52867667 0.47774386 0.44832935 0.41773423 0.38808711 0.30479910 [7] 0.30193801 0.29348330 0.24325279 -0.03169598 Largest eigenvalues: [1] 61745790 56680071 53775274 53295266 51836711 50216010 49592638 49221439 [9] 48490832 47896045 Smallest eigenvalues: [1] 0.50762341 0.43790942 0.36605507 0.36128962 0.35702117 0.29127374 [7] 0.22368624 0.05506251 -1.49015120 -3.46774518 Largest eigenvalues: [1] 61920464 56915126 54709804 53262066 52066457 50586621 49688353 49412124 [9] 49078386 48568808 Smallest eigenvalues: [1] 0.5373217 0.4921865 0.3911930 0.3160646 0.3155764 0.2851261 [7] 0.2301770 0.2091235 0.1528929 -0.5387546 Largest eigenvalues: [1] 59885236 56386070 53927796 52242904 51921123 50612544 49381455 48527053 [9] 48433312 47765034 Smallest eigenvalues: [1] 0.3193982 0.2742213 0.2158687 0.1347838 0.1324331 -0.2499680 [7] -0.3543204 -0.4550118 -5.3538463 -6.7993108 Largest eigenvalues: [1] 61491672 56579458 53821945 53200254 51796781 50229421 49489024 49097235 [9] 48448762 48111195 Smallest eigenvalues: [1] 0.43597619 0.35529175 0.33484908 0.29948128 0.26956299 [6] 0.24300472 0.20844940 0.06841585 -1.14762635 -25.66460462 Largest eigenvalues: [1] 60613711 57268413 54403456 53001567 52417993 51224446 49872351 49354218 [9] 49190286 48623926 Smallest eigenvalues: [1] 0.4457120 0.4265161 0.3292969 0.3132624 0.3118756 0.2643701 [7] 0.2409427 0.2384810 0.2046856 -0.3320168 Largest eigenvalues: [1] 62088896 56185033 53272296 53206329 51522431 49739559 49527626 48785877 [9] 48726901 48164591 Smallest eigenvalues: [1] 0.50525860 0.48665512 0.40186560 0.31861229 0.31623167 0.26425118 [7] 0.17512966 0.17439243 0.06677018 -0.18584037 Largest eigenvalues: [1] 58926610 56239984 53755090 51832699 51823323 50253530 48982801 48781276 [9] 48187672 47839228 Smallest eigenvalues: [1] 0.30335962 0.27107458 0.22332071 0.12996096 0.12941904 [6] 0.11065529 0.03322996 -3.18566404 -7.80800125 -11.10937003 Largest eigenvalues: [1] 60015326 56087388 53942611 52558602 51751557 50119987 49036210 49007735 [9] 48704744 48077439 Smallest eigenvalues: [1] 0.21849841 0.21006266 0.19585000 0.18335438 0.06734078 [6] 0.06555411 -1.38074122 -2.68187884 -17.36305360 -22.25990004 Largest eigenvalues: [1] 61614453 56736952 54078825 53895031 51404379 50131020 50093782 49155341 [9] 48918451 48434383 Smallest eigenvalues: [1] 0.454075098 0.375293298 0.343175203 0.293986910 0.269019008 [6] 0.170290433 0.126068577 0.008295461 -0.173063125 -1.066218434 Largest eigenvalues: [1] 62443975 57213729 54764481 54107169 52154885 50570665 50394932 49512479 [9] 49039240 48586900 Smallest eigenvalues: [1] 0.47654224 0.47405328 0.40542717 0.36764964 0.32185130 0.27098173 [7] -0.02796257 -0.17387545 -0.18435590 -4.93877290 Largest eigenvalues: [1] 59148813 56448666 53597542 51892494 51777076 50195110 48612268 48582809 [9] 48191384 47694596 Smallest eigenvalues: [1] 0.39713474 0.34201073 0.32847861 0.27807093 0.14382892 0.11580935 [7] 0.05878891 0.01022393 -0.10604584 -4.41011592 Largest eigenvalues: [1] 62278253 56949902 54502763 53434316 51704548 50484321 49751664 49039133 [9] 48821830 48448445 Smallest eigenvalues: [1] 0.3960974 0.3870214 0.3262925 0.3242616 0.2713724 0.2672649 [7] 0.1985853 0.1914828 0.1416331 -0.9017774 Largest eigenvalues: [1] 58484695 56931659 53890817 52249253 52170689 50633922 49059325 48957888 [9] 48344596 47994280 Smallest eigenvalues: [1] 0.22984222 0.19473781 0.14173531 0.08821091 0.01332756 -0.05924591 [7] -0.12893169 -0.75964906 -1.15871806 -1.75381416 Largest eigenvalues: [1] 61932311 58385600 54770640 54085080 53457367 51722161 50337228 50198314 [9] 50185155 49052813 Smallest eigenvalues: [1] 0.159957535 0.154988961 0.122071346 0.103456728 0.063762452 [6] 0.009626203 -0.788769032 -13.226342707 -16.071954531 -77.367317742 Largest eigenvalues: [1] 60568366 56202282 53647588 53571091 51687276 50271126 49650738 48838504 [9] 48428981 47552671 Smallest eigenvalues: [1] 0.37639401 0.37411404 0.32809528 0.31800993 0.15742613 [6] 0.15458086 0.05537723 0.02665379 -0.09724736 -21.76266455 Largest eigenvalues: [1] 61970969 56900249 54184364 53280072 51803194 50154715 49581539 49298497 [9] 48813472 48729453 Smallest eigenvalues: [1] 0.55835865 0.52289622 0.50149233 0.46242786 0.35588695 0.33479381 [7] 0.11419346 0.07908370 0.07304577 -2.09408891 Largest eigenvalues: [1] 60423281 56687405 53925098 52826634 51902484 50134608 49539128 49010750 [9] 48854954 48421021 Smallest eigenvalues: [1] 0.4363871 0.4117852 0.3704457 0.2988169 0.2594690 0.2541040 [7] 0.2472919 0.1106023 -0.3151061 -2.2463174 Largest eigenvalues: [1] 62479444 56703453 54250297 53928835 51982903 50437601 50199427 49225524 [9] 48735957 48305471 Smallest eigenvalues: [1] 0.39001993 0.34860670 0.32087413 0.18864156 0.15713521 0.13582955 [7] -0.01219046 -0.11106249 -0.13627916 -4.26527530 Largest eigenvalues: [1] 61128984 56732346 53992964 53217663 51869948 50121186 49515172 49379859 [9] 48991461 48436081 Smallest eigenvalues: [1] 0.29914635 0.29173841 0.22432943 0.21983041 0.20580161 0.15986009 [7] 0.11032136 0.06270175 -0.77642652 -5.48441529 Largest eigenvalues: [1] 62649875 57155768 54490067 54333196 52636938 51381892 50331425 50040806 [9] 49624009 48943595 Smallest eigenvalues: [1] 0.3409712 0.2995508 0.2935446 0.2316799 0.2293897 0.2238680 [7] 0.1195191 -0.1214191 -1.7122432 -9.5012874 Largest eigenvalues: [1] 62062317 56783429 54128018 53048092 51621695 50233678 49520405 48754257 [9] 48727633 47854958 Smallest eigenvalues: [1] 0.23855246 0.23646101 0.19189648 0.09734688 -0.10149375 [6] -0.18790231 -0.18828343 -3.26314013 -4.40746644 -22.44208400 Largest eigenvalues: [1] 61959735 57646600 55074580 53076393 53047418 51747009 50054201 49643340 [9] 49520767 48609208 Smallest eigenvalues: [1] 0.54782995 0.50020943 0.46651002 0.40386465 0.26113576 0.22483265 [7] 0.17237404 -0.03746588 -0.07045131 -0.52104164 Largest eigenvalues: [1] 60706903 56869602 54595345 52467064 52329392 50918970 49807643 48991012 [9] 48836898 48337336 Smallest eigenvalues: [1] 0.4107384 0.3703386 0.3533933 0.3300557 0.2686445 0.2315385 [7] -0.1335953 -0.6894665 -0.6911723 -9.5687108 Largest eigenvalues: [1] 61485116 57369993 54333168 53660042 52105644 50166396 50157911 49865260 [9] 49127593 49011683 Smallest eigenvalues: [1] 0.29818195 0.28513261 0.25574607 0.17288593 0.13953916 [6] 0.07527398 0.06827416 -2.79901952 -5.90286543 -19.79056468 Largest eigenvalues: [1] 62092151 56285121 53498623 53488365 51552733 50158783 49607482 49283143 [9] 48851897 48164440 Smallest eigenvalues: [1] 0.383494390 0.359194054 0.348828618 0.308043557 0.187171097 [6] -0.003795561 -0.131785008 -0.193868547 -2.548813603 -18.394154279 Largest eigenvalues: [1] 59964097 55990257 53581110 51686824 51679979 50210190 48951708 48918447 [9] 48063359 47914438 Smallest eigenvalues: [1] 0.480105662 0.470045790 0.460827249 0.336491777 0.243970141 [6] 0.223312083 0.184523207 0.006941442 -0.150907437 -0.228801851 Largest eigenvalues: [1] 63272550 57219429 54834797 54289989 52004004 50645927 50491490 49451821 [9] 49283944 48787829 Smallest eigenvalues: [1] 0.37460795 0.35093166 0.33409953 0.33132392 0.31179075 0.24012342 [7] 0.18126875 0.11475299 0.04580536 -0.01061992 Largest eigenvalues: [1] 60249844 57321338 54270765 52964472 52243304 51189937 50310611 49404142 [9] 49196141 48688708 Smallest eigenvalues: [1] 0.3954874 0.3369197 0.3149131 0.2860644 0.2648368 0.2517564 [7] 0.2165180 -0.8853363 -1.4741663 -6.4369891 Largest eigenvalues: [1] 61021795 56932466 54688868 53102247 52312690 50992720 49390527 49313578 [9] 49245223 48589550 Smallest eigenvalues: [1] 0.46124141 0.34273903 0.30650608 0.27584418 0.25686014 0.22786718 [7] 0.11179980 0.08336364 -0.09972070 -3.06198213 Largest eigenvalues: [1] 60045626 56836281 54024820 52622129 52140874 50616641 49595008 48876672 [9] 48803178 48009437 Smallest eigenvalues: [1] 0.38810326 0.32790431 0.32466401 0.30947199 0.22131191 0.21718657 [7] 0.13572043 0.09753183 -0.05931946 -0.08945257 Largest eigenvalues: [1] 61425016 57004572 54268286 53878091 51914423 50425227 50088409 49328219 [9] 49103336 48302541 Smallest eigenvalues: [1] 0.4808768 0.4477533 0.3986728 0.3842572 0.3699377 0.2306832 [7] 0.2297420 0.1736829 0.1178753 -1.0841523 Largest eigenvalues: [1] 60813094 56710255 54238088 52724208 51944655 50254366 49223527 49171960 [9] 49032194 48315009 Smallest eigenvalues: [1] 0.3535600 0.3408537 0.3101454 0.2916545 0.1873881 0.1350212 [7] -0.2523438 -0.9252710 -0.9888521 -3.1518995 Largest eigenvalues: [1] 61837632 57611809 54412002 53843953 53097169 51476929 50331822 49979942 [9] 49617249 49335613 Smallest eigenvalues: [1] 0.5059704 0.4812803 0.4766706 0.4335792 0.3550847 0.3075314 [7] 0.2778291 0.2522708 0.2293167 -0.3027754 Largest eigenvalues: [1] 59948355 56610114 53505546 52558601 52029170 50214780 48870221 48821568 [9] 48369744 47414848 Smallest eigenvalues: [1] 0.38034345 0.35545584 0.34592813 0.33273672 0.32648443 0.31745792 [7] 0.28846999 0.16189176 0.13428060 -0.03288469 Largest eigenvalues: [1] 61584032 56813073 54297019 52726826 52101652 50665274 49087892 49021156 [9] 48847098 47902580 Smallest eigenvalues: [1] 0.33706078 0.21899162 0.18213287 0.17438290 0.16506014 0.15150083 [7] 0.15115627 0.13450407 0.01476054 -1.25717332 Largest eigenvalues: [1] 58541625 57066021 53970061 52817677 52019432 51050768 49665726 48799399 [9] 48184684 47995465 Smallest eigenvalues: [1] 0.3190563 0.2938288 0.2856619 0.2089785 0.1863252 0.1368130 [7] 0.1249840 -0.3696651 -0.5290861 -10.2357884 Largest eigenvalues: [1] 60328162 56851709 54278718 52455654 52297597 50644645 49590427 49240832 [9] 48855729 48538495 Smallest eigenvalues: [1] 0.4511547 0.3997581 0.3538266 0.3471897 0.3096604 0.3056124 [7] 0.2294201 0.1702149 -1.8109910 -1.8842552 Largest eigenvalues: [1] 62449256 57096866 54369385 54178792 52245220 50731708 50336783 49959531 [9] 49613124 49275522 Smallest eigenvalues: [1] 0.34472456 0.33926289 0.32336987 0.30743851 0.25213531 0.22632663 [7] 0.18835568 0.13517620 0.05189122 -0.36976699 Largest eigenvalues: [1] 59460519 58011482 54661527 53432448 52696818 51740806 50578330 50086000 [9] 49113356 48867280 Smallest eigenvalues: [1] 0.33114703 0.32095564 0.30484217 0.21789101 0.12444096 [6] -0.07116436 -0.26027412 -2.24406561 -6.45643860 -53.10448723 Largest eigenvalues: [1] 57487998 56419185 53336004 52427585 50671607 50490045 49093795 48138150 [9] 47392577 47308233 Smallest eigenvalues: [1] 0.2487038 0.1218874 0.0126370 -0.1063677 -0.3751204 -2.1610635 [7] -3.5344818 -10.5026740 -12.9080733 -38.4380439 Largest eigenvalues: [1] 60011652 57027561 54132720 52829502 52394903 50931533 49920913 49542703 [9] 48687130 48599236 Smallest eigenvalues: [1] 0.5043314 0.4674775 0.4438305 0.4184888 0.2617872 0.2281800 [7] 0.2194518 0.1257092 0.1195882 -0.4065258 Largest eigenvalues: [1] 61580201 57109972 53813061 53288774 52358517 50477069 49574754 49508185 [9] 49391295 48785623 Smallest eigenvalues: [1] 0.29397676 0.28343614 0.28202910 0.27530875 0.20463956 0.07156716 [7] 0.03669206 -0.02018551 -1.94313736 -4.95922472 Largest eigenvalues: [1] 61308766 56327991 54178169 53081362 51476778 50313279 49459551 49330581 [9] 48958272 48635424 Smallest eigenvalues: [1] 0.42860001 0.35267418 0.33539053 0.31460604 0.28888061 0.24218668 [7] 0.17695307 0.02223382 -0.29773095 -0.57160497 Largest eigenvalues: [1] 60003272 56476546 53764263 52636152 51935498 50304366 49011336 48979363 [9] 48895585 48077438 Smallest eigenvalues: [1] 0.3558276 0.3517814 0.2753354 0.2611108 0.2215411 0.1735605 [7] 0.1498920 -0.7989731 -1.9764232 -3.1533489 Largest eigenvalues: [1] 60850880 57105435 53972151 53165966 52895460 51116548 49516853 49246506 [9] 49049081 48262660 Smallest eigenvalues: [1] 0.25032698 0.24864823 0.19662907 0.19358242 0.06586161 [6] -0.08092775 -0.31459471 -0.64863961 -10.19658544 -68.90544984 Largest eigenvalues: [1] 58459997 55730903 52918431 51715139 51444803 49714262 48728022 48423458 [9] 47798431 47454382 Smallest eigenvalues: [1] 0.5358082 0.4961394 0.4092360 0.3545227 0.3436694 0.2927085 [7] 0.2759035 0.2541941 0.1481678 -1.0055155 Largest eigenvalues: [1] 60290689 56702836 53911717 52402961 52017677 50673730 49230352 49179069 [9] 48700606 48346066 Smallest eigenvalues: [1] 0.4210492 0.4193421 0.3922454 0.3441325 0.3004120 0.2033589 [7] -0.0564633 -3.5679114 -9.9891876 -55.9477940 Largest eigenvalues: [1] 59875544 57760215 54136097 52759751 52476478 50893122 49423083 49172527 [9] 48923185 48335416 Smallest eigenvalues: [1] 0.46940503 0.39951203 0.37368832 0.36420294 0.25247354 0.22709284 [7] 0.19153401 0.07257433 0.02402702 -0.04434930 Largest eigenvalues: [1] 61783590 57900945 55129450 53820789 52453064 50777316 50100028 50010609 [9] 49353870 48872391 Smallest eigenvalues: [1] 0.38379897 0.35492111 0.24568625 0.23418153 0.22972098 0.20332943 [7] 0.13437010 0.02420657 -2.17283038 -2.51410862 Largest eigenvalues: [1] 60868508 57347481 54551179 53414728 52588932 51099484 49954711 49569755 [9] 49466249 48437955 Smallest eigenvalues: [1] 0.42714063 0.35157046 0.33711050 0.24169897 0.23614316 0.22021076 [7] 0.10723145 0.03969452 -0.31057211 -1.59897258 Largest eigenvalues: [1] 61887478 56805517 53898680 53891541 52036930 50448111 50104662 49358051 [9] 49297896 48491635 Smallest eigenvalues: [1] 0.14256191 0.14250161 0.02342479 -0.24950722 -1.42897034 [6] -3.98634130 -5.55561035 -6.62603456 -6.63040944 -114.28439462 Largest eigenvalues: [1] 59992263 56529620 53563024 52779672 52280943 50715776 49258468 49004822 [9] 48907391 48203071 Smallest eigenvalues: [1] 0.4513500 0.3918543 0.3602837 0.3341270 0.3271343 0.3056630 [7] 0.2714532 0.1672799 0.1055999 -0.6934877 Largest eigenvalues: [1] 60622125 57237798 54466228 52697723 52267879 50774691 49212866 49169347 [9] 49047962 48306048 Smallest eigenvalues: [1] 0.46959605 0.45872647 0.36557961 0.36470279 0.33003131 0.28049758 [7] 0.27917951 0.13882972 -0.01067653 -0.03897265 Largest eigenvalues: [1] 58850987 56475300 53658419 52354847 51338741 50582279 49110882 49008203 [9] 48196325 47808108 Smallest eigenvalues: [1] 0.5144844 0.4536761 0.4371657 0.4112515 0.3374469 0.2929794 [7] 0.2205514 0.1697489 0.1542738 -0.4354097 Largest eigenvalues: [1] 60747911 57314365 54092350 52743931 52577360 50919821 49792884 49433942 [9] 49057394 48808371
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 1.097739 | 0.5756892 | 41.5781 | 0.35 | 2.814556 | 1.640583 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + body_temp + PM25
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd,
pollution = pollution25_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempBody_PM25_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 14. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 308 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9471101 | 0.6771254 | 22.52582 | 0.425 | 5.772056 | 2.589453 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + n + body_temp + PM1
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd,
pollution = pollution1_fd)
path_plot <- 'figures/model_EDA_alt_noise_tempBody_PM1_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
pollution = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 14. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 322 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ...
Smallest eigenvalues: [1] 0.14483019 0.13960402 0.12707429 0.09882543 0.09599995 0.06519062 [7] 0.04430862 0.03099529 -3.92924016 -4.39570664 Largest eigenvalues: [1] 48376187 45714509 42890947 42867486 41586334 40306422 39946535 39808216 [9] 39037988 38887276
Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9455276 | 0.6887335 | 21.9582 | 0.555 | 5.737343 | 2.358661 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ noise + temp + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(#altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd,
temperature = temperature_fd)
path_plot <- 'figures/model_EDA_noise_temp_bodyTemp_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 90, norder = 4, lambda = 1e5),
#altitude = list(nbetabasis = 80, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temp_body = list(nbetabasis = 80, norder = 4, lambda = 1e3),
temperature = list(nbetabasis = 80, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 182 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9997611 | 0.5450801 | 14.49862 | 0.04 | 1.126926 | 1.18645 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
EDA ~ alt + noise + temp + body_temp
- First, we have to define some variables.
- Then, execute the cell below. It should compute everything :)
outcome <- EDA_fd
covariates <- list(altitude = altitude_fd,
noise = noise_fd,
temp_body = body_temperature_ENT_fd,
temperature = temperature_fd)
path_plot <- 'figures/model_EDA_alt_noise_temp_bodyTemp_CENTERED'
basis_params <- list(beta_0 = list(nbetabasis = 80, norder = 4, lambda = 1e5),
altitude = list(nbetabasis = 70, norder = 4, lambda = 1e3),
noise = list(nbetabasis = 70, norder = 4, lambda = 1e3),
temp_body = list(nbetabasis = 70, norder = 4, lambda = 1e3),
temperature = list(nbetabasis = 70, norder = 4, lambda = 1e3))
set.seed(42)
############################################################################
## First function prepares the outcome and covariates for fRegress() function
model_1 <- model_fRegress_1(outcome = outcome, covariates = covariates,
path_plot = path_plot, basis_params = basis_params)
outcome <- model_1$outcome
for (cov in names(model_1$covariates)) {
assign(cov, model_1$covariates[[cov]])
}
############################################################################
## Fit the concurrent model
model_concurrent <- fRegress(model_1$formula, betalist = model_1$betafdPar)
############################################################################
## Second function uses the fitted model to plot fitted curves and
## to calculate and plot R^2 and F-statistic
model_2 <- model_fRegress_2(model_concurrent = model_concurrent, outcome = outcome,
covariates = covariates, path_plot = path_plot, HR = HR,
basis_params = basis_params, nperm = nperm, lenght_tt = lenght_tt)
############################################################################
## Plot the figures (they are also saved in the path_plot folder)
options(repr.plot.width = 20, repr.plot.height = 25, repr.plot.res = 300)
model_2$plots[[1]] /
(model_2$plots[[2]] | model_2$plots[[3]])
options(repr.plot.width = 10, repr.plot.height = 5, repr.plot.res = 100)
############################################################################
## Calculate the bootstrap beta functions (first, some variables have to be defined)
ncovariates <- length(covariates)
common_IDs <- model_1$common_IDs
rangeval <- outcome$basis$rangeval
tt <- seq(rangeval[1], rangeval[2], length = lenght_tt)
important_times <- c(0, Times_of_segments$time |> diff() |> as.numeric() |> cumsum())
n_samples <- dim(outcome$coefs)[2]
beta_BS <- array(data = NA, dim = c(length(tt), N_repeats, length(model_concurrent$betaestlist)))
i <- 0
message('Calculating the bootstrap CI for beta functions ...')
while (i < N_repeats) {
try({
BS_sample <- sample(1:n_samples, n_samples, replace = TRUE)
outcome_BS <- outcome[BS_sample]
for (cov in names(covariates)) {assign(paste0(cov, '_BS'), covariates[[cov]][common_IDs][BS_sample])}
# define formula
formula_BS <- paste0('outcome_BS ~ ')
for(cov in names(covariates)[-ncovariates]) {formula_BS <- paste0(formula_BS, paste0(cov, '_BS'), '+')}
formula_BS <- as.formula(paste0(formula_BS, paste0(names(covariates)[ncovariates], '_BS')))
# fit the model
model_concurrentBS <- fRegress(formula_BS, betalist = model_1$betafdPar)
# calculate and save betas
for(j in 1:length(model_concurrent$betaestlist)) {
beta_BS[, i, j] <- c(eval.fd(model_concurrentBS$betaestlist[[j]]$fd, tt))}
i <- i + 1
}, silent = TRUE)}
############################################################################
## Plot the bootstrap CI's using our function
BS_CI <- bootstrap_CI(N_repeats = N_repeats, beta_BS = beta_BS,
n_beta = length(model_concurrent$betaestlist),
model_concurrent = model_concurrent, path_plot = path_plot, lenght_tt = lenght_tt)
############################################################################
## Save important variables into model.RData file
save(model_1, model_2, model_concurrent, beta_BS, BS_CI, file = paste0(path_plot, '/model.RData'))
Final number of observations = 23. Plotting the fitted curves ... Plotting the beta functions ... Calculating the functional R^2 ... Plotting the functional R^2 ... Calculating the functional F-ratio test ...
[1] "Estimated Computing time = 232 seconds."
Plotting the results of the functional F-ratio test ... DONE :-) Calculating the bootstrap CI for beta functions ... Plotting the bootstrap CIs for beta functions (from 100 bootstrap samples) ...
DONE :-)
model_2$df_res_metrics
| RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 95% | 0.9835984 | 0.5460793 | 16.12738 | 0.17 | 1.579801 | 1.178132 |
Global envelope test
GET_results <- vector('list', length = ncovariates)
names(GET_results) <- names(model_1$covariates)
for(j in 1:ncovariates) {
GET_res <- GET_function(J = j, outcome = outcome, model_1 = model_1,
nsim = nsim, model_concurrent = model_concurrent,
beta_BSnew = BS_CI$beta_BS, path_plot = path_plot, lenght_tt = lenght_tt)
GET_results[[j]] <- GET_res
}
options(repr.plot.width = 20, repr.plot.height = 15, repr.plot.res = 200)
(GET_results[[1]]$plot | GET_results[[2]]$plot)/
(GET_results[[3]]$plot | GET_results[[4]]$plot)
save(GET_results, file = paste0(path_plot, '/GET_results.RData'))
Model comparison
Finally, we compare fitted functional models based on various criteria.
# Specify the models folders
models_path <- list.dirs(path = "figures/") |>
(\(x) x[grepl("^figures/model_EDA.*_CENTERED$", x)])() |>
sub("^figures/", "", x = _)
# Create a data frame where the characteristics will be stored
model_comparison <- data.frame(model = NA, N = NA, RMSE = NA, maxR2 = NA, integratedR2 = NA,
pval = NA, qval = NA, Fobs = NA)
# Load all models
for (model_path in models_path) {
load(file = paste0("figures/", model_path, "/model.RData"), verbose = FALSE)
model_comparison <- rbind(
model_comparison,
c(substr(model_path, 7, nchar(model_path) - 9),
length(model_1$common_IDs),
unlist(as.vector(model_2$df_res_metrics))))
}
model_comparison <- model_comparison[-1, ] |>
mutate(N = as.numeric(N),
RMSE = round(as.numeric(RMSE), 6),
maxR2 = round(as.numeric(maxR2), 6),
integratedR2 = as.numeric(integratedR2),
pval = as.numeric(pval),
qval = round(as.numeric(qval), 4),
Fobs = round(as.numeric(Fobs), 4))
model_comparison[(order(model_comparison$RMSE)), ]
| model | N | RMSE | maxR2 | integratedR2 | pval | qval | Fobs | |
|---|---|---|---|---|---|---|---|---|
| <chr> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 22 | EDA_alt_noise_tempBody_PM1 | 14 | 0.945528 | 0.688733 | 21.958200 | 0.555 | 5.7373 | 2.3587 |
| 23 | EDA_alt_noise_tempBody_PM25 | 14 | 0.947110 | 0.677125 | 22.525824 | 0.425 | 5.7721 | 2.5895 |
| 17 | EDA_alt_noise_temp_acc | 31 | 0.959756 | 0.533264 | 14.448738 | 0.090 | 1.1066 | 1.0144 |
| 21 | EDA_alt_noise_temp_steps | 31 | 0.967796 | 0.484247 | 13.279872 | 0.260 | 1.3471 | 0.9115 |
| 25 | EDA_alt_noise_tempEntrant | 19 | 0.971104 | 0.634487 | 14.239710 | 0.095 | 1.8896 | 1.6762 |
| 20 | EDA_alt_noise_temp_speed | 32 | 0.978453 | 0.498659 | 25.745133 | 0.765 | 1.3214 | 0.9233 |
| 24 | EDA_alt_noise_tempEmpatica | 32 | 0.980686 | 0.502600 | 11.136725 | 0.010 | 0.8105 | 0.9532 |
| 19 | EDA_alt_noise_temp_bodyTemp | 23 | 0.983598 | 0.546079 | 16.127379 | 0.170 | 1.5798 | 1.1781 |
| 12 | EDA_alt_noise_speed_PM1 | 19 | 0.990957 | 0.582579 | 15.192438 | 0.215 | 2.7682 | 1.8955 |
| 13 | EDA_alt_noise_speed_PM25 | 19 | 0.992560 | 0.574583 | 15.338634 | 0.190 | 2.6574 | 1.9415 |
| 29 | EDA_noise_temp_bodyTemp | 23 | 0.999761 | 0.545080 | 14.498624 | 0.040 | 1.1269 | 1.1864 |
| 11 | EDA_alt_noise_speed | 32 | 1.008945 | 0.399442 | 10.770685 | 0.765 | 1.2732 | 0.6518 |
| 5 | EDA_alt_noise_acc_PM1 | 18 | 1.009266 | 0.649744 | 15.440150 | 0.245 | 3.0610 | 1.8601 |
| 6 | EDA_alt_noise_acc_PM25 | 18 | 1.010421 | 0.660726 | 15.608628 | 0.200 | 2.8388 | 1.9379 |
| 18 | EDA_alt_noise_temp_body | 23 | 1.015597 | 0.456796 | 13.112231 | 0.285 | 1.3621 | 0.8815 |
| 26 | EDA_alt_temp_body | 28 | 1.017492 | 0.337989 | 6.511186 | 0.190 | 0.8153 | 0.5146 |
| 3 | EDA_airpress_noise_temp | 24 | 1.018808 | 0.412089 | 10.848122 | 0.540 | 1.3142 | 0.6740 |
| 8 | EDA_alt_noise_pollution1 | 19 | 1.018820 | 0.547578 | 11.974803 | 0.415 | 1.9853 | 1.0370 |
| 4 | EDA_alt_noise_acc | 31 | 1.019642 | 0.441674 | 8.819600 | 0.235 | 0.9927 | 0.6200 |
| 9 | EDA_alt_noise_pollution25 | 19 | 1.020716 | 0.555826 | 12.185977 | 0.410 | 2.0415 | 1.0578 |
| 10 | EDA_alt_noise_Sex | 31 | 1.021243 | 0.360871 | 8.206033 | 0.330 | 0.7591 | 0.4893 |
| 14 | EDA_alt_noise_steps | 31 | 1.023609 | 0.343626 | 7.898181 | 0.525 | 1.3688 | 0.6210 |
| 7 | EDA_alt_noise | 32 | 1.026654 | 0.356377 | 6.133042 | 0.265 | 0.6648 | 0.4472 |
| 27 | EDA_alt_temp_pollution1 | 26 | 1.038146 | 0.546560 | 13.712147 | 0.065 | 1.4053 | 1.1640 |
| 28 | EDA_alt_temp_pollution25 | 26 | 1.043578 | 0.512391 | 13.000250 | 0.095 | 1.3735 | 1.0466 |
| 2 | EDA_airpress_noise | 24 | 1.053468 | 0.337832 | 6.318836 | 0.790 | 1.1106 | 0.3901 |
| 16 | EDA_alt_noise_steps_PM25 | 18 | 1.096776 | 0.575932 | 40.109877 | 0.480 | 2.6891 | 1.4899 |
| 15 | EDA_alt_noise_steps_PM1 | 18 | 1.097739 | 0.575689 | 41.578101 | 0.350 | 2.8146 | 1.6406 |
write.csv(model_comparison[(order(model_comparison$RMSE)), ],
file = "model_comparison_EDA_CENTERED.csv")